Cross-Entropy Benchmarking
Cross-entropy benchmarking scores how well a device's random-circuit outputs match ideal probabilities, the basis of early quantum-advantage claims.
The idea
Cross-entropy benchmarking (XEB) evaluates a processor by running random quantum circuits and comparing the bitstrings it produces against the probabilities an ideal circuit would give. A perfect device samples the correct, spiky output distribution; a fully noisy device samples uniformly. The cross-entropy fidelity measures where a real device falls between these extremes.
Porter-Thomas and heavy outputs
A random circuit produces an output distribution with a characteristic Porter-Thomas shape: a few bitstrings are far more likely than average. A working quantum computer preferentially returns these high-probability strings; noise flattens the preference. XEB quantifies this by summing the ideal probabilities of the strings the device actually output, normalized so 1 is ideal and 0 is fully depolarized.
Quantum advantage
- The 2019 Sycamore experiment used XEB on random circuits to claim advantage
- The task is sampling random circuits, chosen because it is hard to simulate classically
- XEB fidelity near a percent on 53 qubits still beat classical simulation at the time
Strengths and criticisms
XEB scales to larger systems than tomography and gives a clean per-circuit fidelity, and the product of individual gate fidelities predicts the whole-circuit XEB well, making it a useful hardware check. Criticisms are that verifying XEB requires classical simulation of the ideal circuit, which becomes infeasible exactly where advantage is claimed, and that improved classical algorithms have repeatedly narrowed the gap. The task itself has no practical use beyond the demonstration.
XEB remains a standard tool for characterizing large random-circuit performance, while application benchmarks address the separate question of usefulness.