Pauli error estimation via Population Recovery

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 l(infinity) 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 < 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 +/- epsilon (i.e., additive precision eta) using just O(1/epsilon(2)eta ) log(n/epsilon) applications of the channel.

Automated summary

This study focuses on learning a Pauli channel or the Pauli error rates of an arbitrary channel, and proposes a simple algorithm using unentangled state preparation and measurements. The algorithm is impervious to limited model of measurement noise, and can achieve higher precision when the noise channel is close to the identity matrix.