Pauli error estimation via Population Recovery

TL;DR

This paper introduces a simple, optimal algorithm for estimating Pauli error rates in quantum channels, using minimal resources and robust to certain measurement noise, with extensions for near-identity noise channels.

Contribution

The authors present a novel reduction to Population Recovery for Pauli error estimation, achieving optimal sample complexity with unentangled measurements and robustness to measurement failures.

Findings

Optimal sample complexity of O(1/ε^2 log(n/ε)) for Pauli error estimation.

Algorithm is robust to limited measurement noise with heralded failures.

Extended method achieves multiplicative precision for near-identity noise channels.

Abstract

Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the "Population Recovery" problem, we give an extremely simple algorithm that learns the Pauli error rates of an $n$-qubit channel to precision $\epsilon$ in $\ell_\infty$ using just $O(1/\epsilon^2) \log(n/\epsilon)$ applications of the channel. This is optimal up to the logarithmic factors. Our algorithm uses only unentangled state preparation and measurements, and the post-measurement classical runtime is just an $O(1/\epsilon)$ factor larger than the measurement data size. It is also impervious to a limited model of measurement noise where heralded measurement failures occur independently with probability $\le 1/4$. We then consider the case where the noise channel is close to the identity, meaning that the no-error outcome occurs with probability $1-\eta$. In the regime of small $\eta$ we extend our algorithm to achieve multiplicative precision $1 \pm \epsilon$ (i.e., additive precision $\epsilon \eta$) using just $O\bigl(\frac{1}{\epsilon^2 \eta}\bigr) \log(n/\epsilon)$ applications of the channel.