Random-circuit sampling is a carefully chosen benchmark. What is sampled mathematically, how is quality assessed, and what can the result be used for?
From a circuit to a probability distribution
Start with 61 qubits in |0…0⟩. A fixed circuit U mixes them with randomly selected single-qubit gates and CZ gates between neighbors. We measure all qubits at the end. For a bitstring x, ideal quantum theory predicts pU(x) = |⟨x|U|0…0⟩|2. The circuit stays fixed across shots; individual outcomes are random draws from that one distribution.
There are 261, about 2.3 × 1018, possible 61-bit strings. A million shots touch only a tiny fraction. A uniform classical generator would also yield almost entirely distinct strings. The task is not to produce arbitrary zeros and ones; it is to sample according to the circuit-dependent probabilities.
Why do those probabilities become difficult?
A single-qubit gate changes local amplitudes. CZ gates couple neighboring qubits, spreading interference and entanglement as depth grows. Randomly chosen gates usually prevent the output from being described as a simple pattern of independent bits. In a sufficiently chaotic regime, the rescaled ideal probabilities z = 2npU(x) approach a broad Porter–Thomas distribution: most outcomes are unlikely while a few are much more likely. That describes the ideal distribution, not something one can read from the number of ones in a measured string.
How do we test whether the processor followed the circuit?
When ideal probabilities can be calculated, linear XEB is useful: FXEB = 2n(1/M) Σi pU(xi) − 1. Uniform samples have expected score zero; an ideal, sufficiently anticoncentrating circuit scores near one. The Nighthawk paper further divides each patch score by the ideal XEB of that same patch circuit. This avoids misreading a patch that has not yet fully anticoncentrated.
For the full 61-qubit circuit, the required ideal probabilities are too costly to score all million outcomes directly. The paper therefore uses smaller patches and reversible mirror circuits as two distinct quality checks. XEB remains a score or proxy: a high score alone does not certify small total-variation distance from the ideal distribution. Our repeated hardware job did not include that additional patch-and-mirror series, leaving its global fidelity open.
What is RCS useful for?
| Use | What RCS provides | Limit |
|---|---|---|
| Processor benchmarking | Test how many qubits, CZ layers and circuit cycles can run together with a measurable signal. | A benchmark score is not an application result. |
| Hardware and compiler improvement | Compare physical layouts, calibration windows, transpilers and mitigation methods on frozen circuits. | Use the same circuits, shots and quality metric. |
| Testing classical methods | A released circuit family lets tensor networks, MPS and other samplers compete on a concrete task. | Runtime comparisons need the same required output quality. |
| Quantum-dynamics research | Random circuits provide a controlled probe of information spreading, entanglement and noise. | The Nighthawk circuit does not automatically model a material or chemical reaction. |
What is it not yet?
An RCS bitstring is usually not the answer to an optimization problem, a molecular energy, or proof that a quantum computer speeds up useful machine-learning tasks. Its direct application is measuring how well a quantum processor executes difficult, checkable circuits. Those measurements can guide better hardware and verification methods; a practical algorithm must then be tested on its own task.
Further reading: Sedrakyan et al. on Nighthawk and Boixo et al. on RCS and XEB.
Project overview and article source
Edukaizen · 25 september 2026 / 25 September 2026