Short answer: The linear cross-entropy benchmark (XEB) compares a quantum chip's sampled outputs with ideal simulated probabilities, and is used to estimate circuit fidelity and to certify quantum advantage claims. Recent papers show its limits and extensions. A 2024 paper finds a fast classical algorithm that reaches 5 to 12 percent of the XEB values from state-of-the-art experiments, showing high XEB alone does not prove faithful simulation. Other 2023 and 2025 papers propose scalable variants. This is about how to read a benchmark, not about any single processor.
What XEB is for
A 2025 paper in a research journal calls cross-entropy benchmarking a central technique for certifying a quantum chip. A 2023 Physical Review A paper says linear XEB has been used extensively for systems of 50 or more qubits, but is fundamentally limited in scale because classical simulation needs exponentially large computational resources.
Where XEB can mislead
The 2024 PRX Quantum paper examines the idea that quantum advantage can be certified with linear XEB. In a benign setting, assuming an honest implementation of a noisy circuit, the authors characterise the conditions under which XEB approximates the fidelity of the quantum dynamics. In an adversarial setting, where all possible classical algorithms count, they show that relatively high XEB values do not imply faithful simulation of quantum dynamics. They present an efficient classical algorithm that reaches XEB values of 5 to 12 percent of those in state-of-the-art experiments within a few seconds on a single GPU machine, by identifying and exploiting several vulnerabilities of the XEB so that no full circuit simulation is needed. The abstract says the algorithm scales better with system size than a noisy quantum device for commonly studied random circuits.
A scalable variant
The 2023 paper proposes Clifford XEB, running linear XEB with random Clifford circuits of constant to logarithmic depth. Clifford circuits can be simulated in polynomial time, so the scheme can scale to much larger systems. In noisy numerical simulations the authors observe exponential decays whose rates correlate with the noise per cycle when errors accumulate multiplicatively, meaning the fidelities of individual gates multiply. They simulate systems of up to 1225 qubits, where the classical processing is easily handled by a workstation.
Generalising with ergodicity
The 2025 paper introduces generalised cross-entropy benchmarking based on ergodicity in random circuit sampling. It notes that Haar random circuits satisfy an ergodicity condition, in which the average of certain post-processing functions over output bit strings is close to the average over the unitary ensemble. For noiseless circuits this holds for polynomials with positive coefficients when the circuits form a unitary 2t-design, and for strong enough noise the condition is violated. The authors formulate the deviation of ergodicity as a benchmarking measure and show it can estimate circuit fidelity for global depolarising noise and weakly correlated noise. For a quadratic post-processing function, their framework recovers Google's result on estimating circuit fidelity through linear cross-entropy benchmarking.
What this does not tell you
These papers examine the benchmark rather than any one device, and the classical algorithm result is about XEB values, not a full simulation of a given experiment. Simulated noise models in the Clifford XEB study may not match hardware.
FAQ
What does XEB measure?
How well sampled outputs match ideal probabilities, used to estimate circuit fidelity.
Can a high XEB be reached classically?
A 2024 paper reaches 5 to 12 percent of experimental XEB values quickly on one GPU machine.
Why use Clifford circuits?
They can be simulated in polynomial time, so the benchmark scales to larger systems.
What did the ergodicity paper add?
A generalised measure for estimating fidelity under certain noise models.
Is XEB alone proof of advantage?
The 2024 paper argues high XEB does not by itself imply faithful simulation.
All field notes