Pauli error estimation via Population Recovery

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 $O\left(\frac{1}{{\epsilon }^2\eta }\right)\log (n/\epsilon )$ applications of the channel.

19 pages. v1: Preliminary version in TQC 2021. v2: Journal version with some additional references and background on Pauli channel estimation. Source code available at https://github.com/sflammia/PauliPopRec

References in corpus (2)

• Entanglement-Free Parameter Estimation of Generalized Pauli Channels
• Efficient average-case population recovery in the presence of insertions and deletions

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• Efficient self-consistent learning of gate set Pauli noise
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• Optimizing Circuit Reusing and its Application in Randomized Benchmarking
• On the Fundamental Resource for Exponential Advantage in Quantum Channel Learning