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 {x_i}_{i=1}^k obtained from an experimental device, the (linear) cross-entropy benchmarking fidelity is defined as.

This means that if a quantum computer did generate those samples, then the quantum computer is too noisy and thus has no chance of performing beyond-classical computations. 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|0^n\rangle|2 . Crossing this point is known as achieving quantum supremacy; and after entering the quantum supremacy regime, XEB can only be estimated.

For Cross-entropy benchmarking, the abstraction is narrower than the article's general subject matter: a positive case must preserve Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments. Retaining only the name, a familiar example, or a downstream effect is insufficient. The specialist roles and tests remain anchored in quantum benchmarking, which is why this identity is domain-specific rather than prime.

How would you explain it like I'm…

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.

Structural Signature¶

Sig role-phrases:

Defining carrier — The Sycamore processor was the first to demonstrate quantum supremacy via XEB.
Constitutive relation — 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.
Operating condition — 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.
Recognition evidence — 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|0^n\rangle|2 .
Admissible variation — Given k samples {x_i}_{i=1}^k obtained from an experimental device, the (linear) cross-entropy benchmarking fidelity is defined as.
Characteristic consequence — 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.
Failure boundary — If F_{XEB} = 1 , the samples were collected from a noiseless quantum computer.

What It Is Not¶

Not the whole field of quantum benchmarking. The node requires the specific identity stated by Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments.
Not an over-broad reading. 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|0^n\rangle|2 .
Not an over-broad reading. Given k samples {x_i}_{i=1}^k obtained from an experimental device, the (linear) cross-entropy benchmarking fidelity is defined as.
Not an over-broad reading. 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.
Not automatically Randomized Benchmarking. Retrieval proximity does not establish equivalence; the two identities must be compared by carrier, operation, and failure boundary.

Scope of Application¶

Cross-entropy benchmarking applies literally inside quantum benchmarking wherever the source-defined carrier and relation can be established. Its documented habitats include:

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|0^n\rangle|2 .
Definition. Given k samples {x_i}_{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.
Interpretation. If F_{XEB} = 1 , the samples were collected from a noiseless quantum computer.

Outside quantum benchmarking, the name should be retained only when these same operational conditions survive; otherwise the comparison belongs to the broader parent Pattern or should be marked as analogy.

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. The strongest recognition evidence in the frozen account is: 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|0^n\rangle|2 . A report should distinguish that evidence from a proxy, consequence, or common implementation. It should also state the qualification 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|0^n\rangle|2 . so that a reader can reproduce the classification rather than infer it from topical resemblance.

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 0^{{n}|C|x_{i}\rangle|}\right) - 1. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit. It is lossy by design: local history and implementation details may be omitted only when they do not alter the defining relation.

Abstract Reasoning¶

Type the carrier. Identify the quantum benchmarking entities to which the claim applies.
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.
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.
Demand recognition evidence. 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|0^n\rangle|2 .
Test variation. Change an implementation or setting while preserving given k samples {x_i}_{i=1}^k obtained from an experimental device, the (linear) cross-entropy benchmarking fidelity is defined as.
Run the collapse test. Remove the defining operation; if the label still seems equally apt, only a topic or correlate was retained.
Reduce cautiously. When the specialist conditions cannot be carried, route the residual comparison to Pattern.

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. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Examples¶

Canonical¶

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|0^n\rangle|2 . This case is canonical because it supplies a concrete carrier and lets the defining relation be checked rather than merely named.

Mapped back: carrier → the entities in the documented case; operation → Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments; recognition evidence → 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|0^n\rangle|2

Applied / In Practice¶

Given k samples {x_i}_{i=1}^k obtained from an experimental device, the (linear) cross-entropy benchmarking fidelity is defined as. The applied case shows how the identity is used under a second setting or qualification while keeping the same operative relation.

Mapped back: changed setting → Definition; invariant → Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments; boundary → the case exits the class when 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|0^n\rangle|2

Structural Tensions¶

T1 — Stable identity versus admissible variation. 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|0^n\rangle|2 . The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Which changes preserve the defining relation, and which replace it?

T2 — Recognition versus proxy. Given k samples {x_i}_{i=1}^k obtained from an experimental device, the (linear) cross-entropy benchmarking fidelity is defined as. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the cited evidence establish the identity or only a correlated sign?

T3 — Definition versus implementation. 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. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Is the observed implementation constitutive, optional, or merely common?

T4 — Scope versus overextension. If F_{XEB} = 1 , the samples were collected from a noiseless quantum computer. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Can every claimed application fill the same typed roles without metaphor?

T5 — Transfer versus domain accent. The Sycamore processor was the first to demonstrate quantum supremacy via XEB. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the receiving case instantiate Cross-entropy benchmarking literally, co-instantiate Pattern, or only resemble it?

T6 — Autonomy versus reduction. 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. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: What does Cross-entropy benchmarking distinguish that the broader parent Pattern leaves together?

Structural–Framed Character¶

Cross-entropy benchmarking is mixed or framed-leaning. Its structural side is the repeatable organization summarized by Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments. Its framed side is the quantum benchmarking vocabulary that fixes the carrier, evidence, exceptions, and admissible transformations.

Evaluative weight: the identity can be stated descriptively even when applications carry practical stakes. Human-practice dependence: the source-grounded carrier determines whether the relation exists independently or is constituted by a practice. Institutional origin: disciplinary conventions stabilize the name and test. Vocabulary portability: 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. Import versus recognition: literal transfer requires the same mechanism; shape alone is analogy.

Its portable skeleton is Pattern. Its character: a recurring specialist identity whose thin organization can be abstracted, while its operational meaning remains domain-bound.

Structural Core vs. Domain Accent¶

What is skeletal. Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments. The stable skeleton is the typed relation expressed in that definition and the entry's recognition and collapse tests. The source identifies these operative conditions: The Sycamore processor was the first to demonstrate quantum supremacy via XEB. 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. It further constrains recognition and variation through: 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. 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|0^n\rangle|2 .

What is domain-bound. quantum benchmarking supplies the operative entities, technical vocabulary, warrants, and exceptions that make Cross-entropy benchmarking literal. Its documented scope includes the condition that Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments. Another bounded application condition is that It quantifies how strongly experimental samples correlate with the ideal output distribution and has been used in demonstrations of quantum supremacy. These are not decorative examples; they determine which carrier and evidence can fill the abstraction's roles.

Why no parent is asserted. Removing those specialist details does not currently yield one live catalog node that is a necessary genus for every instance. The entry is therefore approved as unparented rather than attached by topical resemblance. Its collapse evidence remains specific—Given k samples {xi}{i=1}^k obtained from an experimental device, the (linear) cross-entropy benchmarking fidelity is defined as.—and future graph densification may discover a defensible relation only if it preserves that boundary.

This entry is a kind of Performance Measure.

Approved unparented node. No current live node supplies a defensible necessary genus or structural prerequisite for Cross-entropy benchmarking. The reviewed identity is: Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments. The accelerated suggestion was declined because topical or lexical similarity does not establish hierarchy; the node is admitted without a parent pending later graph densification.
Related reasoning operations. Evidence, representation, comparison, classification, transformation, or evaluation may participate in particular cases, but participation does not make any one of them a necessary parent of every instance.

Relationships to Other Abstractions¶

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

Cross-entropy benchmarking → Performance Measure → Measurement

Neighborhood in Abstraction Space¶

Cross-entropy benchmarking sits in a sparse region of the domain-specific corpus (79^th 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

Quantum Interactive Polynomial Time (QIP) — 0.83
NOON State — 0.83
Quantum Random-Access Code — 0.82
Linear optical quantum computing — 0.82
Quantum Byzantine Agreement — 0.82

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

Not to Be Confused With¶

Pattern. The parent omits the specialist differentia. Tell: Can the case establish Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments?
Randomized Benchmarking. A scalable quantum-control characterization protocol that estimates an average gate-error parameter from survival-probability decay across random, length-varying gate sequences followed by a recovery operation. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Algorithmic qubits. A vendor-introduced quantum-computer benchmark reporting the largest circuit width whose implementation passes a suite of application-oriented algorithm tests under specified fidelity thresholds. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Counterfactual quantum computation. A quantum protocol that infers a computational outcome from an interference branch in which the outcome-producing device did not run. Tell: Which entry's carrier, operation, and failure condition are satisfied?
A measurement, proxy, or consequence. Those may provide evidence without being the identity. Tell: Would Cross-entropy benchmarking remain present if the detector or downstream effect changed?
A metaphorical analogue. A similar shape outside quantum benchmarking lacks the specialist mechanism. Tell: Do the native roles transfer literally, or only the parent Pattern?

References¶

Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Cross-entropy_benchmarking (revision 1331179033).

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.