Fast Estimation of Sparse Quantum Noise
As quantum computers approach the fault tolerance threshold, diagnosing and
characterizing the noise on large scale quantum devices is increasingly
important. One of the most important classes of noise channels is the class of
Pauli channels, for reasons of both theoretical tractability and experimental
relevance. Here we present a practical algorithm for estimating the $s$ nonzero
Pauli error rates in an $s$-sparse, $n$-qubit Pauli noise channel, or more
generally the $s$ largest Pauli error rates. The algorithm comes with rigorous
recovery guarantees and uses only $O(n^2)$ measurements, $O(s n^2)$ classical
processing time, and Clifford quantum circuits. We experimentally validate a
heuristic version of the algorithm that uses simplified Clifford circuits on
data from an IBM 14-qubit superconducting device and our open source
implementation. These data show that accurate and precise estimation of the
probability of arbitrary-weight Pauli errors is possible even when the signal
is two orders of magnitude below the measurement noise floor.
Robin Harper Wenjun Yu Steven T. Flammia