Randomized Benchmarking with Synthetic Quantum Circuits

TL;DR

This paper introduces a new framework for randomized benchmarking that uses synthetic quantum circuits and classical post-processing to improve efficiency, especially for high-dimensional quantum systems with symmetry.

Contribution

The authors develop a general approach to enhance randomized benchmarking using synthetic circuits, extending its applicability to systems with high symmetry and reducible representations.

Findings

Synthetic RB achieves over 100x sample efficiency improvement for high-spin systems.

The framework applies to any benchmarking group with reducible superoperator representations.

Demonstrated effectiveness for systems with rotational symmetry, such as SU(2).

Abstract

Noise characterization methods such as randomized benchmarking (RB) are critical for the development of scalable quantum computers. Modern RB protocols for multiqubit systems extract physically relevant error rates by exploiting the structure of the group representation generated by the set of benchmarked operations. However, existing techniques become prohibitively inefficient for representations that are highly reducible yet decompose into irreducible subspaces of high dimension. These situations prevail when benchmarking high-dimensional systems such as qudits or bosonic modes, where experimental control is limited to implementing a small subset of all possible unitary operations. We introduce a broad framework for enhancing the sample efficiency of RB that is sufficiently powerful to extend the practical reach of RB beyond the multiqubit setting. Our strategy, which applies to any benchmarking group, uses "synthetic" quantum circuits with classical post-processing of both input and output data to leverage the full structure of reducible superoperator representations. To demonstrate the efficacy of our approach, we develop a detailed theory of RB for systems with rotational symmetry. Such systems carry a natural action of the group $\text{SU}(2)$, and they form the basis for several novel quantum error-correcting codes. We show that, for measuring rotationally invariant error rates of experimentally accessible high-spin systems, our synthetic RB protocols offer a sample complexity advantage of more than two orders of magnitude relative to standard approaches such as character RB.