Quantum advantages for Pauli channel estimation

TL;DR

This paper demonstrates that entangled measurements significantly reduce the number of samples needed to estimate Pauli channels in quantum computing, showing exponential advantages over traditional methods.

Contribution

It introduces an entangled measurement protocol that exponentially outperforms ancilla-free methods for Pauli channel estimation, with tight bounds and practical benchmarking applications.

Findings

Entangled measurements achieve exponential sample complexity reduction.

Ancilla-assisted protocol requires only O(n/ε²) samples, versus exponential rounds without ancillas.

Practical noise-resilient benchmarking benefits from the proposed estimation method.

Abstract

We show that entangled measurements provide an exponential advantage in sample complexity for Pauli channel estimation, which is both a fundamental problem and a practically important subroutine for benchmarking near-term quantum devices. The specific task we consider is to simultaneously learn all the eigenvalues of an $n$-qubit Pauli channel to $\pm\varepsilon$ precision. We give an estimation protocol with an $n$-qubit ancilla that succeeds with high probability using only $O(n/\varepsilon^{2})$ copies of the Pauli channel, while prove that any ancilla-free protocol (possibly with adaptive control and channel concatenation) would need at least $\Omega(2^{n/3})$ rounds of measurement. We further study the advantages provided by a small number of ancillas. For the case that a $k$-qubit ancilla ($k\le n$) is available, we obtain a sample complexity lower bound of $\Omega(2^{(n-k)/3})$ for any non-concatenating protocol, and a stronger lower bound of $\Omega(n2^{n-k})$ for any non-adaptive, non-concatenating protocol, which is shown to be tight. We also show how to apply the ancilla-assisted estimation protocol to a practical quantum benchmarking task in a noise-resilient and sample-efficient manner, given reasonable noise assumptions. Our results provide a practically-interesting example for quantum advantages in learning and also bring new insight for quantum benchmarking.