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• AACU VALUE Rubrics

Using rubrics

A rubric is a type of scoring guide that assesses and articulates specific components and expectations for an assignment. Rubrics can be used for a variety of assignments: research papers, group projects, portfolios, and presentations.  

Why use rubrics? 

Rubrics help instructors: 

• Assess assignments consistently from student-to-student. 
• Save time in grading, both short-term and long-term. 
• Give timely, effective feedback and promote student learning in a sustainable way. 
• Clarify expectations and components of an assignment for both students and course teaching assistants (TAs). 
• Refine teaching methods by evaluating rubric results. 

Rubrics help students: 

• Understand expectations and components of an assignment. 
• Become more aware of their learning process and progress. 
• Improve work through timely and detailed feedback. 

Considerations for using rubrics 

When developing rubrics consider the following:

• Although it takes time to build a rubric, time will be saved in the long run as grading and providing feedback on student work will become more streamlined.  
• A rubric can be a fillable pdf that can easily be emailed to students. 
• They can be used for oral presentations. 
• They are a great tool to evaluate teamwork and individual contribution to group tasks. 
• Rubrics facilitate peer-review by setting evaluation standards. Have students use the rubric to provide peer assessment on various drafts. 
• Students can use them for self-assessment to improve personal performance and learning. Encourage students to use the rubrics to assess their own work. 
• Motivate students to improve their work by using rubric feedback to resubmit their work incorporating the feedback. 

Getting Started with Rubrics 

• Start small by creating one rubric for one assignment in a semester.  
• Ask colleagues if they have developed rubrics for similar assignments or adapt rubrics that are available online. For example, the  AACU has rubrics  for topics such as written and oral communication, critical thinking, and creative thinking. RubiStar helps you to develop your rubric based on templates.  
• Examine an assignment for your course. Outline the elements or critical attributes to be evaluated (these attributes must be objectively measurable). 
• Create an evaluative range for performance quality under each element; for instance, “excellent,” “good,” “unsatisfactory.” 
• Avoid using subjective or vague criteria such as “interesting” or “creative.” Instead, outline objective indicators that would fall under these categories. 
• The criteria must clearly differentiate one performance level from another. 
• Assign a numerical scale to each level. 
• Give a draft of the rubric to your colleagues and/or TAs for feedback. 
• Train students to use your rubric and solicit feedback. This will help you judge whether the rubric is clear to them and will identify any weaknesses. 
• Rework the rubric based on the feedback. 

Rubric Best Practices, Examples, and Templates

A rubric is a scoring tool that identifies the different criteria relevant to an assignment, assessment, or learning outcome and states the possible levels of achievement in a specific, clear, and objective way. Use rubrics to assess project-based student work including essays, group projects, creative endeavors, and oral presentations.

Rubrics can help instructors communicate expectations to students and assess student work fairly, consistently and efficiently. Rubrics can provide students with informative feedback on their strengths and weaknesses so that they can reflect on their performance and work on areas that need improvement.

How to Get Started

Best practices, moodle how-to guides.

• Workshop Recording (Fall 2022)
• Workshop Registration

Step 1: Analyze the assignment

The first step in the rubric creation process is to analyze the assignment or assessment for which you are creating a rubric. To do this, consider the following questions:

• What is the purpose of the assignment and your feedback? What do you want students to demonstrate through the completion of this assignment (i.e. what are the learning objectives measured by it)? Is it a summative assessment, or will students use the feedback to create an improved product?
• Does the assignment break down into different or smaller tasks? Are these tasks equally important as the main assignment?
• What would an “excellent” assignment look like? An “acceptable” assignment? One that still needs major work?
• How detailed do you want the feedback you give students to be? Do you want/need to give them a grade?

Step 2: Decide what kind of rubric you will use

Types of rubrics: holistic, analytic/descriptive, single-point

Holistic Rubric. A holistic rubric includes all the criteria (such as clarity, organization, mechanics, etc.) to be considered together and included in a single evaluation. With a holistic rubric, the rater or grader assigns a single score based on an overall judgment of the student’s work, using descriptions of each performance level to assign the score.

Advantages of holistic rubrics:

• Can p lace an emphasis on what learners can demonstrate rather than what they cannot
• Save grader time by minimizing the number of evaluations to be made for each student
• Can be used consistently across raters, provided they have all been trained

Disadvantages of holistic rubrics:

• Provide less specific feedback than analytic/descriptive rubrics
• Can be difficult to choose a score when a student’s work is at varying levels across the criteria
• Any weighting of c riteria cannot be indicated in the rubric

Analytic/Descriptive Rubric . An analytic or descriptive rubric often takes the form of a table with the criteria listed in the left column and with levels of performance listed across the top row. Each cell contains a description of what the specified criterion looks like at a given level of performance. Each of the criteria is scored individually.

Advantages of analytic rubrics:

• Provide detailed feedback on areas of strength or weakness
• Each criterion can be weighted to reflect its relative importance

Disadvantages of analytic rubrics:

• More time-consuming to create and use than a holistic rubric
• May not be used consistently across raters unless the cells are well defined
• May result in giving less personalized feedback

Single-Point Rubric . A single-point rubric is breaks down the components of an assignment into different criteria, but instead of describing different levels of performance, only the “proficient” level is described. Feedback space is provided for instructors to give individualized comments to help students improve and/or show where they excelled beyond the proficiency descriptors.

Advantages of single-point rubrics:

• Easier to create than an analytic/descriptive rubric
• Perhaps more likely that students will read the descriptors
• Areas of concern and excellence are open-ended
• May removes a focus on the grade/points
• May increase student creativity in project-based assignments

Disadvantage of analytic rubrics: Requires more work for instructors writing feedback

Step 3 (Optional): Look for templates and examples.

You might Google, “Rubric for persuasive essay at the college level” and see if there are any publicly available examples to start from. Ask your colleagues if they have used a rubric for a similar assignment. Some examples are also available at the end of this article. These rubrics can be a great starting point for you, but consider steps 3, 4, and 5 below to ensure that the rubric matches your assignment description, learning objectives and expectations.

Step 4: Define the assignment criteria

Make a list of the knowledge and skills are you measuring with the assignment/assessment Refer to your stated learning objectives, the assignment instructions, past examples of student work, etc. for help.

  Helpful strategies for defining grading criteria:

• Collaborate with co-instructors, teaching assistants, and other colleagues
• Brainstorm and discuss with students
• Can they be observed and measured?
• Are they important and essential?
• Are they distinct from other criteria?
• Are they phrased in precise, unambiguous language?
• Revise the criteria as needed
• Consider whether some are more important than others, and how you will weight them.

Step 5: Design the rating scale

Most ratings scales include between 3 and 5 levels. Consider the following questions when designing your rating scale:

• Given what students are able to demonstrate in this assignment/assessment, what are the possible levels of achievement?
• How many levels would you like to include (more levels means more detailed descriptions)
• Will you use numbers and/or descriptive labels for each level of performance? (for example 5, 4, 3, 2, 1 and/or Exceeds expectations, Accomplished, Proficient, Developing, Beginning, etc.)
• Don’t use too many columns, and recognize that some criteria can have more columns that others . The rubric needs to be comprehensible and organized. Pick the right amount of columns so that the criteria flow logically and naturally across levels.

Step 6: Write descriptions for each level of the rating scale

Artificial Intelligence tools like Chat GPT have proven to be useful tools for creating a rubric. You will want to engineer your prompt that you provide the AI assistant to ensure you get what you want. For example, you might provide the assignment description, the criteria you feel are important, and the number of levels of performance you want in your prompt. Use the results as a starting point, and adjust the descriptions as needed.

Building a rubric from scratch

For a single-point rubric , describe what would be considered “proficient,” i.e. B-level work, and provide that description. You might also include suggestions for students outside of the actual rubric about how they might surpass proficient-level work.

For analytic and holistic rubrics , c reate statements of expected performance at each level of the rubric.

• Consider what descriptor is appropriate for each criteria, e.g., presence vs absence, complete vs incomplete, many vs none, major vs minor, consistent vs inconsistent, always vs never. If you have an indicator described in one level, it will need to be described in each level.
• You might start with the top/exemplary level. What does it look like when a student has achieved excellence for each/every criterion? Then, look at the “bottom” level. What does it look like when a student has not achieved the learning goals in any way? Then, complete the in-between levels.
• For an analytic rubric , do this for each particular criterion of the rubric so that every cell in the table is filled. These descriptions help students understand your expectations and their performance in regard to those expectations.

Well-written descriptions:

• Describe observable and measurable behavior
• Use parallel language across the scale
• Indicate the degree to which the standards are met

Step 7: Create your rubric

Create your rubric in a table or spreadsheet in Word, Google Docs, Sheets, etc., and then transfer it by typing it into Moodle. You can also use online tools to create the rubric, but you will still have to type the criteria, indicators, levels, etc., into Moodle. Rubric creators: Rubistar , iRubric

Step 8: Pilot-test your rubric

Prior to implementing your rubric on a live course, obtain feedback from:

• Teacher assistants

Try out your new rubric on a sample of student work. After you pilot-test your rubric, analyze the results to consider its effectiveness and revise accordingly.

• Limit the rubric to a single page for reading and grading ease
• Use parallel language . Use similar language and syntax/wording from column to column. Make sure that the rubric can be easily read from left to right or vice versa.
• Use student-friendly language . Make sure the language is learning-level appropriate. If you use academic language or concepts, you will need to teach those concepts.
• Share and discuss the rubric with your students . Students should understand that the rubric is there to help them learn, reflect, and self-assess. If students use a rubric, they will understand the expectations and their relevance to learning.
• Consider scalability and reusability of rubrics. Create rubric templates that you can alter as needed for multiple assignments.
• Maximize the descriptiveness of your language. Avoid words like “good” and “excellent.” For example, instead of saying, “uses excellent sources,” you might describe what makes a resource excellent so that students will know. You might also consider reducing the reliance on quantity, such as a number of allowable misspelled words. Focus instead, for example, on how distracting any spelling errors are.

Example of an analytic rubric for a final paper

Example of a holistic rubric for a final paper, single-point rubric, more examples:.

• Single Point Rubric Template ( variation )
• Analytic Rubric Template make a copy to edit
• A Rubric for Rubrics
• Bank of Online Discussion Rubrics in different formats
• Mathematical Presentations Descriptive Rubric
• Math Proof Assessment Rubric
• Kansas State Sample Rubrics
• Design Single Point Rubric

Technology Tools: Rubrics in Moodle

• Moodle Docs: Rubrics
• Moodle Docs: Grading Guide (use for single-point rubrics)

Tools with rubrics (other than Moodle)

• Google Assignments
• Turnitin Assignments: Rubric or Grading Form

Other resources

• DePaul University (n.d.). Rubrics .
• Gonzalez, J. (2014). Know your terms: Holistic, Analytic, and Single-Point Rubrics . Cult of Pedagogy.
• Goodrich, H. (1996). Understanding rubrics . Teaching for Authentic Student Performance, 54 (4), 14-17. Retrieved from   
• Miller, A. (2012). Tame the beast: tips for designing and using rubrics.
• Ragupathi, K., Lee, A. (2020). Beyond Fairness and Consistency in Grading: The Role of Rubrics in Higher Education. In: Sanger, C., Gleason, N. (eds) Diversity and Inclusion in Global Higher Education. Palgrave Macmillan, Singapore.

• Basics for GSIs
• Advancing Your Skills

Examples of Rubric Creation

Creating a rubric takes time and requires thought and experimentation. Here you can see the steps used to create two kinds of rubric: one for problems in a physics exam for a small, upper-division physics course, and another for an essay assignment in a large, lower-division sociology course.

Physics Problems

In STEM disciplines (science, technology, engineering, and mathematics), assignments tend to be analytical and problem-based. Holistic rubrics can be an efficient, consistent, and fair way to grade a problem set. An analytical rubric often gives a more clear picture of what a student should direct their future learning efforts on. Since holistic rubrics try to label overall understanding, they can lead to more regrade requests when compared to analytical rubric with more explicit criteria. When starting to grade a problem, it is important to think about the relevant conceptual ingredients in the solution. Then look at a sample of student work to get a feel for student mistakes. Decide what rubric you will use (e.g., holistic or analytic, and how many points). Apply the holistic rubric by marking comments and sorting the students’ assignments into stacks (e.g., five stacks if using a five-point scale). Finally, check the stacks for consistency and mark the scores. The following is a sample homework problem from a UC Berkeley Physics Department undergraduate course in mechanics.

Homework Problem

Learning objective.

Solve for position and speed along a projectile’s trajectory.

Desired Traits: Conceptual Elements Needed for the Solution

• Decompose motion into vertical and horizontal axes.
• Identify that the maximum height occurs when the vertical velocity is 0.
• Apply kinematics equation with g as the acceleration to solve for the time and height.
• Evaluate the numerical expression.

A note on analytic rubrics: If you decide you feel more comfortable grading with an analytic rubric, you can assign a point value to each concept. The drawback to this method is that it can sometimes unfairly penalize a student who has a good understanding of the problem but makes a lot of minor errors. Because the analytic method tends to have many more parts, the method can take quite a bit more time to apply. In the end, your analytic rubric should give results that agree with the common-sense assessment of how well the student understood the problem. This sense is well captured by the holistic method.

Holistic Rubric

A holistic rubric, closely based on a rubric by Bruce Birkett and Andrew Elby:

[a] This policy especially makes sense on exam problems, for which students are under time pressure and are more likely to make harmless algebraic mistakes. It would also be reasonable to have stricter standards for homework problems.

Analytic Rubric

The following is an analytic rubric that takes the desired traits of the solution and assigns point values to each of the components. Note that the relative point values should reflect the importance in the overall problem. For example, the steps of the problem solving should be worth more than the final numerical value of the solution. This rubric also provides clarity for where students are lacking in their current understanding of the problem.

Try to avoid penalizing multiple times for the same mistake by choosing your evaluation criteria to be related to distinct learning outcomes. In designing your rubric, you can decide how finely to evaluate each component. Having more possible point values on your rubric can give more detailed feedback on a student’s performance, though it typically takes more time for the grader to assess.

Of course, problems can, and often do, feature the use of multiple learning outcomes in tandem. When a mistake could be assigned to multiple criteria, it is advisable to check that the overall problem grade is reasonable with the student’s mastery of the problem. Not having to decide how particular mistakes should be deducted from the analytic rubric is one advantage of the holistic rubric. When designing problems, it can be very beneficial for students not to have problems with several subparts that rely on prior answers. These tend to disproportionately skew the grades of students who miss an ingredient early on. When possible, consider making independent problems for testing different learning outcomes.

Sociology Research Paper

An introductory-level, large-lecture course is a difficult setting for managing a student research assignment. With the assistance of an instructional support team that included a GSI teaching consultant and a UC Berkeley librarian [b] , sociology lecturer Mary Kelsey developed the following assignment:

This was a lengthy and complex assignment worth a substantial portion of the course grade. Since the class was very large, the instructor wanted to minimize the effort it would take her GSIs to grade the papers in a manner consistent with the assignment’s learning objectives. For these reasons Dr. Kelsey and the instructional team gave a lot of forethought to crafting a detailed grading rubric.

Desired Traits

• Use and interpretation of data
• Reflection on personal experiences
• Application of course readings and materials
• Organization, writing, and mechanics

For this assignment, the instructional team decided to grade each trait individually because there seemed to be too many independent variables to grade holistically. They could have used a five-point scale, a three-point scale, or a descriptive analytic scale. The choice depended on the complexity of the assignment and the kind of information they wanted to convey to students about their work.

Below are three of the analytic rubrics they considered for the Argument trait and a holistic rubric for all the traits together. Lastly you will find the entire analytic rubric, for all five desired traits, that was finally used for the assignment. Which would you choose, and why?

Five-Point Scale

Three-point scale, simplified three-point scale, numbers replaced with descriptive terms.

For some assignments, you may choose to use a holistic rubric, or one scale for the whole assignment. This type of rubric is particularly useful when the variables you want to assess just cannot be usefully separated. We chose not to use a holistic rubric for this assignment because we wanted to be able to grade each trait separately, but we’ve completed a holistic version here for comparative purposes.

Final Analytic Rubric

This is the rubric the instructor finally decided to use. It rates five major traits, each on a five-point scale. This allowed for fine but clear distinctions in evaluating the students’ final papers.

[b] These materials were developed during UC Berkeley’s 2005–2006 Mellon Library/Faculty Fellowship for Undergraduate Research program. M embers of the instructional team who worked with Lecturer Kelsey in developing the grading rubric included Susan H askell-Khan, a GSI Center teaching consultant and doctoral candidate in history, and Sarah McDaniel, a teaching librarian with the Doe/Moffitt Libraries.

Research Paper Rubric

Mailing address.

Pomona College 333 N. College Way Claremont , CA 91711

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Give back to pomona.

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Rubric Design

Main navigation, articulating your assessment values.

Reading, commenting on, and then assigning a grade to a piece of student writing requires intense attention and difficult judgment calls. Some faculty dread “the stack.” Students may share the faculty’s dim view of writing assessment, perceiving it as highly subjective. They wonder why one faculty member values evidence and correctness before all else, while another seeks a vaguely defined originality.

Writing rubrics can help address the concerns of both faculty and students by making writing assessment more efficient, consistent, and public. Whether it is called a grading rubric, a grading sheet, or a scoring guide, a writing assignment rubric lists criteria by which the writing is graded.

Why create a writing rubric?

• It makes your tacit rhetorical knowledge explicit
• It articulates community- and discipline-specific standards of excellence
• It links the grade you give the assignment to the criteria
• It can make your grading more efficient, consistent, and fair as you can read and comment with your criteria in mind
• It can help you reverse engineer your course: once you have the rubrics created, you can align your readings, activities, and lectures with the rubrics to set your students up for success
• It can help your students produce writing that you look forward to reading

How to create a writing rubric

Create a rubric at the same time you create the assignment. It will help you explain to the students what your goals are for the assignment.

• Consider your purpose: do you need a rubric that addresses the standards for all the writing in the course? Or do you need to address the writing requirements and standards for just one assignment?  Task-specific rubrics are written to help teachers assess individual assignments or genres, whereas generic rubrics are written to help teachers assess multiple assignments.
• Begin by listing the important qualities of the writing that will be produced in response to a particular assignment. It may be helpful to have several examples of excellent versions of the assignment in front of you: what writing elements do they all have in common? Among other things, these may include features of the argument, such as a main claim or thesis; use and presentation of sources, including visuals; and formatting guidelines such as the requirement of a works cited.
• Then consider how the criteria will be weighted in grading. Perhaps all criteria are equally important, or perhaps there are two or three that all students must achieve to earn a passing grade. Decide what best fits the class and requirements of the assignment.

Consider involving students in Steps 2 and 3. A class session devoted to developing a rubric can provoke many important discussions about the ways the features of the language serve the purpose of the writing. And when students themselves work to describe the writing they are expected to produce, they are more likely to achieve it.

At this point, you will need to decide if you want to create a holistic or an analytic rubric. There is much debate about these two approaches to assessment.

Comparing Holistic and Analytic Rubrics

Holistic scoring .

Holistic scoring aims to rate overall proficiency in a given student writing sample. It is often used in large-scale writing program assessment and impromptu classroom writing for diagnostic purposes.

General tenets to holistic scoring:

• Responding to drafts is part of evaluation
• Responses do not focus on grammar and mechanics during drafting and there is little correction
• Marginal comments are kept to 2-3 per page with summative comments at end
• End commentary attends to students’ overall performance across learning objectives as articulated in the assignment
• Response language aims to foster students’ self-assessment

Holistic rubrics emphasize what students do well and generally increase efficiency; they may also be more valid because scoring includes authentic, personal reaction of the reader. But holistic sores won’t tell a student how they’ve progressed relative to previous assignments and may be rater-dependent, reducing reliability. (For a summary of advantages and disadvantages of holistic scoring, see Becker, 2011, p. 116.)

Here is an example of a partial holistic rubric:

Summary meets all the criteria. The writer understands the article thoroughly. The main points in the article appear in the summary with all main points proportionately developed. The summary should be as comprehensive as possible and should be as comprehensive as possible and should read smoothly, with appropriate transitions between ideas. Sentences should be clear, without vagueness or ambiguity and without grammatical or mechanical errors.

A complete holistic rubric for a research paper (authored by Jonah Willihnganz) can be  downloaded here.

Analytic Scoring

Analytic scoring makes explicit the contribution to the final grade of each element of writing. For example, an instructor may choose to give 30 points for an essay whose ideas are sufficiently complex, that marshals good reasons in support of a thesis, and whose argument is logical; and 20 points for well-constructed sentences and careful copy editing.

General tenets to analytic scoring:

• Reflect emphases in your teaching and communicate the learning goals for the course
• Emphasize student performance across criterion, which are established as central to the assignment in advance, usually on an assignment sheet
• Typically take a quantitative approach, providing a scaled set of points for each criterion
• Make the analytic framework available to students before they write  

Advantages of an analytic rubric include ease of training raters and improved reliability. Meanwhile, writers often can more easily diagnose the strengths and weaknesses of their work. But analytic rubrics can be time-consuming to produce, and raters may judge the writing holistically anyway. Moreover, many readers believe that writing traits cannot be separated. (For a summary of the advantages and disadvantages of analytic scoring, see Becker, 2011, p. 115.)

For example, a partial analytic rubric for a single trait, “addresses a significant issue”:

• Excellent: Elegantly establishes the current problem, why it matters, to whom
• Above Average: Identifies the problem; explains why it matters and to whom
• Competent: Describes topic but relevance unclear or cursory
• Developing: Unclear issue and relevance

A  complete analytic rubric for a research paper can be downloaded here.  In WIM courses, this language should be revised to name specific disciplinary conventions.

Whichever type of rubric you write, your goal is to avoid pushing students into prescriptive formulas and limiting thinking (e.g., “each paragraph has five sentences”). By carefully describing the writing you want to read, you give students a clear target, and, as Ed White puts it, “describe the ongoing work of the class” (75).

Writing rubrics contribute meaningfully to the teaching of writing. Think of them as a coaching aide. In class and in conferences, you can use the language of the rubric to help you move past generic statements about what makes good writing good to statements about what constitutes success on the assignment and in the genre or discourse community. The rubric articulates what you are asking students to produce on the page; once that work is accomplished, you can turn your attention to explaining how students can achieve it.

Works Cited

Becker, Anthony.  “Examining Rubrics Used to Measure Writing Performance in U.S. Intensive English Programs.”   The CATESOL Journal  22.1 (2010/2011):113-30. Web.

White, Edward M.  Teaching and Assessing Writing . Proquest Info and Learning, 1985. Print.

Further Resources

CCCC Committee on Assessment. “Writing Assessment: A Position Statement.” November 2006 (Revised March 2009). Conference on College Composition and Communication. Web.

Gallagher, Chris W. “Assess Locally, Validate Globally: Heuristics for Validating Local Writing Assessments.” Writing Program Administration 34.1 (2010): 10-32. Web.

Huot, Brian.  (Re)Articulating Writing Assessment for Teaching and Learning.  Logan: Utah State UP, 2002. Print.

Kelly-Reilly, Diane, and Peggy O’Neil, eds. Journal of Writing Assessment. Web.

McKee, Heidi A., and Dànielle Nicole DeVoss DeVoss, Eds. Digital Writing Assessment & Evaluation. Logan, UT: Computers and Composition Digital Press/Utah State University Press, 2013. Web.

O’Neill, Peggy, Cindy Moore, and Brian Huot.  A Guide to College Writing Assessment . Logan: Utah State UP, 2009. Print.

Sommers, Nancy.  Responding to Student Writers . Macmillan Higher Education, 2013.

Straub, Richard. “Responding, Really Responding to Other Students’ Writing.” The Subject is Writing: Essays by Teachers and Students. Ed. Wendy Bishop. Boynton/Cook, 1999. Web.

White, Edward M., and Cassie A. Wright.  Assigning, Responding, Evaluating: A Writing Teacher’s Guide . 5th ed. Bedford/St. Martin’s, 2015. Print.

• Quantum Research

Landmark IBM error correction paper published on the cover of Nature

Ibm has created a quantum error-correcting code about 10 times more efficient than prior methods — a milestone in quantum computing research..

27 Mar 2024

Rafi Letzter

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Today, the paper detailing those results was published as the cover story of the scientific journal Nature. 1

Last year, we demonstrated that quantum computers had entered the era of utility , where they are now capable of running quantum circuits better than classical computers can. Over the next few years, we expect to find speedups over classical computing and extract business value from these systems. But there are also algorithms with mathematically proven speedups over leading classical methods that require tuning quantum circuits with hundreds of millions, to billions, of gates. Expanding our quantum computing toolkit to include those algorithms requires us to find a way to compute that corrects the errors inherent to quantum systems — what we call quantum error correction.

Read how a paper from IBM and UC Berkeley shows a path toward useful quantum computing

Quantum error correction requires that we encode quantum information into more qubits than we would otherwise need. However, achieving quantum error correction in a scalable and fault-tolerant way has, to this point, been out of reach without considering scales of one million or more physical qubits. Our new result published today greatly reduces that overhead, and shows that error correction is within reach.

While quantum error correction theory dates back three decades, theoretical error correction techniques capable of running valuable quantum circuits on real hardware have been too impractical to deploy on quantum system. In our new paper, we introduce a new code, which we call the gross code , that overcomes that limitation.

This code is part of our broader strategy to bring useful quantum computing to the world.

While error correction is not a solved problem, this new code makes clear the path toward running quantum circuits with a billion gates or more on our superconducting transmon qubit hardware.

What is error correction?

Quantum information is fragile and susceptible to noise — environmental noise, noise from the control electronics, hardware imperfections, state preparation and measurement errors, and more. In order to run quantum circuits with millions to billions of gates, quantum error correction will be required.

Error correction works by building redundancy into quantum circuits. Many qubits work together to protect a piece of quantum information that a single qubit might lose to errors and noise.

On classical computers, the concept of redundancy is pretty straightforward. Classical error correction involves storing the same piece of information across multiple bits. Instead of storing a 1 as a 1 or a 0 as a 0, the computer might record 11111 or 00000. That way, if an error flips a minority of bits, the computer can treat 11001 as 1, or 10001 as 0. It’s fairly easy to build in more redundancy as needed to introduce finer error correction.

Things are more complicated on quantum computers. Quantum information cannot be copied and pasted like classical information, and the information stored in quantum bits is more complicated than classical data. And of course, qubits can decohere quickly, forgetting their stored information.

Research has shown that quantum fault tolerance is possible, and there are many error correcting schemes on the books. The most popular one is called the “surface code,” where qubits are arranged on a two-dimensional lattice and units of information are encoded into sub-units of the lattice.

But these schemes have problems.

First, they only work if the hardware’s error rates are better than some threshold determined by the specific scheme and the properties of the noise itself — and beating those thresholds can be a challenge.

Second, many of those schemes scale inefficiently — as you build larger quantum computers, the number of extra qubits needed for error correction far outpaces the number of qubits the code can store.

At practical code sizes where many errors can be corrected, the surface code uses hundreds of physical qubits per encoded qubit worth of quantum information, or more. So, while the surface code is useful for benchmarking and learning about error correction, it’s probably not the end of the story for fault-tolerant quantum computers.

Exploring “good” codes

The field of error correction buzzed with excitement in 2022 when Pavel Panteleev and Gleb Kalachev at Moscow State University published a landmark paper proving that there exist asymptotically good codes — codes where the number of extra qubits needed levels off as the quality of the code increases.

This has spurred a lot of new work in error correction, especially in the same family of codes that the surface code hails from, called quantum low-density parity check, or qLDPC codes. These qLDPC codes are quantum error correcting codes where the operations responsible for checking whether or not an error has occurred only have to act on a few qubits, and each qubit only has to participate in a few checks.

But this work was highly theoretical, focused on proving the possibility of this kind of error correction. It didn’t take into account the real constraints of building quantum computers. Most importantly, some qLDPC codes would require many qubits in a system to be physically linked to high numbers of other qubits. In practice, that would require quantum processors folded in on themselves in psychedelic hyper-dimensional origami, or entombed in wildly complex rats’ nests of wires.

In our paper, we looked for fault-tolerant quantum memory with a low qubit overhead, high error threshold, and a large code distance.

Bravyi, S., Cross, A., Gambetta, J., et al. High-threshold and low-overhead fault-tolerant quantum memory. Nature (2024). https://doi.org/10.1038/s41586-024-07107-7

In our Nature paper, we specifically looked for fault-tolerant quantum memory with a low qubit overhead, high error threshold, and a large code distance.

Let’s break that down:

Fault-tolerant: The circuits used to detect errors won't spread those errors around too badly in the process, and they can be corrected faster than they occur

Quantum memory: In this paper, we are only encoding and storing quantum information. We are not yet doing calculations on the encoded quantum information.

High error threshold: The higher the threshold, the higher amount of hardware errors the code will allow while still being fault tolerant. We were looking for a code that allowed us to operate the memory reliably at physical error rates as high as 0.001, so we wanted a threshold close to 1 percent.

Large code distance: Distance is the measure of how robust the code is — how many errors it takes to completely flip the value from 0 to 1 and vice versa. In the case of 00000 and 11111, the distance is 5. We wanted one with a large code distance that corrects more than just a couple errors. Large-distance codes can suppress noise by orders of magnitude even if the hardware quality is only marginally better than the code threshold. In contrast, codes with a small distance become useful only if the hardware quality is significantly better than the code threshold.

Low qubit overhead: Overhead is the number of extra qubits required for correcting errors. We want the number of qubits required to do error correction to be far less than we need for a surface code of the same quality, or distance.

We’re excited to report that our team’s mathematical analysis found concrete examples of qLDPC codes that met all of these required conditions. These fall into a family of codes called “Bivariate Bicycle (BB)” codes. And they are going to shape not only our research going forward, but how we architect physical quantum systems.

The gross code

While many qLDPC code families show great promise for advancing error correction theory, most aren’t necessarily pragmatic for real-world application. Our new codes lend themselves better to practical implementation because each qubit needs only to connect to six others, and the connections can be routed on just two layers.

To get an idea of how the qubits are connected, imagine they are put onto a square grid, like a piece of graph paper. Curl up this piece of graph paper so that it forms a tube, and connect the ends of the tube to make a donut. On this donut, each qubit is connected to its four neighbors and two qubits that are farther away on the surface of the donut. No more connections needed.

The good news is we don’t actually have to embed our qubits onto a donut to make these codes work — we can accomplish this by folding the surface differently and adding a few other long-range connectors to satisfy mathematical requirements of the code. It’s an engineering challenge, but much more feasible than a hyper-dimensional shape.

We explored some codes that have this architecture and focused on a particular [[144,12,12]] code. We call this code the gross code because 144 is a gross (or a dozen dozen). It requires 144 qubits to store data — but in our specific implementation, it also uses another 144 qubits to check for errors, so this instance of the code uses 288 qubits. It stores 12 logical qubits well enough that fewer than 12 errors can be detected. Thus: [[144,12,12]].

Using the gross code, you can protect 12 logical qubits for roughly a million cycles of error checks using 288 qubits. Doing roughly the same task with the surface code would require nearly 3,000 qubits.

This is a milestone. We are still looking for qLDPC codes with even more efficient architectures, and our research on performing error-corrected calculations using these codes is ongoing. But with this publication, the future of error correction looks bright.

Fig. 1 | Tanner graphs of surface and BB codes.

Fig. 1 | Tanner graphs of surface and BB codes. a, Tanner graph of a surface code, for comparison. b, Tanner graph of a BB code with parameters [[144, 12, 12]] embedded into a torus. Any edge of the Tanner graph connects a data and a check vertex. Data qubits associated with the registers q(L) and q(R) are shown by blue and orange circles. Each vertex has six incident edges including four short-range edges (pointing north, south, east and west) and two long-range edges. We only show a few long-range edges to avoid clutter. Dashed and solid edges indicate two planar subgraphs spanning the Tanner graph, see the Methods. c, Sketch of a Tanner graph extension for measuring Z ˉ \={Z} and X ˉ \={X} following ref. 50, attaching to a surface code. The ancilla corresponding to the X ˉ \={X} measurement can be connected to a surface code, enabling load-store operations for all logical qubits by means of quantum teleportation and some logical unitaries. This extended Tanner graph also has an implementation in a thickness-2 architecture through the A and B edges (Methods).

Fig. 2 | Syndrome measurement circuit.

Fig. 2 | Syndrome measurement circuit. Full cycle of syndrome measurements relying on seven layers of CNOTs. We provide a local view of the circuit that only includes one data qubit from each register q(L) and q(R) . The circuit is symmetric under horizontal and vertical shifts of the Tanner graph. Each data qubit is coupled by CNOTs with three X-check and three Z-check qubits: see the Methods for more details.

Why error correction matters

Today, our users benefit from novel error mitigation techniques — methods for reducing or eliminating the effect of noise when calculating observables, alongside our work suppressing errors at the hardware level. This work brought us into the era of quantum utility. IBM researchers and partners all over the world are exploring practical applications of quantum computing today with existing quantum systems. Error mitigation lets users begin looking for quantum advantage on real quantum hardware.

But error mitigation comes with its own overhead, requiring running the same executions repeatedly so that classical computers can use statistical methods to extract an accurate result. This limits the scale of the programs you can run, and increasing that scale requires tools beyond error mitigation — like error correction.

Last year, we debuted a new roadmap laying out our plan to continuously improve quantum computers over the next decade. This new paper is an important example of how we plan to continuously increasing the complexity (number of gates) of the quantum circuits that can be run on our hardware. It will allow us to transition from running circuits with 15,000 gates to 100 million, or even 1 billion gates.

Bravyi, S., Cross, A.W., Gambetta, J.M. et al. High-threshold and low-overhead fault-tolerant quantum memory. Nature 627, 778–782 (2024). https://doi.org/10.1038/s41586-024-07107-7

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