Dear quanta,
At 11am we'll have a group meeting (6-310) and Annie will talk about
quantum walks.
At 1:30pm we'll have Steve Flammia (Sydney) speak in the seminar (6C-442).
title: Efficient learning of Pauli channels
abstract: Pauli channels are ubiquitous in quantum information, both as a
dominant noise source in many computing architectures and as a practical
model for analyzing error correction and fault tolerance. Here we prove
several results on efficiently learning Pauli channels, and more generally
the Pauli projection of a quantum channel. We first derive a protocol for
learning a Pauli channel on n qubits with high probability to a relative
precision ε using O(ε^{−2} n 2^n) measurements, which is efficient in the
Hilbert space dimension. The estimate is robust to state preparation and
measurement errors which, together with the relative precision, makes it
especially appropriate for applications involving characterization of
high-accuracy quantum gates. Next we show that the error rates for an
s-sparse Pauli channel can be estimated to a relative precision ε using
O(ε^{−2} s^2 log s) measurements. Finally, we show that when the Pauli
channel is given by a Markov field with at most k-local correlations, we
can learn an entire n-qubit Pauli channel to relative precision ε with only
O_k(ε^{−2} n^2 log n) measurements, which is efficient in the number of
qubits. The algorithms themselves are quite practical, and I will show
experimental results for full characterization of the noise in a 16 qubit
device. These results enable a host of applications beyond just
characterizing noise in a large-scale quantum system: they pave the way to
tailoring quantum codes, optimizing decoders, and customizing fault
tolerance protocols to suit a particular device. This is joint work with
Robin Harper and Joel Wallman.
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