An ideal, noiseless random circuit doesn't spread its output evenly over all bitstrings — quantum interference makes some outcomes noticeably more likely than a uniform guess and others less so, producing a jagged "speckled" probability distribution (the pale bars, fixed once you pick a circuit). A real, noisy processor's output relaxes toward a flat, uniform distribution as errors accumulate — the more noise, the flatter the measured histogram (the solid bars, which fill in shot by shot).
Cross-entropy benchmarking never asks "was this one outcome correct?" — that question isn't well posed for a random circuit. Instead it scores the whole distribution at once:
F_XEB = ⟨ D · p_ideal(x_measured) ⟩ − 1
Every measured shot contributes D·p_ideal(x) for the bitstring x it landed on, averaged over all shots so far. A speckled Porter–Thomas distribution has the property that this average works out to ≈2 when sampled from the ideal circuit itself (giving F_XEB → 1) and to exactly 1 when sampled uniformly at random (giving F_XEB → 0) — so the single running average tracks the injected fidelity directly, with no single shot ever individually "checked".
- Qubits — sets the outcome space size D = 2ⁿ; more qubits, more bars, sparser sampling.
- New circuit — redraws the fixed ideal "speckled" distribution (a fresh Porter–Thomas pattern), as if compiling a new random circuit.
- Noise level — the injected true fidelity is 1 − noise; each shot is drawn from a mixture of the ideal distribution and the uniform one in that ratio, mimicking a depolarizing channel.
- Shots / frame — how many simulated circuit executions run each animation frame; more shots converge the XEB estimate faster.
This is exactly the logic used to validate real superconducting and photonic quantum processors: run the same random circuit thousands of times, compare the empirical outcome frequencies against the classically-precomputed ideal distribution, and read the gap as a single fidelity number — no ground truth per shot required.