Pauli channels can be estimated from syndrome measurements in quantum error correction

Abstract

The performance of quantum error correction 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 rates 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. 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 vanishing error rates, and applies even if high weight errors occur frequently. Moreover, it also allows for measurement errors within the framework of quantum data-syndrome codes. Our proof combines Boolean Fourier analysis, combinatorics and elementary algebraic geometry. It is our hope that this work opens up interesting applications, such as the online adaptation of a decoder to time-varying noise.

15 pages, 1 figure; Version 2: Updated with journal (Quantum) version, including a new example

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Cited by in corpus (15)

• Decoding algorithms for surface codes
• Learning correlated noise in a 39-qubit quantum processor
• Learning logical Pauli noise in quantum error correction
• Data-driven decoding of quantum error correcting codes using graph neural networks
• Optimization of decoder priors for accurate quantum error correction
• Mitigating errors in logical qubits
• A generalized cycle benchmarking algorithm for characterizing mid-circuit measurements
• Fault-tolerant compiling of classically hard IQP circuits on hypercubes
• Quantum computer error structure probed by quantum error correction syndrome measurements
• Efficient self-consistent learning of gate set Pauli noise
• Disti-Mator: an entanglement distillation-based state estimator
• A double selection entanglement distillation-based state estimator
• Scalable and fault-tolerant preparation of encoded k-uniform states
• Bayesian inference of general noise-model parameters from the syndrome statistics of surface codes
• Calibration of syndrome measurements in a single experiment