A generalized cycle benchmarking algorithm for characterizing mid-circuit measurements

TL;DR

This paper introduces a cycle benchmarking algorithm tailored for characterizing noisy mid-circuit measurements in quantum computing, providing a systematic and learnable approach to understand measurement noise.

Contribution

The paper develops a Fourier-based cycle benchmarking algorithm for MCMs and establishes a theory of noise learnability, enabling comprehensive noise characterization.

Findings

The algorithm effectively estimates noise parameters in simulated quantum circuits.

It can test the independence of measurement noise from state preparation noise.

Numerical simulations demonstrate the practical applicability of the method.

Abstract

Mid-circuit measurements (MCMs) are crucial ingredients in the development of fault-tolerant quantum computation. While there have been rapid experimental progresses in realizing MCMs, a systematic method for characterizing noisy MCMs is still under exploration. In this work we develop a cycle benchmarking (CB)-type algorithm to characterize noisy MCMs. The key idea is to use a joint Fourier transform on the classical and quantum registers and then estimate parameters in the Fourier space, analogous to Pauli fidelities used in CB-type algorithms for characterizing the Pauli noise channel of Clifford gates. Furthermore, we develop a theory of the noise learnability of MCMs, which determines what information can be learned about the noise model (in the presence of state preparation and terminating measurement (SPAM) noise) and what cannot, which shows that all learnable information can be learned using our algorithm. As an application, we show how to use the learned information to test the independence between measurement noise and state preparation noise in an MCM. Finally, we conduct numerical simulations to illustrate the practical applicability of the algorithm. Similar to other CB-type algorithms, we expect the algorithm to provide a useful toolkit that is of experimental interest.