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Randomized Mirror Circuits

System-level

Sandia's scalable whole-processor test that runs self-inverting random circuits across the width × depth plane and maps where a device still returns the right bitstring.

Measures
Average polarization P = (S − 1/2^w)/(1 − 1/2^w) of mirror circuits at each width w and depth d, mapped as volumetric capability regions
Introduced by
Proctor, Rudinger, Young, Nielsen & Blume-Kohout (Sandia) (2020)
Also known as
Mirror circuit benchmarks, Mirror circuits, Mirrored circuits average polarization, Periodic mirror circuits

Randomized mirror circuits are the Sandia Quantum Performance Lab’s scalable whole-processor benchmark, introduced by Proctor, Rudinger, Young, Nielsen and Blume-Kohout in 2020 and published as Nature Physics 18, 75 (2022). They attack the scaling wall of Quantum Volume-style tests (verifying a generic random circuit’s output requires classical simulation) by making every test circuit undo itself, so the ideal output is a known bitstring at any size.

How it works

Each mirror circuit is a random circuit followed by a uniformly random Pauli layer and then the first half’s layer-by-layer quasi-inverse, all wrapped in random single-qubit Clifford layers. Its ideal output is a specific, efficiently computed bitstring. At each shape (width w, depth d) an ensemble of circuits is run, and the probability S of observing the ideal bitstring is rescaled to the polarization P = (S − 1/2^w)/(1 − 1/2^w), which sets random guessing to zero. Average polarization is then mapped over the width × depth plane as capability regions in the volumetric benchmarking framework. Alongside the randomized ensembles, structured “periodic” mirror circuits probe more orderly, algorithm-like programs.

Strengths and limitations

Because no classical simulation is needed, the benchmark scales to any width, and running full-width layers makes the score reflect crosstalk and contextual errors rather than isolated gate specs. The flagship demonstration on twelve IBM and Rigetti processors found structured periodic circuits failing at sizes up to an order of magnitude smaller than random ones, so capability regions depend on the ensemble sampled, and random-circuit results alone can overstate practical capability. Polarization is a rescaled success probability, not a fidelity, and can be zero or negative under coherent errors. The name also needs care: mirror RB is a separate RB-style protocol spun out of this construction, and Quantinuum’s mirror benchmarking is an independently developed relative.

Notable results

NPL’s February 2025 metrics review standardizes the benchmark as metric M4.2, “mirrored circuits average polarization”, with an implementation in QCMet. Sandia’s pyGSTi ships mirror-circuit benchmarking modules, including 2025 mirror circuit fidelity estimation, and 2025 follow-on featuremetric benchmarking builds directly on the construction.

Key papers

Reference implementations

  • Mirror randomized benchmarking : Scalable RB variant built from mirror circuits (motion-reversal sequences with random Pauli layers) that avoids compiling expensive inversion gates and extends layer-error estimates to many-qubit widths.
  • Mirror Benchmarking : Quantinuum's system-level benchmark that fits the exponential decay of mirrored random circuits' survival probability, with a decay rate that also gauges how coherent the noise is.
  • Volumetric benchmarking : Sandia framework that generalizes Quantum Volume from square circuits to the full width × depth plane, mapping the frontier of circuit shapes a device can execute.
  • Quantum Volume : Single-number, full-system benchmark that scores a device by the largest random square circuit it can run while still generating heavy outputs reliably.