2019/07/31 by Steven T. Flammia, Joel J. Wallman · 3 citations
Computer Science · Physics and Astronomy · #Channel (broadcasting) #Hilbert space #Markov process #Pauli exclusion principle #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum channel #Quantum error correction #Quantum information #Qubit #quant-ph
paper · pdf · doi:10.1145/3408039
published as ACM Transactions on Quantum Computing 1 (1), 1-32 (2020) · 31 pages, 1 figure; v3 some typos fixed
openalex created_date 2019/08/13 · openalex publication_date 2020/12/07 · arxiv created 2022/02/22 · arxiv updated 2022/02/23 · openalex updated_date 2026/08/05
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 procedure for learning a Pauli channel on n qubits with high probability to a relative precision ϵ using O (ϵ -2 n2 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 arbitrary set of s Pauli errors can be estimated to a relative precision ϵ using O (ϵ -4 log s log s/ϵ) 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. 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 procedures to suit a particular device.