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4 Writing the Materials and Methods (Methodology) Section

The Materials and Methods section briefly describes how you did your research. In other words, what did you do to answer your research question? If there were materials used for the research or materials experimented on you list them in this section. You also describe how you did the research or experiment. The key to a methodology is that another person must be able to replicate your research—follow the steps you take. For example if you used the internet to do a search it is not enough to say you “searched the internet.” A reader would need to know which search engine and what key words you used.

Open this section by describing the overall approach you took or the materials used. Then describe to the readers step-by-step the methods you used including any data analysis performed. See Fig. 2.5 below for an example of materials and methods section.

Writing tips:

• Explain procedures, materials, and equipment used
• Example: “We used an x-ray fluorescence spectrometer to analyze major and trace elements in the mystery mineral samples.”
• Order events chronologically, perhaps with subheadings (Field work, Lab Analysis, Statistical Models)
• Use past tense (you did X, Y, Z)
• Quantify measurements
• Include results in the methods! It’s easy to make this mistake!
• Example: “W e turned on the machine and loaded in our samples, then calibrated the instrument and pushed the start button and waited one hour. . . .”

Technical Writing @ SLCC Copyright © 2020 by Department of English, Linguistics, and Writing Studies at SLCC is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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Chapter 5:  Materials and Methods

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• ORGANIZATION
• SUMMARY OF GUIDELINES FOR THE MATERIALS AND METHODS SECTION
• EXERCISE 5.1: A CLEARLY WRITTEN METHODS SECTION
• EXERCISE 5.2: CONTENT AND ORGANIZATION IN THE METHODS SECTION
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For hypothesis-testing papers, the function of the Materials and Methods section (often referred to as the Methods section) is to tell the reader what experiments you did to answer the question posed in the Introduction. Similarly, for descriptive studies, the Methods section tells what experiments you did to obtain the message stated in the Introduction. For methods papers, the Methods section has two functions: it describes the new method in complete detail and also tells what experiments you did to test the new method. For all types of paper, the Methods section should include sufficient detail and references to permit a trained scientist to evaluate your work fully or to repeat the experiments exactly as you did them.

Hypothesis-Testing and Descriptive Papers

We saw that the first step in the story line of a hypothesis-testing or a descriptive paper is presented in the Introduction. This first step is either the question being asked or the structure being described. In either case, the second step in the story line is an overview of the experiments you did. This overview of the experiments gives the strategy of the experiments, the plan that connects the methods to each other and to the question or the message.

Where the overview of the experiments is presented depends on the type of research:

Methods Papers

For a Methods paper, the first step in the story line is a statement that you are presenting a new or improved material, method, or apparatus. The second step in the story line has two parts: a complete description of the new method, material, or apparatus; and a description of how this new method, material, or apparatus was tested. These two steps are described in the Methods section.

In this chapter, we will consider only Methods sections for hypothesis-testing papers.

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• How to Write Your Methods

Ensure understanding, reproducibility and replicability

What should you include in your methods section, and how much detail is appropriate?

Why Methods Matter

The methods section was once the most likely part of a paper to be unfairly abbreviated, overly summarized, or even relegated to hard-to-find sections of a publisher’s website. While some journals may responsibly include more detailed elements of methods in supplementary sections, the movement for increased reproducibility and rigor in science has reinstated the importance of the methods section. Methods are now viewed as a key element in establishing the credibility of the research being reported, alongside the open availability of data and results.

A clear methods section impacts editorial evaluation and readers’ understanding, and is also the backbone of transparency and replicability.

For example, the Reproducibility Project: Cancer Biology project set out in 2013 to replicate experiments from 50 high profile cancer papers, but revised their target to 18 papers once they understood how much methodological detail was not contained in the original papers.

What to include in your methods section

What you include in your methods sections depends on what field you are in and what experiments you are performing. However, the general principle in place at the majority of journals is summarized well by the guidelines at PLOS ONE : “The Materials and Methods section should provide enough detail to allow suitably skilled investigators to fully replicate your study. ” The emphases here are deliberate: the methods should enable readers to understand your paper, and replicate your study. However, there is no need to go into the level of detail that a lay-person would require—the focus is on the reader who is also trained in your field, with the suitable skills and knowledge to attempt a replication.

A constant principle of rigorous science

A methods section that enables other researchers to understand and replicate your results is a constant principle of rigorous, transparent, and Open Science. Aim to be thorough, even if a particular journal doesn’t require the same level of detail . Reproducibility is all of our responsibility. You cannot create any problems by exceeding a minimum standard of information. If a journal still has word-limits—either for the overall article or specific sections—and requires some methodological details to be in a supplemental section, that is OK as long as the extra details are searchable and findable .

Imagine replicating your own work, years in the future

As part of PLOS’ presentation on Reproducibility and Open Publishing (part of UCSF’s Reproducibility Series ) we recommend planning the level of detail in your methods section by imagining you are writing for your future self, replicating your own work. When you consider that you might be at a different institution, with different account logins, applications, resources, and access levels—you can help yourself imagine the level of specificity that you yourself would require to redo the exact experiment. Consider:

• Which details would you need to be reminded of? 
• Which cell line, or antibody, or software, or reagent did you use, and does it have a Research Resource ID (RRID) that you can cite?
• Which version of a questionnaire did you use in your survey? 
• Exactly which visual stimulus did you show participants, and is it publicly available? 
• What participants did you decide to exclude? 
• What process did you adjust, during your work? 

Tip: Be sure to capture any changes to your protocols

You yourself would want to know about any adjustments, if you ever replicate the work, so you can surmise that anyone else would want to as well. Even if a necessary adjustment you made was not ideal, transparency is the key to ensuring this is not regarded as an issue in the future. It is far better to transparently convey any non-optimal methods, or methodological constraints, than to conceal them, which could result in reproducibility or ethical issues downstream.

Visual aids for methods help when reading the whole paper

Consider whether a visual representation of your methods could be appropriate or aid understanding your process. A visual reference readers can easily return to, like a flow-diagram, decision-tree, or checklist, can help readers to better understand the complete article, not just the methods section.

Ethical Considerations

In addition to describing what you did, it is just as important to assure readers that you also followed all relevant ethical guidelines when conducting your research. While ethical standards and reporting guidelines are often presented in a separate section of a paper, ensure that your methods and protocols actually follow these guidelines. Read more about ethics .

Existing standards, checklists, guidelines, partners

While the level of detail contained in a methods section should be guided by the universal principles of rigorous science outlined above, various disciplines, fields, and projects have worked hard to design and develop consistent standards, guidelines, and tools to help with reporting all types of experiment. Below, you’ll find some of the key initiatives. Ensure you read the submission guidelines for the specific journal you are submitting to, in order to discover any further journal- or field-specific policies to follow, or initiatives/tools to utilize.

Tip: Keep your paper moving forward by providing the proper paperwork up front

Be sure to check the journal guidelines and provide the necessary documents with your manuscript submission. Collecting the necessary documentation can greatly slow the first round of peer review, or cause delays when you submit your revision.

Randomized Controlled Trials – CONSORT The Consolidated Standards of Reporting Trials (CONSORT) project covers various initiatives intended to prevent the problems of  inadequate reporting of randomized controlled trials. The primary initiative is an evidence-based minimum set of recommendations for reporting randomized trials known as the CONSORT Statement . 

Systematic Reviews and Meta-Analyses – PRISMA The Preferred Reporting Items for Systematic Reviews and Meta-Analyses ( PRISMA ) is an evidence-based minimum set of items focusing  on the reporting of  reviews evaluating randomized trials and other types of research.

Research using Animals – ARRIVE The Animal Research: Reporting of In Vivo Experiments ( ARRIVE ) guidelines encourage maximizing the information reported in research using animals thereby minimizing unnecessary studies. (Original study and proposal , and updated guidelines , in PLOS Biology .) 

Laboratory Protocols Protocols.io has developed a platform specifically for the sharing and updating of laboratory protocols , which are assigned their own DOI and can be linked from methods sections of papers to enhance reproducibility. Contextualize your protocol and improve discovery with an accompanying Lab Protocol article in PLOS ONE .

Consistent reporting of Materials, Design, and Analysis – the MDAR checklist A cross-publisher group of editors and experts have developed, tested, and rolled out a checklist to help establish and harmonize reporting standards in the Life Sciences . The checklist , which is available for use by authors to compile their methods, and editors/reviewers to check methods, establishes a minimum set of requirements in transparent reporting and is adaptable to any discipline within the Life Sciences, by covering a breadth of potentially relevant methodological items and considerations. If you are in the Life Sciences and writing up your methods section, try working through the MDAR checklist and see whether it helps you include all relevant details into your methods, and whether it reminded you of anything you might have missed otherwise.

Summary Writing tips

The main challenge you may find when writing your methods is keeping it readable AND covering all the details needed for reproducibility and replicability. While this is difficult, do not compromise on rigorous standards for credibility!

• Keep in mind future replicability, alongside understanding and readability.
• Follow checklists, and field- and journal-specific guidelines.
• Consider a commitment to rigorous and transparent science a personal responsibility, and not just adhering to journal guidelines.
• Establish whether there are persistent identifiers for any research resources you use that can be specifically cited in your methods section.
• Deposit your laboratory protocols in Protocols.io, establishing a permanent link to them. You can update your protocols later if you improve on them, as can future scientists who follow your protocols.
• Consider visual aids like flow-diagrams, lists, to help with reading other sections of the paper.
• Be specific about all decisions made during the experiments that someone reproducing your work would need to know.

Don’t

• Summarize or abbreviate methods without giving full details in a discoverable supplemental section.
• Presume you will always be able to remember how you performed the experiments, or have access to private or institutional notebooks and resources.
• Attempt to hide constraints or non-optimal decisions you had to make–transparency is the key to ensuring the credibility of your research.
• How to Write a Great Title
• How to Write an Abstract
• How to Report Statistics
• How to Write Discussions and Conclusions
• How to Edit Your Work

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Materials and methods

The study’s methods are one of the most important parts used to judge the overall quality of the paper. In addition the Methods section should give readers enough information so that they can repeat the experiments. Reviewers should look for potential sources of bias in the way the study was designed and carried out, and for places where more explanation is needed.

The specific types of information in a Methods section will vary from field to field and from study to study. However, some general rules for Methods sections are:

• It should be clear from the Methods section how all of the data in the Results section were obtained.
• The study system should be clearly described. In medicine, for example, researchers need to specify the number of study subjects; how, when, and where the subjects were recruited, and that the study obtained appropriate ‘informed consent’ documents; and what criteria subjects had to meet to be included in the study.
• In most cases, the experiments should include appropriate controls or comparators. The conditions of the controls should be specified.
• The outcomes of the study should be defined, and the outcome measures should be objectively validated.
• The methods used to analyze the data must be statistically sound.
• For qualitative studies, an established qualitative research method (e.g. grounded theory is often used in sociology) must be used as appropriate for the study question.
• If the authors used a technique from a published study, they should include a citation and a summary of the procedure in the text. The method also needs to be appropriate to the present experiment.
• All materials and instruments should be identified, including the supplier’s name and location. For example, “Tests were conducted with a Vulcanizer 2.0 (XYZ Instruments, Mumbai, India).”
• The Methods section should not have information that belongs in another section (such as the Introduction or Results).

You may suggest if additional experiments would greatly improve the quality of the manuscript. Your suggestions should be in line with the study’s aims. Remember that almost any study could be strengthened by further experiments, so only suggest further work if you believe that the manuscript is not publishable without it.

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Methodology

Research Methods | Definitions, Types, Examples

Research methods are specific procedures for collecting and analyzing data. Developing your research methods is an integral part of your research design . When planning your methods, there are two key decisions you will make.

First, decide how you will collect data . Your methods depend on what type of data you need to answer your research question :

• Qualitative vs. quantitative : Will your data take the form of words or numbers?
• Primary vs. secondary : Will you collect original data yourself, or will you use data that has already been collected by someone else?
• Descriptive vs. experimental : Will you take measurements of something as it is, or will you perform an experiment?

Second, decide how you will analyze the data .

• For quantitative data, you can use statistical analysis methods to test relationships between variables.
• For qualitative data, you can use methods such as thematic analysis to interpret patterns and meanings in the data.

Table of contents

Methods for collecting data, examples of data collection methods, methods for analyzing data, examples of data analysis methods, other interesting articles, frequently asked questions about research methods.

Data is the information that you collect for the purposes of answering your research question . The type of data you need depends on the aims of your research.

Qualitative vs. quantitative data

Your choice of qualitative or quantitative data collection depends on the type of knowledge you want to develop.

For questions about ideas, experiences and meanings, or to study something that can’t be described numerically, collect qualitative data .

If you want to develop a more mechanistic understanding of a topic, or your research involves hypothesis testing , collect quantitative data .

You can also take a mixed methods approach , where you use both qualitative and quantitative research methods.

Primary vs. secondary research

Primary research is any original data that you collect yourself for the purposes of answering your research question (e.g. through surveys , observations and experiments ). Secondary research is data that has already been collected by other researchers (e.g. in a government census or previous scientific studies).

If you are exploring a novel research question, you’ll probably need to collect primary data . But if you want to synthesize existing knowledge, analyze historical trends, or identify patterns on a large scale, secondary data might be a better choice.

Descriptive vs. experimental data

In descriptive research , you collect data about your study subject without intervening. The validity of your research will depend on your sampling method .

In experimental research , you systematically intervene in a process and measure the outcome. The validity of your research will depend on your experimental design .

To conduct an experiment, you need to be able to vary your independent variable , precisely measure your dependent variable, and control for confounding variables . If it’s practically and ethically possible, this method is the best choice for answering questions about cause and effect.

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Your data analysis methods will depend on the type of data you collect and how you prepare it for analysis.

Data can often be analyzed both quantitatively and qualitatively. For example, survey responses could be analyzed qualitatively by studying the meanings of responses or quantitatively by studying the frequencies of responses.

Qualitative analysis methods

Qualitative analysis is used to understand words, ideas, and experiences. You can use it to interpret data that was collected:

• From open-ended surveys and interviews , literature reviews , case studies , ethnographies , and other sources that use text rather than numbers.
• Using non-probability sampling methods .

Qualitative analysis tends to be quite flexible and relies on the researcher’s judgement, so you have to reflect carefully on your choices and assumptions and be careful to avoid research bias .

Quantitative analysis methods

Quantitative analysis uses numbers and statistics to understand frequencies, averages and correlations (in descriptive studies) or cause-and-effect relationships (in experiments).

You can use quantitative analysis to interpret data that was collected either:

• During an experiment .
• Using probability sampling methods .

Because the data is collected and analyzed in a statistically valid way, the results of quantitative analysis can be easily standardized and shared among researchers.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Chi square test of independence
• Statistical power
• Descriptive statistics
• Degrees of freedom
• Pearson correlation
• Null hypothesis
• Double-blind study
• Case-control study
• Research ethics
• Data collection
• Hypothesis testing
• Structured interviews

Research bias

• Hawthorne effect
• Unconscious bias
• Recall bias
• Halo effect
• Self-serving bias
• Information bias

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

A sample is a subset of individuals from a larger population . Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.

In statistics, sampling allows you to test a hypothesis about the characteristics of a population.

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts and meanings, use qualitative methods .
• If you want to analyze a large amount of readily-available data, use secondary data. If you want data specific to your purposes with control over how it is generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

Methodology refers to the overarching strategy and rationale of your research project . It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.

Methods are the specific tools and procedures you use to collect and analyze data (for example, experiments, surveys , and statistical tests ).

In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section .

In a longer or more complex research project, such as a thesis or dissertation , you will probably include a methodology section , where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.

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Writing and Publishing Scientific Papers

Part ii. writing the paper.

10. How to Write the Material and Methods Section

Texte intégral.

1 Although traditionally, this section is only called “Material and Methods” (rarely: Study Site, Material and Methods), it can be composed of the following parts: study site, study organism, material, methods, statistical evaluation.

2 The aim of this section in scientific papers is to enable readers to assess the reliability of your work, and to be able to repeat it for verification if they want to do so. Science is about unearthing nature’s laws, and the cornerstone of the scientific method requires that experiments are repeatable: if the experiment is repeated under the same conditions, the same result should be obtained. A material and methods section should give enough detail to evaluate and, if needed, to repeat the experiments reported in the article.

3 You should carefully consider your potential readership. This allows you to provide enough, but not superfluous, information. Once you have reflected on what can be assumed as known by this readership about your setting, organisms, methods, etc., you can give detail accordingly: not too little, and not too much.

4 During peer review, this section is closely scrutinised. If the reviewer is in any doubt that the experiments are repeatable, or that the methods are appropriate, the manuscript will be rejected as unreliable, no matter how wonderful the findings are.

5 When describing your study site, consider your potential readership and give details accordingly (geographical particulars, history of the site, location, co-ordinates, maps). The aim is not to enable the reader to find your sampling plot, but to give a general understanding, a “feel” for the environment you worked in. Information on habitat, with photos, maps, drawings, is often useful, or wholly necessary.

Study Organism

6 Here, you should name all the species, strains, cultivars or races that were used in the experiments. You should also give precise information on their origin, storage or husbandry, including temperatures, photoperiod, feeding regimes, control, etc. Depending on the readership, you should consider giving other background information on life history, and the organism’s distribution in nature. If there is a long list of organisms or strains, consider preparing a table with this information.

7 Here, you should list all the materials necessary for your experiments. Give exact names, not generic or trade names, of chemicals used. Give a source (manufacturer with location) if the chemical in question is delicate (e.g. an enzyme), or rare, or its quality is critical. This would give additional information to the reader. This is, however, neither advertisement nor endorsement (for legal reasons, this should often be made explicit in the paper — see, e.g. the US public organisation policy: disclaimer: “The mention of any trade name does not constitute endorsement by XXX organisation”). For equipment used, give the name, specification/type, manufacturer, and conditions of use.

Sampling Methods and Measurements

8 Here, you should detail the procedures: how did you perform the observations, measurements, experiments? How many times, under what conditions? If you use a new method, give all the details necessary so that the reader can repeat your experiment from reading this section. If you used a published method, a reference to the original publication, preferably the one that first published the method, is usually sufficient with minimum description. If you modified a published method, detail the modification only. If the method is published, you should cite it — but consider where it was published? Is it a frequently used method? When was it published? A rarely-used method, published long ago in an obscure journal, needs a more detailed description than a much-used, current one. If the original publication is not widely available, you will have to provide detailed description. Editors often welcome more detail, especially if the published method is not in very wide use (with the appropriate reference, naturally). If you modified a published method that is widely available, detail the modification only.

9 When describing the procedure, be aware that only SI (Système International) units of measurement are allowed. A few units in common use are not official SI measurements and they cannot be used. Also, be aware of the precise use of measurement units — for example, in common use, weight is often given as grams, kilograms, etc., but these are units of mass, not of weight.

10 Any larger set of samples, measurements, or experiments will have the occasional error, a missing sample, a lost or mislaid tube. Do not keep silent about them. Indicate, clearly, how you dealt with errors, missing data, missing traps. This will not decrease your credibility — on the contrary.

Evaluation Methods/Statistics

11 Data will mostly be evaluated by using a statistical program. In most cases, a reference to the program (indicate the version used) is sufficient; give detail only if the method used is new. However, avoid the neophyte description: what’s new for you may not be new for readers. An experienced colleague can give advice on this matter. In general, it is always a good idea to discuss your chosen statistical method with others. Here, you should give a reason for the choice of statistical test, as well as stating how you tested the eventual conditions for using the chosen test (testing for assumptions for a given statistical test). The mention of the use of a commercial statistical program naturally assumes that you have valid access to the program in question. It is not unheard of program developers to search for the mention of their product in the literature to find out about illegal use.

12 Be careful with details when writing a material and methods section — your reputation is on the line! The reader was not by your side when the studies were done, so she will use the detail and clarity of this section as an indirect indication of your reliability and thoroughness.

13 A common error in this section is not offering enough detail. This does not happen because of the authors’ desire to hide anything — it is simply a mark of routine: many parts of the experimental protocol may become almost routine, and the small details are forgotten as they never change and are taken for granted. When the description is prepared, these details, vital for others, are often not included. A good test is whether a colleague, on reading the section, thinks she can repeat the experiment based on the given description of methods. Such a check is useful, because the writer often is too close to the methods, having done them countless times during the experimental process and, thus, omits some obvious but important, detail.

14 Specifically, take care with numbers, spelling, and punctuation. In this section, many “strange” names will occur: of chemicals, organisms, strains; concentrations, times and units of measurement are important. Meticulousness is the key word here: if you cannot be trusted to do simple things well, such as describing a method that you used hundreds of times, can you expect the readers to trust you when it comes to more significant and complicated aspects of reporting your research?

15 The order of description should be chronological; the description of what was done first should precede the later actions. However, you have to first mention all study sites, then all organisms, followed by a full list of all materials used, experiment-by-experiment and so on. Thus, if someone is only interested in all the details of, for example, your second experiment, she will have to jump from one part of this section to another. This seems a small price to pay for a consistent structure, which is followed by most journals.

16 This section describes your own work and, thus, the past tense is used, mostly, in this section. When describing the details, beware of the syntax. The following description is taken from Day and Gastel’s book (Day and Gastel, 2006), who, tongue-in-cheek, called it “the painful method”: “After standing in hot water for an hour, the flasks were examined”. I hope this was not performed as the sentence implies — probably the flasks, and not the researchers, were standing in hot water that long.

When to Write this Section?

17 It is best to start writing this section first, possibly even while working on the experiments. Otherwise, many details will be lost. Details and precision are vital here, and they are much easier to document during the work, or soon after, than weeks or months later. Additionally, there is often a practical reason, too. Most scientific work is done in teams; it is much easier to convince the team members to write their respective methods section while they are doing the work, or soon afterwards. Once the experiments are completed, and the team moves on to further projects, writing a complete methods section will take longer, and be done less satisfactorily.

18 Meticulousness pays, because, as stated above, reviewers are often of the opinion that if you cannot be trusted in doing simple things, you cannot expect trust in significant and complicated aspects of research. Science, in the view of many of its eminent practitioners is, after all, “99 % perspiration and 1 % inspiration”, so precise work, and the ability to describe things accurately, is a necessary condition of credibility. Science may well comprise a lot of precise work and fewer grand ideas; you prove your mastery of the methods applied by being able to describe them with clarity, in sufficient detail.

Le texte seul est utilisable sous licence CC BY 4.0 . Les autres éléments (illustrations, fichiers annexes importés) sont « Tous droits réservés », sauf mention contraire.

A Primer for the Non-English Speaker

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How to Write a Methods Section for a Psychology Paper

Tips and Examples of an APA Methods Section

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Emily is a board-certified science editor who has worked with top digital publishing brands like Voices for Biodiversity, Study.com, GoodTherapy, Vox, and Verywell.

Verywell / Brianna Gilmartin 

The methods section of an APA format psychology paper provides the methods and procedures used in a research study or experiment . This part of an APA paper is critical because it allows other researchers to see exactly how you conducted your research.

Method refers to the procedure that was used in a research study. It included a precise description of how the experiments were performed and why particular procedures were selected. While the APA technically refers to this section as the 'method section,' it is also often known as a 'methods section.'

The methods section ensures the experiment's reproducibility and the assessment of alternative methods that might produce different results. It also allows researchers to replicate the experiment and judge the study's validity.

This article discusses how to write a methods section for a psychology paper, including important elements to include and tips that can help.

What to Include in a Method Section

So what exactly do you need to include when writing your method section? You should provide detailed information on the following:

• Research design
• Participants
• Participant behavior

The method section should provide enough information to allow other researchers to replicate your experiment or study.

Components of a Method Section

The method section should utilize subheadings to divide up different subsections. These subsections typically include participants, materials, design, and procedure.

Participants 

In this part of the method section, you should describe the participants in your experiment, including who they were (and any unique features that set them apart from the general population), how many there were, and how they were selected. If you utilized random selection to choose your participants, it should be noted here.

For example: "We randomly selected 100 children from elementary schools near the University of Arizona."

At the very minimum, this part of your method section must convey:

• Basic demographic characteristics of your participants (such as sex, age, ethnicity, or religion)
• The population from which your participants were drawn
• Any restrictions on your pool of participants
• How many participants were assigned to each condition and how they were assigned to each group (i.e., randomly assignment , another selection method, etc.)
• Why participants took part in your research (i.e., the study was advertised at a college or hospital, they received some type of incentive, etc.)

Information about participants helps other researchers understand how your study was performed, how generalizable the result might be, and allows other researchers to replicate the experiment with other populations to see if they might obtain the same results.

In this part of the method section, you should describe the materials, measures, equipment, or stimuli used in the experiment. This may include:

• Testing instruments
• Technical equipment
• Any psychological assessments that were used
• Any special equipment that was used

For example: "Two stories from Sullivan et al.'s (1994) second-order false belief attribution tasks were used to assess children's understanding of second-order beliefs."

For standard equipment such as computers, televisions, and videos, you can simply name the device and not provide further explanation.

Specialized equipment should be given greater detail, especially if it is complex or created for a niche purpose. In some instances, such as if you created a special material or apparatus for your study, you might need to include an illustration of the item in the appendix of your paper.

In this part of your method section, describe the type of design used in the experiment. Specify the variables as well as the levels of these variables. Identify:

• The independent variables
• Dependent variables
• Control variables
• Any extraneous variables that might influence your results.

Also, explain whether your experiment uses a  within-groups  or between-groups design.

For example: "The experiment used a 3x2 between-subjects design. The independent variables were age and understanding of second-order beliefs."

The next part of your method section should detail the procedures used in your experiment. Your procedures should explain:

• What the participants did
• How data was collected
• The order in which steps occurred

For example: "An examiner interviewed children individually at their school in one session that lasted 20 minutes on average. The examiner explained to each child that he or she would be told two short stories and that some questions would be asked after each story. All sessions were videotaped so the data could later be coded."

Keep this subsection concise yet detailed. Explain what you did and how you did it, but do not overwhelm your readers with too much information.

Tips for How to Write a Methods Section

In addition to following the basic structure of an APA method section, there are also certain things you should remember when writing this section of your paper. Consider the following tips when writing this section:

• Use the past tense : Always write the method section in the past tense.
• Be descriptive : Provide enough detail that another researcher could replicate your experiment, but focus on brevity. Avoid unnecessary detail that is not relevant to the outcome of the experiment.
• Use an academic tone : Use formal language and avoid slang or colloquial expressions. Word choice is also important. Refer to the people in your experiment or study as "participants" rather than "subjects."
• Use APA format : Keep a style guide on hand as you write your method section. The Publication Manual of the American Psychological Association is the official source for APA style.
• Make connections : Read through each section of your paper for agreement with other sections. If you mention procedures in the method section, these elements should be discussed in the results and discussion sections.
• Proofread : Check your paper for grammar, spelling, and punctuation errors.. typos, grammar problems, and spelling errors. Although a spell checker is a handy tool, there are some errors only you can catch.

After writing a draft of your method section, be sure to get a second opinion. You can often become too close to your work to see errors or lack of clarity. Take a rough draft of your method section to your university's writing lab for additional assistance.

A Word From Verywell

The method section is one of the most important components of your APA format paper. The goal of your paper should be to clearly detail what you did in your experiment. Provide enough detail that another researcher could replicate your study if they wanted.

Finally, if you are writing your paper for a class or for a specific publication, be sure to keep in mind any specific instructions provided by your instructor or by the journal editor. Your instructor may have certain requirements that you need to follow while writing your method section.

Frequently Asked Questions

While the subsections can vary, the three components that should be included are sections on the participants, the materials, and the procedures.

• Describe who the participants were in the study and how they were selected.
• Define and describe the materials that were used including any equipment, tests, or assessments
• Describe how the data was collected

To write your methods section in APA format, describe your participants, materials, study design, and procedures. Keep this section succinct, and always write in the past tense. The main heading of this section should be labeled "Method" and it should be centered, bolded, and capitalized. Each subheading within this section should be bolded, left-aligned and in title case.

The purpose of the methods section is to describe what you did in your experiment. It should be brief, but include enough detail that someone could replicate your experiment based on this information. Your methods section should detail what you did to answer your research question. Describe how the study was conducted, the study design that was used and why it was chosen, and how you collected the data and analyzed the results.

Erdemir F. How to write a materials and methods section of a scientific article ? Turk J Urol . 2013;39(Suppl 1):10-5. doi:10.5152/tud.2013.047

Kallet RH. How to write the methods section of a research paper . Respir Care . 2004;49(10):1229-32. PMID: 15447808.

American Psychological Association.  Publication Manual of the American Psychological Association  (7th ed.). Washington DC: The American Psychological Association; 2019.

American Psychological Association. APA Style Journal Article Reporting Standards . Published 2020.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Setting the Scene: Best Practices for Writing Materials and Methods

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This free white paper tackles the best ways to write the Materials and Methods section of a scientific manuscript.

Updated on March 3, 2014

The Materials and Methods (or “Methods section”) is the section of a research paper that provides the reader

with all the information needed to understand your work and how the reported results were produced. Having read

the Introduction, the reader already knows why your work is important, so the next step is to connect that section to

the experimental design used to address your research questions.

Below is a preview of our free white paper tackling the best way to write the Materials and Methods section of a scientific manuscript. It covers the following topics:

Purpose and Structure

• Key Information
• Notation and Terminology
• Equipment and Materials Citations
• Acquisition and Definition of the Results
• Statistical Methods
• Concluding Statements

Depending on the type of paper, the Methods section can encompass anything from the parameters of a literature search to the methods employed in a field study to the details of bench work in the lab. The common feature is that the information needs to be presented in a way that is clear and familiar to the reader. It is important to note that the purpose of the Methods section is not just to convey what you did; a thorough and well-organized Methods section reflects your knowledge and understanding of appropriate research techniques and increases the reader's confidence in your work.

The Methods section is easiest to follow when it begins by providing a clear context for the detailed descriptions of the methods and materials used in the study. This context is best achieved by beginning with general characteristics and parameters (e.g., identification of sample sources or populations, descriptions of geographic areas, or characterizations of study participants). A reader who understands the foundation of your experiments will more easily understand the procedures that follow.

The underlying principle for what information to provide in the Methods section is that the reader should be able to replicate your study. This section must explain the methods used with enough detail to answer any of the reader's questions about how the study was performed. Because the Methods section is meant to convey how the research was conducted, conforming to the accepted conventions of the field is extremely important.

Generally, the Methods section should assemble familiar concepts and research activities into a logical series of events. Terminology and sentence structure should be consistent within the paper and conform to the conventions of the field, and repetition is accepted or even expected. Because Methods sections often rely on lists of information, consistency - i.e., the presentation of like elements using the same terminology, notation, and sentence structure - is especially important.

The information in the Methods section should follow the order of execution as closely as possible, although similar procedures should be presented together. For example, descriptions of sample or data collection should be described together, even if these are performed at different times or with intervening analysis, because a purely chronological account would mean switching back and forth between procedures.

Continue reading "Setting the Scene: Best Practices for Writing Materials and Methods" by downloading the full white paper here .

Check out our other "Best Practices for Writing" white papers to get tips for other sections of your research manuscript:

Getting a Strong Start: Best Practices for Writing an Introduction

Reaping the Rewards: Best Practices for Writing a Results Section

Michael Bendiksby, PhD

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Research Paper Writing: 5. Methods / Materials

• 1. Getting Started
• 2. Abstract
• 3. Introduction
• 4. Literature Review
• 5. Methods / Materials
• 6. Results / Analysis
• 7. Discussion
• 8. Conclusion
• 9. Reference

Methods / Materials Overview

These sections of the research paper should be concise. The audience reading the paper will always want to know what materials or methods that were used. The methods and materials may be under subheadings in the section or incorporated together. The main objective for these sections is to provide specialized materials, general procedures, and methods to judge the scientific value of the paper.

What to include in the sections

• Described separately
• Include the chemicals, biological, and any equipment
• Do not include common supplies, such as test tubes, pipette tips, beakers, etc. or standard lab equipment
• Single out sources like a specific type of equipment, enzyme, or a culture
• These should be mentioned in a separate paragraph with its own heading or highlighted in the procedure section if there is one
• Refer to solutions by name and describe
• Describes in detail how the analysis was conducted
• Be brief when presenting methods under the title devoted to a specific technique or groups of procedures
• Simplify and report what the procedure was
• Report the method by name
• Use third person passive voice, and avoid using first person
• Use normal text in these sections
• Avoid informal lists
• Use complete sentences

Example of a Methods Section

Publication Manual of the American Psychological Association Sixth Ed. 2010

• << Previous: 4. Literature Review
• Next: 6. Results / Analysis >>
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Writing the materials and methods

Affiliation.

• 1 Department of Biomedical Imaging, Biomedical Imaging and Interventional Journal, University of Malaya, Kuala Lumpur, Malaysia. [email protected]
• PMID: 19037549

When writing scientific papers to share their research findings with their peers, it is not enough for researchers to just communicate the results of their study; it is equally important to explain the process by which they arrived at their results, so that the study can be replicated to validate the observations. The materials and methods section is used to describe the experimental design and provide sufficient details so that a competent colleague can repeat the experiment. A good materials and methods section will enable readers to evaluate the research performed and replicate the study, if necessary.

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Materials and method: The “Recipe” of a research

Ashish kumar.

Editor, Journal of Indian Society of Periodontology, Professor and Head, Department of Periodontics, Dental College, Regional Institute of Medical Sciences (RIMS), Lamphelpat, Imphal-795004, Manipur, India. E-mail: moc.liamffider@79ramukhsihsa

In any research article, the detailed description and process of an experiment is provided in the section termed as “Materials and Method.” The Materials and Method section is also called Method section in few journals. This section describes how the experiment was conducted to arrive at the results. The aim of this section in any research article is to describe the process in detail for “reproducibility” which means that procedure of the experiment and related materials should be adequately described so that the other researchers working on the similar topic/area, should be able to conduct a similar experiment and replicate the results to allow corroboration of the inferences of the research. The reproducibility of the results is crucial for their scientific merit.[ 1 ] This section has been equated to “recipe section” which describes what to use, how much to use and how to use to come to the final product.[ 2 ]

Vital details of the research need to be described in this section. At the beginning of the section, the study design needs a description in terms of well-defined commonly used nomenclature (longitudinal, cross-over study”, “randomised controlled trial”, etc). The mention of the study design in the initial part of materials and method section is important as it helps the readers understand the research based on the merits and limitations of study design. The inclusion of study designs also help in understanding the type of statistical tests that can be appropriately applied in evaluating the data.[ 3 ] Randomisation being a crucial aspect of many clinical studies, has to be defined clearly.

The information about sample size, inclusion and exclusion criteria (sample characteristics) also should find a description in this aspect of the material and method section. An adequate sample size of a study would be able to provide the precision of our estimates and thus have adequate power of study to draw conclusions and justify answers to query being explored in the research.[ 3 ] The information of the sample characteristics is important to accomplish the aims of the experiment (hypothesis). Apart from this, the details of the approval from ethical board and trial registration should be mentioned here.[ 4 ]

The next aspect of Materials and Method should incorporate the description of materials in terms of quantity, precise technical descriptions and the method of preparations, if any. The details of the manufacturers of chemical reagents and equipment should also find a mention here. Generic names should be preferred over trade names. If study has usage of microorganisms or experimental animals, a clear description of such entities in terms of species/strains or genus species is required.[ 5 ]

The description of the method of the experiment should be accurate, concise but complete. The process should be written as a explanation of a process, not as a laboratory manual procedure. If the methods, devices, or techniques which have been used by authors, are in routine usage, and are widely known and published, then such methods do not require detailed description. But the authors should compulsorily mention the original article or references from where the readers can get information about the method in detail to replicate the procedure. If any treatment is being investigated, then exact treatment protocol should be described. Techniques/method which are new or uncommon should be explained fully and any related references should also be mentioned.

The statistical aspects should mention the statistical tests and the statistical computer packages that were used for data analysis. Use of an uncommon statistical test needs an explanation of its usage in the context of the study and a reference to the method for readers to refer.[ 5 ]

The material and method section may or may not have subheadings, depending upon the journal guidelines. The subdivisions can be: Study design, setting, subjects, data collection and data analysis[ 2 ] or overall design of the study, inclusion and exclusion criteria, sample sizes and statistical power.[ 6 ]

It is of paramount importance that a consistency is maintained between the “Materials and Method” section and “Results” section of the article. Procedures described in Methods section should correlate with the results described in the Results section for readers to understand the association of the specific methodology to results.[ 4 ]

Often, few issues arise while writing Materials and Method like inclusion of unnecessary details or results. Limitations on number of references that can be cited in journals, many times, leads to this section being extremely concise and lacks details required for the “reproducibility”.[ 7 ] The details of the procedure are not completely mentioned by authors sometimes because of commercial reasons.[ 7 ] These situations result in compromise with the basic principle of “reproducibility” while writing this section.

In certain cases, the authors are apprehensive of results being reproduced and validity of their results being challenged. To avoid any questions being raised on the methodology and results, the authors provide insufficient details in this section to avoid reproducibility.[ 7 ]

The aim of any research is progression of knowledge in that particular field. One of the essential requirement for progression of scientific knowledge is “reproducibility” and the assessment of the validity of available results. This is achievable only if the authors provide sufficient details in the “Materials and Method section”.[ 7 ]

Writing this section should be simple and easy especially when this part is written after the completion of the study, as the authors would have performed the experiment themselves. This is one of the first sections written while writing a research article.

“History has repeatedly shown that when a new method or material becomes available, new uses for it arise.”

Wilson Greatbatch

Training videos   |   Faqs

Materials and Methods Examples and Writing Tips

Abstract | Introduction | Literature Review | Research question | Materials & Methods | Results | Discussion | Conclusion

In this blog, we look at how to write the materials and methods section of a research paper. In most research papers, the materials and methods section follows the literature review section. This is generally the easiest section to write because you are simply reproducing what you did in your experiments. It is always a good idea to start writing your research paper with the materials and methods section.

1. What is the purpose of the materials and methods section?

Materials and methods should describe how you did your research and detail the experimental procedure. One of the most important things to bear in mind while writing the materials and methods section is that it should have enough detail so that other researchers in your field can replicate your experiments and reproduce your results.  You should provide all the steps in a logical order so that your readers can follow your description easily.

2. Materials and Methods Examples

The structure of the methods section will very much depend on your discipline. If you are not sure about the structure, then the best place to start will be to go through the methods section of some previously published papers from your chosen journal. We will look at some examples of materials and methods structure in different disciplines. 

2.1. Materials & methods example #1 (Engineering paper)

If you are writing an engineering sciences research paper in which you are introducing a new method, your materials and methods section would typically include the following information.

You can start with the top-level summary of the method. You can try to answer these questions. Are you proposing a new method? Or,  Are you using a standard method from the literature?  Or, Are you extending a previously published method? If so, is it your previous work? or work published by a different author?

Then you can talk about the reasons for choosing this method. You can quote previous papers that have used this method successfully to support your arguments. Then, you can talk about the actual implementation details of the methods.

Then you can talk about how the methods were validated to confirm that they are suitable for your research. You can also include information about any pilot or preliminary studies you conducted before the full study. Then you can explain how you propose to test and evaluate the methods to prove that they are better than the existing methods. Here, you can talk about metrics and statistical tests you will be using to evaluate your method.

2.2. Materials & methods example #2 (Measurement paper)

If you are writing a paper that deals with measurements, you would typically include the following information in your materials and methods section.

You can start by talking about the experimental setup. You can try to answer these questions. What equipment was used to perform the measurements? What was the make and the model of the equipment?  How many technicians took the measurements?  How experienced were the technicians?

Then you can talk about the parameters that were measured during the experiment. Then you can talk about the actual measurement procedure. How were the samples prepared for the measurements?  How many measurements were taken? Were the measurements repeated for consistency? Was there a time interval between successive measurements?

Then you can talk about measurement conditions and constraints. Were the measurements performed at room temperature or under special conditions? Were there any practical difficulties while performing the measurements, if so, how did you overcome them?

Most importantly, you must list all the calculations in the form of detailed equations and formulas so that readers know exactly how the data was produced.

2.3. Materials & methods example #3 (Survey questionnaire paper)

If you are writing a survey questionnaire paper , you would typically include the following information in your materials and methods section.

You can start by talking about your participants. Who is your target population? What are their demographics? How did you recruit them?  How did participants provide consent for your study? What sampling method did you use to select the participants?

Then you can talk about the survey type. Was it a phone interview? Was it a personal interview? Was it an online survey? Or, Was it a written survey?

Then you can talk about the questionnaire design. How did you choose the questions? How many questions were there? What type of questions were they? Were they open ended questions, or close ended questions, or rating scale questions, or a mixture of different types of questions?

Then you can talk about how the questionnaire was administered. If it is an online survey, how did you get the questionnaire to the participants? Did you email them? Or did you post the survey forms?

If you are doing a personal interview. How did you conduct the interviews? Was it one to one interview, or was it done in batches, or did you use focus groups? How did the participants behave during the interview?

Then you can talk about questionnaire testing. Did you test your questionnaire before the main study? Did you have to make any changes after initial testing?  Did you have to translate the questionnaire into multiple languages? Then finally you can talk about different types of statistical tests you used to analyze the survey responses.

2.4. Materials & methods example #4 (Medical clinical trial paper)

If you are writing a medical research paper , your materials and methods section would typically include the following information.

You can start by providing information about the study design. Was it a randomized trial, or an observational trial? Was it a prospective study, or a retrospective study? Was the study double-blinded, or single-blinded?

Then, you can talk about how the ethical approval was obtained for the study and clarify if the clinical trial was registered. if so, then provide the registration number.

Then, you can talk about how the participants were recruited for the study, and explain the inclusion and exclusion criteria. Then, you can talk about how the participants were grouped into control and placebo groups, and explain how the medication was administered.

Then, you can talk about what outcomes were measured. What was the primary outcome? What was the secondary outcome? What was the follow up period? You can try to answer these questions. Then you can finish off with some information about the statistical tests you used to analyze the data.

3. Frequently Asked Questions

One of the common mistakes people make is using vague language in materials and methods. Reviewers won’t like it, and they will reject the paper on the basis that the section is not elaborate enough for other researchers to reproduce your experiments.

Make sure you write the materials and methods section in past tense, since you are reporting something that has already happened.

Acronyms & Abbrevations: Try to use acronyms and abbreviations for long method names. Abbreviations and acronyms are a great way to make your writing concise and save time. Define the acronyms and abbreviations during their first occurrence then use the short form in the rest of the text. The common practice is to put the acronym and abbreviations in parentheses after the full term.

Use different layouts: Another problem you are likely to face is that your methods section can sound like manual if you have too much text in it. In particular, if you are dealing with a very complex procedure, the readers might find it dry and tedious. So try to provide some variety to the layout. Try to use bullet points and numberings instead of long paragraphs to make it easy for the readers to understand the procedure. You can use flow diagrams to illustrate the process rather than describing it.

When you are using a standard method that is well described in literature, the standard practice is to reference the paper rather than repeating the entire procedure. You can also provide a brief summary of the procedure in your own words.

For example, you can say something like this, “The details of the procedure have been reported previously in…”, and reference the previous paper. And then, you can follow it up with a brief summary of the method from the previous paper.

If you are extending a previous method, then you can do something like this. You can say that, “Some minor modifications were made to the method described in…” and reference the previous paper.  And then, you can follow it up with the list of refinements you made to the previous method in order to adapt it to your work.

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• http://orcid.org/0000-0002-2207-9958 Chantelle Garritty 1 , 2 ,
• http://orcid.org/0000-0001-7622-843X Barbara Nussbaumer-Streit 3 ,
• Candyce Hamel 1 , 4 ,
• Declan Devane 5
• Cochrane Rapid Reviews Methods Group
• 1 School of Epidemiology and Public Health , University of Ottawa , Ottawa , Ontario , Canada
• 2 Global Health and Guidelines Division , Public Health Agency of Canada , Ottawa , Ontario , Canada
• 3 Cochrane Austria, Department for Evidence-based Medicine and Evaluation , University for Continuing Education Krems , Krems , Niederösterreich , Austria
• 4 Canadian Association of Radiologists , Ottawa , Ontario , Canada
• 5 Cochrane Ireland and Evidence Synthesis Ireland, School of Nursing and Midwifery , University of Galway , Galway , Ireland
• Correspondence to Dr Chantelle Garritty, School of Epidemiology and Public Health, University of Ottawa, Ottawa, Canada; garritty{at}gmail.com

This paper, part of the Cochrane Rapid Review Methods Group series, offers guidance on determining when to conduct a rapid review (RR) instead of a full systematic review (SR). While both review types aim to comprehensively synthesise evidence, RRs, conducted within a shorter time frame of typically 6 months or less, involve streamlined methods to expedite the process. The decision to opt for an RR depends on the urgency of the research question, resource availability and the impact on decision outcomes. The paper categorises scenarios where RRs are appropriate, including urgent decision-making, informing guidelines, assessing new technologies and identifying evidence gaps. It also outlines instances when RRs may be inappropriate, cautioning against conducting them solely for ease, quick publication or only cost-saving motives.

When deciding on an RR, it is crucial to consider both conceptual and practical factors. These factors encompass the urgency of needing timely evidence, the consequences of waiting for a full SR, the potential risks associated with incomplete evidence, and the risk of not using synthesised evidence in decision-making, among other considerations. Key factors to weigh also include having a clearly defined need, a manageable scope and access to the necessary expertise. Overall, this paper aims to guide informed judgements about whether to choose an RR over an SR based on the specific research question and context. Researchers and decision-makers are encouraged to carefully weigh potential trade-offs when opting for RRs.

• Systematic Reviews as Topic
• Clinical Decision-Making

Data availability statement

Data sharing not applicable as no datasets generated and/or analysed for this study.

This is an open access article distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited, appropriate credit is given, any changes made indicated, and the use is non-commercial. See:  http://creativecommons.org/licenses/by-nc/4.0/ .

https://doi.org/10.1136/bmjebm-2023-112722

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WHAT IS ALREADY KNOWN ON THIS TOPIC

Rapid reviews (RRs) are increasingly prevalent in the published literature due to their speed and efficiency in providing evidence synthesis compared with full systematic reviews (SRs). While methods guidance for conducting RRs exists, there is currently a lack of specific guidance on determining when it is appropriate to do an RR over an SR.

WHAT THIS STUDY ADDS

This paper outlines considerations for determining the appropriateness of conducting an RR. It emphasises the importance of context and the research question balanced against the backdrop of time-sensitive decision-making needs. It discusses suitable scenarios and potential limitations, and provides guiding questions for making a balanced assessment of appropriateness for RRs that is broadly applicable to RR producers and users.

HOW THIS STUDY MIGHT AFFECT RESEARCH, PRACTICE OR POLICY

This paper offers a framework for making informed judgements about whether to opt for RRs over an SR. Policy-makers, healthcare providers and researchers can use the provided considerations to determine when an RR is most viable and valuable. Organisations involved in producing or commissioning RRs can also apply the guiding questions to ensure the appropriateness of evidence synthesis for timely decision-making and relevant policy development.

Introduction

This paper is part of a Cochrane Rapid Reviews Methods Group series providing methodological guidance for rapid reviews (RRs). 1–5 The main goal of this paper is to explain how to assess whether it is appropriate to conduct an RR instead of a full systematic review (SR).

Various literature review types exist, each serving distinct purposes based on the research question, available resources and timeline. 6 SRs and RRs aim to answer a clearly defined research question and comprehensively review, synthesise and analyse existing evidence to make conclusions. However, an RR is typically conducted in a shorter time frame and is often a less resource-intensive way to synthesise evidence than a full SR. 7 This is achieved by streamlining or accelerating certain steps of the review process. 8 Generally, RRs are conducted over 6 months or less, a much shorter timeline than the 1–2 years needed for most SRs. 9 But RRs should not be defined solely by the time taken to conduct the review, as other reviews may be conducted in short periods (eg, by assigning additional resources or if the review has zero or few included studies). Instead, RRs should be defined by the abbreviated methods used to reduce the time to completion.

The similarities in the methodologies between RRs and SRs raise the question of when an RR is appropriate to conduct for evidence synthesis. RRs have proven useful in both emergent (eg, COVID-19 pandemic, disaster relief) 10–12 and non-emergent yet urgent situations where there is still a need for timely evidence (eg, to inform the development of a new health policy or programme) 13–15 or in resource-limited environments (eg, low-income countries). 16–19 However, there are cases where an RR may not be appropriate. For example, a full SR is likely preferable if the evidence synthesis will be used to make decisions or develop guidelines on a large scale (eg, international, regional), which could have wide-sweeping resource or implementation implications and if time allows to wait for evidence to inform a decision.

RRs present a challenge in maintaining rigorous methodology and ensuring the validity of findings within tight deadlines. RRs may be more biased and less reliable than well-conducted SRs due to time constraints, limited scope and potential biases introduced by the accelerated review process. 20 21 The exact degree of bias remains to be determined. However, many published SRs are of low quality (ie, quality of conduct and/or reporting) and are susceptible to biases. 22 Hence, the evidence synthesis type alone is insufficient to judge its reliability and quality. Regardless of which evidence synthesis approach is taken, it is essential to follow sound methodological guidance 9 23 24 and ensure transparent reporting of methods. 25

Several organisations produce or commission RRs within academia, government, research institutions and non-profit organisations to provide evidence for decision-making related to clinical care, healthcare funding, services, policy, technologies and programme development. 26–29 Although methods guidance is available to support the conduct of RRs, 9 24 30 there are no specific guiding principles on when it is appropriate to use an RR approach instead of an SR. This decision, which is often situational and involves several factors, is left to the discretion of the author teams that produce evidence syntheses and the organisations that commission them.

Cochrane, a global leader in producing high-quality SRs and methodological guidance, conducts RRs driven primarily by requests for timely evidence for decision-making and only for urgent and high-priority topics. 9 It, too, needs more concrete criteria when making this determination. Therefore, this paper aims to outline considerations to support whether it is appropriate to undertake an RR. To replace arbitrary decision-making, this paper discusses the importance of considering the specific context surrounding an RR topic and the research question(s) to be addressed. Potential limitations are also discussed along with scenarios where RRs may be appropriate. Last, guiding considerations to help to make a balanced assessment are presented. Although examined within the context of Cochrane, an organisation that has been instrumental in leading the development of RR methods guidance, 9 it is widely applicable to those who produce, request or use RRs.

When is it appropriate to do an RR?

In evidence synthesis, various approaches can be considered for quick action when time is limited. Decision-makers can rely on existing SRs that are up to date and relevant to the question at hand. If this is not available, another option is to update an existing SR by incorporating the latest evidence to ensure its relevance. It is important to note that not all updates will simply involve repeating the original steps of the review. The process could be time-consuming, especially if there are changes in the broader context of clinical decision-making or if updated methods need to be considered. These factors can contribute to a lengthy updating process, sometimes taking several months or longer to complete. If there are no existing reviews to work from, accelerated SRs, often confused with RRs, actually refer to traditional SRs conducted more quickly, often facilitated by additional resources such as expertise and an expanded review team. Accelerated SRs aim to maintain the methodological rigour and comprehensiveness of SRs, while also expediting their completion, distinguishing them from RRs. If these methods cannot meet the required timelines, or when initiating any new synthesis is impractical, decisions may be based on the best available evidence without a formal synthesis. The choice among these synthesis types depends on the urgency with which decision-makers need evidence, the availability of resources and expertise, and the impact on decision outcomes. RRs emerge as a distinct and valuable option when there is an immediate need for evidence, and other methods cannot adequately balance timeliness with the breadth and depth of a traditional SR. General distinctions between SRs and RRs, and other types of evidence syntheses have been previously published. 6 31 32

Conducting an RR is appropriate in various scenarios for reasons that can often overlap. The categories outlined below address a variety of practical scenarios where timely access to synthesised evidence is crucial. They provide a clear framework for considering when to use RRs in decision-making and research, helping healthcare professionals, policy-makers, decision-makers and researchers better understand when and how to employ RRs effectively. Regardless of the scenario, the appropriateness of conducting an RR should depend on the specific context and the urgency of the decision or inquiry.

Urgent decision-making: RRs are valuable when policy-makers, healthcare providers or public health authorities face urgent decisions, such as responding to disease outbreaks, natural disasters or emerging health threats and need evidence to inform immediate actions. 33 34 RRs can also guide clinical care decisions by synthesising available evidence for healthcare professionals requiring evidence for time-sensitive direct patient care decisions. 35 36

Informing guidelines: RRs are valuable for informing the rapid development or updating of clinical practice guidelines recommendations, ensuring that healthcare practices are based on the latest evidence. 28 37 38

New or emerging technologies and interventions: RRs may be suitable when assessing the evidence on newly introduced medical technologies, interventions or diagnostic tools that have potential clinical implications. 39

Rapidly evolving research areas: RRs can help provide an up-to-date synthesis of evidence in rapidly evolving fields, such as infectious diseases, biotechnology or digital health interventions. 40

Identify evidence gaps: RRs can efficiently identify evidence gaps and areas where evidence is scarce or lacking, guiding future research priorities. 41

Justify or inform new primary research: RRs can justify or inform the design of new primary studies in situations with limited resources. 42

Resource constraints: RRs provide a valuable alternative to full SRs by offering a concise yet evidence-based summary within project constraints in situations with limited resources, such as low-resource settings or tight timelines with limited funding. 19 43

Time-sensitive opportunities: RRs expedite the research process and provide timely evidence to support proposals or initiatives when time is critical, such as time-limited funding opportunities or to meet decision-makers’ urgent evidence needs. 14

Other possible scenarios: RRs may be conducted as a precursor to SR and can offer initial insights and may help identify whether there is a need for a more comprehensive SR to validate findings further. This approach is context-dependent and should be considered based on the specific research question. RRs can also assist researchers and decision-makers in gauging whether additional evidence is through SRs or primary research. This is particularly relevant when existing evidence is scarce, outdated or not directly applicable to the target population or context. By extension, RRs can also support grant submissions for SRs or primary studies.

When is it inappropriate to conduct an RR?

There are instances when conducting an RR may not be justified or inappropriate. One such situation arises when the researchers need more experience in conducting SRs, leading them to opt for an RR merely because it is perceived as easier. RRs may be more difficult, and the researcher should be aware of the potential biases introduced by the accelerated methods.

Similarly, if the primary motivation behind conducting an RR is to achieve a quick publication, and this is perceived to be less work, it may compromise the rigour and comprehensiveness of the review process. Another concern arises when the decision to conduct an RR is primarily driven by the desire to save money, even though the subject under investigation has far-reaching consequences and requires evidence-based decision-making.

Further, if there are already up-to-date full SRs available on the specific topic of interest, conducting an RR might duplicate efforts and fail to add significant value to the existing evidence base. Lastly, conducting an RR only for academic purposes should be discouraged unless, in the context of evidence-based research, the findings have immediate practical implications, such as contributing to the broader knowledge base to potentially inform future research or decision-making processes. In such cases, it is essential to carefully assess the need for an RR and consider alternative approaches for conducting more comprehensive and reliable research.

Considerations when deciding to do an RR

Undertaking RRs is predicated on their utility in scenarios where traditional SR processes are unable to meet the necessary time and resource constraints. It is also important to consider the pros and cons of this approach, as it offers the advantage of resource-efficient evidence synthesis but also comes with potential drawbacks. 21 44 Limitations of RRs include potential methodological weaknesses, biases due to the expedited methods used and a narrower scope, which could impact the trustworthiness of their findings. Some of these limitations can also be found in SRs that are not well conducted or well reported. 21 Moreover, limitations can arise from inadequately reported or conducted primary studies included in a review, irrespective of the type of evidence synthesis (see online supplemental file 1 for potential limitations of RRs and approaches to mitigate drawbacks). Regardless of the type of synthesis being conducted, if the process is poorly executed or inadequately reported, it can lead to unreliable results. To address these limitations, it is crucial to adhere to best practices 9 23 24 and maintain transparent reporting. 25

Supplemental material

At the outset, the initial planning stage of any RR may be guided by a set of factors categorised as either conceptual or practical. Conceptual factors represent higher-level considerations or broader aspects influencing the need for an RR. Considerations involve assessing the reasons for needing an RR, the potential risks of incomplete evidence, the novelty of the situation and the level of uncertainty among decision-makers. It also includes evaluating the impact on decision-making if waiting for an SR or going without any evidence synthesis and considering whether the findings from the RR will be acted on promptly. These factors help determine the urgency and importance of obtaining timely evidence. Practical factors represent the more operational and logistical aspects determining the feasibility of implementing an RR approach.

Guiding questions to help assess the appropriateness of conducting an RR include

Conceptual factors.

Why is an RR needed, and what are the potential risks to the populations being studied if the evidence is incomplete? When considering the need for an RR, examining the event or situation driving the request is crucial. RRs have demonstrated utility in informing urgent health issues, such as rapidly spreading infectious diseases, where immediate access to evidence is crucial for decision-making. 37 However, conducting an RR comes with risks if the evidence base is incomplete, potentially leading to suboptimal decision-making. Balancing the need for timely evidence synthesis and ensuring completeness is vital to minimise potential negative impacts on target populations. While decision-makers might be willing to prioritise speed over certainty, 45 it is essential to approach this with caution. The potential risks and trade-offs linked to incomplete evidence should be carefully considered in the context of each RR.

Is there a need for an RR based on a ‘novel’ event? RRs may be beneficial for reviewing evidence in cases of new events, such as introducing treatment interventions, detecting new virus strains, considering new distinct outcomes or introducing new technologies. Depending on the degree of novelty, one should assess whether to rapidly review what could be a limited or premature literature base or to conduct a full SR. 38

Is there significant uncertainty for decision-makers as to the best position to take? RRs can be valuable when facing uncertainty and time constraints in decision-making. Decision-makers may need clarification about the best course of action, or there may be conflicting viewpoints and opinions in the field. Therefore, assess the level of uncertainty and divergence among views to determine if an RR is the most appropriate approach.

What would be the impact of waiting for an SR? The impact of waiting for an SR vs an RR depends on the specific situation and context. While waiting for an SR can help ensure a more thorough and reliable evidence synthesis, it also takes longer and delays decision-making. On the other hand, choosing an RR provides evidence faster but may come with limitations in terms of comprehensiveness, reliability and potential bias. The decision between the two approaches hinges on the urgency of the decision and the level of evidence needed. If the event or situation is expected to last beyond the typical time frame of 1–6 months for RRs, then an RR may not be the appropriate choice. However, if decision-making would otherwise proceed without evidence, even a moderately robust RR could be better than having no evidence to inform healthcare decisions.

What would be the risk of not using evidence synthesis to inform decision-making? The risk of not using any evidence synthesis to inform decision-making should be carefully considered. Proceeding without any evidence synthesis, whether an RR or SR, could lead to suboptimal choices that negatively impact the well-being and outcomes of the populations involved. In contrast, conducting even a moderately robust RR can be a more suitable option to quickly provide relevant evidence than having no evidence. Assessing the potential impact of forgoing evidence synthesis or delaying decision-making while waiting for synthesis is essential.

Will the findings from the RR be rapidly acted on? If there is no existing mechanism for disseminating and implementing the findings of the RR, there may be no point in developing it. It will be necessary to carefully consider the decision-making context (eg, the existing health system, infrastructure, acceptability and resource implications) before embarking on an RR process. 38

Practical factors

How quickly does the uncertainty need to be addressed? Evaluate the urgency/time sensitivity of the research question. If there is a pressing need for evidence to inform immediate decision-making or address an emerging issue, an RR may be more appropriate due to its shorter turnaround time. On the other hand, if time is less critical and a comprehensive synthesis is required, an SR may be preferred.

What are the stakeholders needs and expectations? Engage with decision-makers, policy-makers and relevant stakeholders to determine their priorities. Some stakeholders may prioritise rigour and comprehensiveness and therefore, prefer an SR while others may require timely evidence and lean towards an RR. Aligning with stakeholder preferences can help determine the most appropriate approach.

What is the scope of the research question? Consider the breadth and complexity of the research question. If the question is narrowly focused and specific, an RR may be sufficient to address it. However, an SR is more likely to be appropriate if the research question requires a comprehensive analysis of a wide range of studies and outcomes.

What are the available resources? Assess the availability of resources, including personnel, funding and expertise that are available for the review. Conducting an SR can be resource-intensive and time-consuming. However, an RR may also be all consuming and intense but over a more condensed time frame. An RR may be more feasible if resources are limited, as it typically requires fewer resources and can be conducted by a smaller team. Both require a team with expertise in SR methods.

Within Cochrane, the decision to conduct an RR is influenced by two main factors: the urgency of the question and whether it addresses a high-priority issue. High-priority situations may include, for example, urgent requests from funding agencies or the need to inform a quickly convened guideline panel. A full SR is deemed impractical due to time constraints in these cases. By considering the above-mentioned factors, we can better understand both the conceptual underpinnings and the practical considerations to help make an informed judgement about whether an RR or an SR is more appropriate for a specific research question and context.

Equity considerations for RRs

Low-resource settings face specific challenges in synthesising and delivering evidence to knowledge users. In these settings, limited resources may hinder the comprehensive conduct of SRs, leading to delays or knowledge gaps. RRs become particularly relevant in such contexts, offering a more feasible and timelier alternative to full SRs. Their appropriateness in low-resource settings stems from the ability to provide a concise, evidence-based summary within project constraints, aligning with the need for efficient resource use. Moreover, RRs expedite access to available evidence for decision-making in time-sensitive scenarios, addressing equity concerns through the provision of timely and relevant information to knowledge users.

Conversely, RRs may pose several concerns from an equity perspective. While RRs offer a quick and efficient approach to evidence synthesis, conducting them for subgroups can pose several limitations. One major concern is the potential for missing relevant studies on specific subpopulations. The expedited nature of RRs may lead to a more cursory search, increasing the risk of overlooking studies that focus on particular demographic, geographical or clinical subgroups. This limitation can result in a skewed representation of the evidence, potentially leading to inaccurate conclusions or recommendations for certain populations. Furthermore, exclusions based on language or publication type are common shortcuts in RRs to expedite the review process. However, this practice could introduce a language bias and exclude valuable studies, particularly those published in languages other than the primary language of the review. This exclusion may disproportionately impact research from certain regions or communities, contributing to disparities in evidence representation. Therefore, while RRs offer several advantages, researchers and decision-makers should be cautious and consider the trade-offs carefully when opting for RRs, particularly when focusing on specific subpopulations.

Ethics statements

Patient consent for publication.

Not applicable.

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Supplementary materials

Supplementary data.

This web only file has been produced by the BMJ Publishing Group from an electronic file supplied by the author(s) and has not been edited for content.

• Data supplement 1

Twitter @cgarritty

Collaborators On behalf of the Cochrane Rapid Reviews Methods Group: Chantelle Garritty, Barbara Nussbaumer-Streit, Candyce Hamel, Declan Devane.

Contributors All authors (CG, BN-S, CH and DD) contributed to the conceptualisation of this paper on behalf of the Cochrane Rapid Reviews Methods Group. CG wrote the first draft of the manuscript. All authors (CG, BN-S, CH and DD) read and approved the final version. CG is the guarantor and attests that all authors meet authorship criteria and that no others meeting the criteria have been omitted.

Funding The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

Competing interests None declared.

Patient and public involvement Patients and/or the public were not involved in the design, or conduct, or reporting, or dissemination plans of this research.

Provenance and peer review Not commissioned; externally peer reviewed.

Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.

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Disentangling Hype from Practicality: On Realistically Achieving Quantum Advantage

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• Introduction

Key Insights

Operating on fundamentally different principles than conventional computers, quantum computers promise to solve a variety of important problems that seemed forever intractable on classical computers. Leveraging the quantum foundations of nature, the time to solve certain problems on quantum computers grows more slowly with the size of the problem than on classical computers—this is called quantum speedup. Going beyond quantum supremacy, 2 which was the demonstration of a quantum computer outperforming a classical one for an artificial problem, an important question is finding meaningful applications (of academic or commercial interest) that can realistically be solved faster on a quantum computer than on a classical one. We call this a practical quantum advantage, or quantum practicality for short.

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• Most of today’s quantum algorithms may not achieve practical speedups. Material science and chemistry have a huge potential and we hope more practical algorithms will be invented based on our guidelines.
• Due to limitations of input and output bandwidth, quantum computers will be practical for “big compute” problems on small data, not big data problems.
• Quadratic speedups delivered by algorithms such as Grover’s search are insufficient for practical quantum advantage without significant improvements across the entire software/hardware stack.

There is a maze of hard problems that have been suggested to profit from quantum acceleration: from cryptanalysis, chemistry and materials science, to optimization, big data, machine learning, database search, drug design and protein folding, fluid dynamics and weather prediction. But which of these applications realistically offer a potential quantum advantage in practice? For this, we cannot only rely on asymptotic speedups but must consider the constants involved. Being optimistic in our outlook for quantum computers, we identify clear guidelines for quantum practicality and use them to classify which of the many proposed applications for quantum computing show promise and which ones would require significant algorithmic improvements to become practical and relevant.

To establish reliable guidelines, or lower bounds for the required speedup of a quantum computer, we err on the side of being optimistic for quantum and overly pessimistic for classical computing. Despite our overly optimistic assumptions, our analysis shows a wide range of often-cited applications is unlikely to result in a practical quantum advantage without significant algorithmic improvements. We compare the performance of only a single classical chip fabricated like the one used in the NVIDIA A100 GPU that fits around 54 billion transistors 15 with an optimistic assumption for a hypothetical quantum computer that may be available in the next decades with 10,000 error-corrected logical qubits, 10μs gate time for logical operations, the ability to simultaneously perform gate operations on all qubits and all-to-all connectivity for fault tolerant two-qubit gates. a

I/O bandwidth. We first consider the fundamental I/O bottleneck that limits quantum computers in their interaction with the classical world, which determines bounds for data input and output bandwidths. Scalable implementations of quantum random access memory (QRAM 8 , 9 ) demand a fault-tolerant error corrected implementation and the bandwidth is then fundamentally limited by the number of quantum gate operations or measurements that can be performed per unit time. We assume only a single gate operation per input bit. For our optimistic future quantum computer, the resulting rate is 10,000-times smaller than for an existing classical chip (see Table 1 ). We immediately see that any problem limited by accessing classical data, such as search problems in databases, will be solved faster by classical computers. Similarly, a potentially exponential quantum speedup in linear algebra problems 12 vanishes when the matrix must be loaded from classical data, or when the full solution vector should be read out. Generally, quantum computers will be practical for “big compute” problems on small data , not big data problems.

Crossover scale. With quantum speedup, asymptotically fewer operations will be needed on a quantum computer than on a classical computer. Due to the high operational complexity and slower gate operations, however, each operation on a quantum computer will be slower than a corresponding classical one. As sketched in the accompanying figure , classical computers will always be faster for small problems and quantum advantage is realized beyond a problem-dependent crossover scale where the gain due to quantum speedup overcomes the constant slowdown of the quantum computer. To have real practical impact, the crossover time must be short, not more than weeks. Constants matter in determining the utility for applications, as with any runtime estimate in computing.

Compute performance. To model performance, we employ the well-known work-depth model from classical parallel computing to determine upper bounds of classical silicon-based computations and an extension for quantum computations. In this model, the work is the total number of operations and applies to both classical and quantum executions. In Table 1 , we provide concrete examples using three types of operations: logical operations, 16-bit floating point, and 32-bit integer or fixed-point arithmetic operations for numerical modeling. For the quantum costs, we consider only the most expensive parts in our estimates, again benefiting quantum computers; for arithmetic, we count just the dominant cost of multiplications, assuming additions are free. Furthermore, for floating point multiplication, we consider only the cost of the multiplication of the mantissa (10 bits in fp16). We ignore all further overheads incurred by the quantum algorithm due to reversible computations, as well as the significant cost of mapping to a specific hardware architecture with limited qubit connectivity.

Crossover times for classical and quantum computation. To estimate lower bounds for the crossover times, we consider that while both classical and quantum computers must evaluate the same functions (usually called oracles) that describe a problem, quantum computers require fewer evaluations thereof due to quantum speedup. At the root of many quantum acceleration proposals lies a quadratic quantum speedup, including the well-known Grover algorithm. 10 , 11 For such an algorithm, a problem that needs X function calls on a quantum computer requires quadratically more, namely on the order of X 2 calls on a classical computer. To overcome the large constant performance difference between a quantum computer and a classical computer, which Table 1 shows to be more than a factor of 10 10 , many function calls X >> 10 10 is needed for the quantum speedup to deliver a practical advantage. In Table 2 , we estimate upper bounds for the complexity of the function that will lead to a cross-over time of 10 6 seconds, or approximately two weeks.

We see that with quadratic speedup even a single floating point or integer operation leads to crossover times of several months. Furthermore, at most 68 binary logical operations can be afforded to stay within our desired crossover time of two weeks, which is too low for any non-trivial application. Keeping in mind that these estimates are pessimistic for classical computation (a single of today’s classical chips) and overly optimistic for quantum computing (only considering the multiplication of the mantissa and assuming all-to-all qubit connectivity), we come to the clear conclusion that quadratic speedups are insufficient for practical quantum advantage. The numbers look better for cubic or quartic speedups where thousands or millions of operations may be feasible, and we conclude, similarly to Babbush et al., 3 that at least cubic or quartic speedups are required for a practical quantum advantage.

As a result of our overly optimistic assumptions in favor of quantum computing, these conclusions will remain valid even with significant advances in quantum technology of multiple orders of magnitude.

Practical and impractical applications. We can now use these considerations to discuss several classes of applications where our fundamental bounds draw a line for quantum practicality. The most likely problems to allow for a practical quantum advantage are those with exponential quantum speedup. This includes the simulation of quantum systems for problems in chemistry, materials science, and quantum physics, as well as cryptanalysis using Shor’s algorithm. 16 The solution of linear systems of equations for highly structured problems 12 also has an exponential speedup, but the I/O limitations discussed above will limit the practicality and undo this advantage if the matrix has to be loaded from memory instead of being computed based on limited data or knowledge of the full solution is required (as opposed to just some limited information obtained by sampling the solution).

Equally important, we identify likely dead ends in the maze of applications. A large range of problem areas with quadratic quantum speedups, such as many current machine learning training approaches, accelerating drug design and protein folding with Grover’s algorithm, speeding up Monte Carlo simulations through quantum walks, as well as more traditional scientific computing simulations including the solution of many non-linear systems of equations, such as fluid dynamics in the turbulent regime, weather, and climate simulations will not achieve quantum advantage with current quantum algorithms in the foreseeable future. We also conclude that the identified I/O limits constrain the performance of quantum computing for big data problems, unstructured linear systems, and database search based on Grover’s algorithm such that a speedup is unlikely in those cases. Furthermore, Aaronson et al. 1 show the achievable quantum speedup of unstructured black-box algorithms is limited to O ( N 4 ). This implies that any algorithm achieving higher speedup must exploit structure in the problem it solves.

These considerations help with separating hype from practicality in the search for quantum applications and can guide algorithmic developments. Specifically, our analysis shows it is necessary for the community to focus on super-quadratic speedups, ideally exponential speedups, and one needs to carefully consider I/O bottlenecks when deriving algorithms to exploit quantum computation best. Therefore, the most promising candidates for quantum practicality are small-data problems with exponential speedup. Specific examples where this is the case are quantum problems in chemistry and materials science, 5 which we identify as the most promising application. We recommend using precise requirements models 4 to get more reliable and realistic (less optimistic) estimates in cases where our rough guidelines indicate a potential practical quantum advantage.

Here, we provide more details for how we obtained the numbers mentioned earlier. We compare our quantum computer with a single microprocessor chip like the one used in the NVIDIA A100 GPU. 15 The A100 chip is around 850 mm 2 in size and manufactured in TSMC’s 7nm N7 silicon process. A100 shows that such a chip fits around 54.2 billion transistors and can operator at a cycle time of around 0.7ns.

Determining peak operation throughputs. In Table 1 , we provide concrete examples using three types of operations: logical operations, 16-bit floating point, and 32-bit integer arithmetic operations for numerical modeling. Other datatypes could be modeled using our methodology as well.

Classical NVIDIA A100. According to its datasheet, NVIDIA’s A100 GPU, a SIMT-style von Neumann load store architecture, delivers 312 tera-operations per second (Top/s) with half precision floating point (fp16) through tensor cores and 78Top/s through the normal processing pipeline. NVIDIA assumes a 50/50 mix of addition and multiplication operations and thus, we divide the number by two, yielding 195Top/s fp16 performance. The datasheet states 19.5Top/s for 32-bit integer operations, again assuming a 50/50 mix of addition and multiplication, leading to an effective 9.75Top/s. The binary tensor core performance is listed as 4,992Top/s with a limited set of instructions.

Classical special-purpose ASIC. Our main analysis assumes that we build a special-purpose ASIC using a similar technology. If we were to fill the equivalent chip-space of an A100 with a specialized circuit, we would use existing execution units, for which the size is typically measured in gate equivalents (GE). A 16-bit floating point unit (FPU) with addition and multiplication functions requires approximately 7kGE, a 32-bit integer unit requires 18kGE, 14 and we assume 50GE for a simple binary operation. All units include operand buffer registers and support a set of programmable instructions. We note that simple addition or multiplication circuits would be significantly cheaper. If we assume a transistor-to-gate ratio of 10 13 and that 50% of the total chip area is used for control logic of a dataflow ASIC with the required buffering, we can fit 54.2 B /(7 k • 10 • 2) = 387 k fp16 units. Similarly, we can fit 54.2 B (18 k • 10 • 2) = 151 k int32, or 54.2 B /(50 • 10 • 2) = 54.2M bin2 units on our hypothetical chip. Assuming a cycle time of 0.7ns, this leads to a total operation rate of 0.55 fp16, 0.22 int32, and 77.4 bin Pop/s for an application-specific ASIC with the A100’s technology and budget. The ASIC thus leads to a raw speedup between approximately 2x and 15x over a programmable circuit. Thus, on classical silicon, the performance ranges approximately between 10 13 and 10 16 op/s for binary, int32, and fp16 types.

Our analysis shows a wide range of often-cited applications is unlikely to result in a practical quantum advantage without significant algorithmic improvements.

Hypothetical future quantum computer. To determine the costs of N -bit multiplication on a quantum computer, we choose the controlled adder from Gidney 6 and implement the multiplication using N single-bit controlled adders, each requiring 2 N CCZ magic states. These states are produced in so called “magic state factories” that are implemented on the physical chip. While the resulting multiplier is entirely sequential, we found that this construction allows for more units to be placed on one chip than for a low-depth adder and/or for a tree-like reduction of partial products since the number of CCZ states is lower (and thus fewer magic state factories are required), and the number of work-qubits is lower. The resulting multiplier has a CCZ-depth and count of 2 N 2 using 5 N – 1 qubits (2 N input, 2 N – 1 output, N ancilla for the addition).

To compute the space overhead due to CCZ factories, we first use the analysis of Gidney and Fowler 7 to compute the number of physical qubits per factory when aiming for circuits (programs) using ≈ 10 8 CCZ magic states with physical gate errors of 10 -3 . We approximate the overhead in terms of logical qubits by dividing the physical space overhead by 2 d 2 , where we choose the error-correcting code distance d = 2 • 31 2 to be the same as the distance used for the second level of distillation. 7 Thus we divide Gidney and Fowler’s 147,904 physical qubits per factory (for details consult the anciliary spreadsheet (field B40) of Gidney and Fowler) by 2 d 2 = 2 • 31 2 and get an equivalent space of 77 logical qubits per factory.

For the multiplier of the 10-bit mantissa of an fp16 floating point number, we need 2 • 10 2 = 200 CCZ states and 5 • 10 = 50 qubits. Since each factory takes 5.5 cycles 7 and we can pipeline the production of CCZ states, we assume 5.5 factories per multiplication unit such that multipliers do not wait for magic state production on average. Thus, each multiplier requires 200 cycles and 5 N + 5.5 • 77 = 50 + 5.5 • 77 = 473.5 qubits. With a total of 10,000 logical qubits, we can implement 21 10-bit multipliers on our hypothetical quantum chip. With 10μs cycle time, the 200-cycle latency, we get the final rate of less than 10 5 cycle/ s / (200 cycle/op ) • 21= 10.5 kop/s. For int32 ( N =32), the calculation is equivalent. For binary, we assume two input and one output qubit for the (binary) adder (Toffoli gate) which does not need ancillas. The results are summarized in Table 1 .

A note on parallelism. We assumed massively parallel execution of the oracle on both the classical and quantum computer (that is, oracles with a depth of one). If the oracle does not admit such parallelization, for example, if depth = work in the worst-case scenario, then the comparison becomes more favorable towards the quantum computer. One could model this scenario by allowing the classical computer to only perform one operation per cycle. With a 2GHz clock frequency, this would mean a slowdown of about 100,000 times for fp16 on the GPU. In this extremely unrealistic algorithmic worst case, the oracle would still have to consist of only several thousands of fp16 operations with a quadratic speedup. However, we note that in practice, most oracles have low depth and parallelization across a single chip is achievable, which is what we assumed.

Determining maximum operation counts per oracle call. In Table 2 , we list the maximum number of operations of a certain type that can be run to achieve a quantum speedup within a runtime of 10 6 seconds (a little more than two weeks). The maximum number of classical operations that can be performed with a single classical chip in 10 6 seconds would be: 0.55 fp16, 0.22 int32, and 77.4 bin Zop. Similarly, assuming the rates from Table 1 , for a quantum chip: 7, 4, 2, and 350 Gop, respectively.

We now assume that all calculations are used in oracle calls on the quantum computer and we ignore all further costs on the quantum machine. We start by modeling algorithms that provide polynomial X k speedup, for small constants k. For example, for Grover’s algorithms, 11 k + 2. It is clear quantum computers are asymptotically faster (in the number of oracle queries) for any k >1. However, we are interested to find the oracle complexity (that is, the number of operations required to evaluate it) for which a quantum computer is faster than a classical computer within the time-window of 10 6 seconds.

Let the number of operations required to evaluate a single oracle call be M and let the number of required invocations be N. It takes a classical computer time T c = N k • M • t c , whereas a quantum computer solves the same problem in time T q = N k • M • t q where t c and t q denote the time to evaluate an operation on a classical and on a quantum computer, respectively. By demanding that the quantum computer should solve the problem faster than the classical computer and within 10 6 seconds, we find

which allows us to compute the maximal number of basic operations per oracle evaluation such that the quantum computer still achieves a practical speedup:

Acknowledgments. We thank L. Benini for helpful discussions about ASIC and processor design and related overheads and W. van Dam and anonymous reviewers for comments that improved an earlier draft.

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May 2023 Issue

Published: May 1, 2023

Vol. 66 No. 5

Pages: 82-87

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