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 ϵ in ℓ∞ using just O(1/ϵ2)log⁡(n/ϵ) 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/ϵ) 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−η. In the regime of small η we extend our algorithm to achieve multiplicative precision 1±ϵ (i.e., additive precision ϵη) using just O(1ϵ2η)log⁡(n/ϵ) applications of the channel.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 23, 2021
- Source ID
- 10.22331/q-2021-09-23-549
Entities
People
- Ryan O'donnell
- Steven T. Flammia
Organizations
- Army Research Office
- California Institute of Technology
- Carnegie Mellon University
- National Science Foundation