SAMOP 2021 – wissenschaftliches Programm

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QI: Fachverband Quanteninformation

QI 6: Quantum Computing and Algorithms II

QI 6.4: Vortrag

Mittwoch, 22. September 2021, 12:00–12:15, H3

Pauli channels can be estimated from syndrome measurements in quantum error correction — •Thomas Wagner, Dagmar Bruß, Hermann Kampermann, and Martin Kliesch — Heinrich-Heine-Universität Düsseldorf

Large scale quantum computation requires quantum error correction. The performance can be significantly improved if detailed information about the noise is available, allowing to optimize both codes and decoders. It has been proposed to estimate error parameters from the syndrome measurements done anyway during quantum error correction. While these measurements preserve the encoded quantum state, it is currently not clear how much information about the noise can be extracted in this way. So far, apart from the limit of vanishing error rates, rigorous results have only been established for some specific codes.

In this work, we rigorously resolve the question for arbitrary stabilizer codes. We prove that a surprisingly high amount of information can be extracted from the syndromes. The main result is that a stabilizer code can be used to estimate Pauli channels with correlations across a number of qubits given by the pure distance. This result does not rely on the limit of low error rates, and applies even if high weight errors occur frequently. Our proof combines Boolean Fourier analysis, combinatorics, elementary algebraic geometry and iterated Schur complements. It is our hope that this work opens up interesting applications, such as the online adaptation of a decoder to time-varying noise.