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Mirror randomized benchmarking

Component-level

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.

Measures
Average infidelity of a many-qubit layer of native Clifford gates, from the effective-polarization decay of mirror circuits
Introduced by
Proctor, Seritan & colleagues (Sandia) (2021)
Also known as
MRB, Mirror RB

Mirror randomized benchmarking (mirror RB) makes randomized benchmarking scalable by building its random sequences as mirror circuits: each circuit runs a sequence of random layers and then retraces it in reverse, so no large multi-qubit inversion ever has to be compiled. Introduced by Proctor and colleagues at Sandia (posted 2021, published in PRL in 2022), it extends RB-style error-per-layer estimates far beyond the widths where standard or direct RB are feasible.

How it works

A mirror RB circuit applies random layers of native Clifford gates for half its depth, then the inverse of each layer in reverse order, with layers of uniformly random Pauli gates interleaved throughout (as in randomized compiling) and random single-qubit gates at the start and end. Ideally the circuit maps its input to one known target bit string. Rather than raw success probability, the effective polarization (a Hamming-distance-weighted statistic that discounts outcomes that land near the target by luck) summarizes each circuit’s results, and a fit of its decay against benchmark depth estimates the average infidelity of a random layer. The interleaved Pauli layers twirl the noise so the decay is a reliable single exponential.

Strengths and limitations

Mirror circuits are trivially invertible, so circuits are cheap to generate at any width: the introducing paper validated the method in simulations of up to 225 qubits and ran it on up to 16 qubits of a cloud device, where comparison against few-qubit results revealed substantial crosstalk error. The caveats: the error per layer is defined relative to the chosen layer-sampling distribution, and the standard protocol covers Clifford layer sets. Because the second half mirrors the first, motion reversal could in principle echo away coherent errors; the random Pauli layers are designed to scramble such cancellations, and binary RB later removed the mirror structure altogether.

Naming note: this component-level protocol is distinct from randomized mirror circuits as used in Sandia’s full-device capability benchmarks (Nature Physics, 2022), and from Quantinuum’s mirror benchmarking, a related but separate protocol.

Key papers

Reference implementations

  • Randomized Benchmarking : Estimates average gate error from the exponential decay of survival probability over increasingly long random Clifford sequences, robust to state-preparation and measurement errors.
  • Direct randomized benchmarking : Benchmarks random layers of native gates directly instead of compiled multi-qubit Cliffords, measuring gates as they are actually used and scaling well beyond standard RB.
  • Randomized Mirror Circuits : 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.
  • 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.