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Cross-entropy benchmarking

Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments.

Version
v1 · 2026-09-28 · History
Domain-specific #
8789
Domain group
Natural Sciences
Origin domain
Physics
Subdomains
Quantum Benchmarking, Quantum Computing → Physics

Core Idea

Cross-entropy benchmarking is treated here as the recurring quantum benchmarking identity summarized by this source-grounded definition: Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments. Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments. It quantifies how strongly experimental samples correlate with the ideal output distribution and has been used in demonstrations of quantum supremacy. Given k samples {xi}{i=1}^k obtained from an experimental device, the (linear) cross-entropy benchmarking fidelity is defined as.

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Did It Pick the Likely Ones?

Scientists build special quantum computers and give them puzzles that make random-looking answers, where a perfect machine would give some answers more often than others. Cross-entropy benchmarking checks the machine's answers: if it keeps landing on the answers a perfect machine favors, it's working well. If its answers look like plain guessing, it's too noisy.

Scoring a Quantum Computer's Picks

A quantum computer can run a random circuit, a jumbled set of steps, and then give out strings of 0s and 1s. For each circuit, a perfect quantum computer would produce some strings more often than others. Cross-entropy benchmarking collects the machine's real outputs and checks whether they tend to be the strings the perfect version would make more often. A high score means the machine matches the ideal well; a score like pure random guessing means it is too noisy to beat ordinary computers. It has been used in experiments claiming quantum supremacy, where a quantum computer does something ordinary computers can't practically do.

Random-Circuit Sampling Fidelity

Cross-entropy benchmarking (XEB) is a statistical measure for judging how well a quantum computer performs in random circuit sampling experiments. A random quantum circuit C is applied to all qubits starting at zero, and the ideal probability of each output bitstring x is P(x) = |<x|C|0^n>|^2. The device is run to collect k sample bitstrings. XEB measures how strongly those experimental samples correlate with the ideal output distribution: if the samples tend to be bitstrings with high ideal probability, the score is high. If the samples look like uniform random guessing, the device is too noisy to do anything beyond what classical computers can. XEB has been used in quantum supremacy demonstrations. A catch: computing the ideal probabilities needs classical simulation, so once a device is in the regime classical computers can't simulate, XEB can only be estimated, not computed exactly.

 

Cross-entropy benchmarking (XEB) is a statistical measure of performance in random circuit sampling experiments. For an n-qubit circuit C applied to the all-zeros input, the ideal output probability of bitstring x is P(x) = |<x|C|0^n>|^2. Given k samples x_1, ..., x_k from the experimental device, the linear XEB fidelity is computed from the ideal probabilities of the observed samples, normalized so that samples from a uniform, fully noisy source give a value of zero and ideal sampling gives a positive value. It therefore quantifies how strongly the device's samples correlate with the ideal output distribution. A device whose samples score like the uniform distribution is too noisy to perform beyond-classical computation. XEB has been used as the headline metric in quantum supremacy demonstrations. Because evaluating P(x) requires classical simulation, once the experiment enters the regime where that simulation is infeasible, XEB can no longer be computed directly and can only be estimated.

Scope of Application

  • Documented setting. Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments.

  • Documented setting. It quantifies how strongly experimental samples correlate with the ideal output distribution and has been used in demonstrations of quantum supremacy.

  • Definition. The output probability for bitstrings x\in{0,1}^n for C acting on all 0 input 0^n is P(x)=|\langle x|C|0n\rangle|2 .

  • Definition. Given k samples {xi}{i=1}^k obtained from an experimental device, the (linear) cross-entropy benchmarking fidelity is defined as.

  • Definition. F{\rm XEB}= 2^{n} \langle P(x{i}) \rangle{k} - 1 = \frac{2^{n}}{k} \left(\sum{i=1}^{k}|\langle 0{n}|C|x{i}\rangle|\right) - 1.

Clarity

A clear use of Cross-entropy benchmarking names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments.

Manages Complexity

Cross-entropy benchmarking compresses multiple quantum benchmarking details into a stable diagnostic relation. The source shows both the central mechanism—generating samples took 200 seconds on the quantum processor when it would have taken 10,000 years on Summit at the time of the experiment.—and the practical consequence—f{\rm XEB}= 2^{n} \langle P(x{i}) \rangle{k} - 1 = \frac{2^{n}}{k} \left(\sum{i=1}^{k}|\langle.

Abstract Reasoning

  1. Type the carrier. Identify the quantum benchmarking entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments.
  3. Check operation and conditions. As of 2021, the latest demonstration of quantum supremacy by Zuchongzhi 2.1 with n = 60 , 24 cycles and an XEB of 0.000366 holds.
  4. Demand recognition evidence.

Knowledge Transfer

Within the home domain. Knowledge about Cross-entropy benchmarking transfers literally when a new case preserves the same carrier type, relation, and recognition test. Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments. It quantifies how strongly experimental samples correlate with the ideal output distribution and has been used in demonstrations of quantum supremacy. Beyond the home domain. No canonical parent is asserted for Cross-entropy benchmarking.

Relationships to Other Abstractions

Local relationship map for Cross-entropy benchmarkingParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Cross-entropybenchmarkingDOMAINDomain-specific abstraction: Performance Measure — is a kind ofPerformanceMeasureDOMAIN

Current abstraction Cross-entropy benchmarking Domain-specific

Parents (1) — more general patterns this builds on

  • Cross-entropy benchmarking is a kind of Performance Measure Domain-specific

    Cross-entropy benchmarking satisfies the defining boundary of Performance Measure: A performance measure is a formally defined quantity that maps observations from a specified system, task, operating regime, and evaluation procedure to a value interpreted as effectiveness, quality, reliability, capacity, accuracy, efficiency, or another declared performance dimension.

Hierarchy path (1) — routes to 1 parentless root

Neighborhood in Abstraction Space

Cross-entropy benchmarking sits in a sparse region of the domain-specific corpus (79th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Quantum States & Information Measures (25 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08