The learnability of Pauli noise

TL;DR

This paper precisely characterizes which aspects of Pauli noise on Clifford gates are learnable, demonstrating the optimality of cycle benchmarking and experimentally analyzing IBM's CNOT gate.

Contribution

It provides a mathematical framework distinguishing learnable and unlearnable noise information, and experimentally validates the limits of noise characterization on real quantum hardware.

Findings

Cycle benchmarking learns all learnable noise information.

Experimentally characterized IBM's CNOT noise up to 2 unlearnable degrees.

Lower bound on state preparation noise derived from data.

Abstract

Recently, several quantum benchmarking algorithms have been developed to characterize noisy quantum gates on today's quantum devices. A well-known issue in benchmarking is that not everything about quantum noise is learnable due to the existence of gauge freedom, leaving open the question of what information about noise is learnable and what is not, which has been unclear even for a single CNOT gate. Here we give a precise characterization of the learnability of Pauli noise channels attached to Clifford gates, showing that learnable information corresponds to the cycle space of the pattern transfer graph of the gate set, while unlearnable information corresponds to the cut space. This implies the optimality of cycle benchmarking, in the sense that it can learn all learnable information about Pauli noise. We experimentally demonstrate noise characterization of IBM's CNOT gate up to 2 unlearnable degrees of freedom, for which we obtain bounds using physical constraints. In addition, we give an attempt to characterize the unlearnable information by assuming perfect initial state preparation. However, based on the experimental data, we conclude that this assumption is inaccurate as it yields unphysical estimates, and we obtain a lower bound on state preparation noise.