Learning logical Pauli noise in quantum error correction

Abstract

The characterization of quantum devices is crucial for their practical implementation but can be costly in experimental effort and classical postprocessing. Therefore, it is desirable to measure only the information that is relevant for specific applications and develop protocols that require little additional effort. In this work, we focus on the characterization of quantum computers in the context of stabilizer quantum error correction. For arbitrary stabilizer codes, subsystem codes, and data syndrome codes, we prove that the logical error channel induced by Pauli noise can be estimated from syndrome data under minimal conditions. More precisely, for any such code, we show that the estimation is possible as long as the code can correct the noise.

arXiv comment5+8 pages; v2: close to published version

References in corpus (36)

• Suppressing quantum errors by scaling a surface code logical qubit
• Randomized Benchmarking of Quantum Gates
• A Theory of Quantum Error-Correcting Codes
• Noise tailoring for scalable quantum computation via randomized compiling
• Characterizing Quantum Gates via Randomized Benchmarking
• Exponential suppression of bit or phase flip errors with repetitive error correction
• Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Stabilizer Formalism for Operator Quantum Error Correction
• Quantum certification and benchmarking
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• Quantum error correction with only two extra qubits
• Efficient learning of quantum noise
• Detecting crosstalk errors in quantum information processors
• Theory of quantum system certification: a tutorial
• Efficient estimation of Pauli channels
• Statistical mechanical models for quantum codes with correlated noise
• Calibrated decoders for experimental quantum error correction
• Exact Performance of Concatenated Quantum Codes
• Code Deformation and Lattice Surgery Are Gauge Fixing
• Ability of stabilizer quantum error correction to protect itself from its own imperfection
• Fast Estimation of Sparse Quantum Noise
• Hard decoding algorithm for optimizing thresholds under general Markovian noise
• Pauli error estimation via Population Recovery
• Beyond single-shot fault-tolerant quantum error correction
• Benchmarking near-term devices with quantum error correction
• Guaranteed recovery of quantum processes from few measurements
• Compressive gate set tomography
• Learning time-dependent noise to reduce logical errors: Real time error rate estimation in quantum error correction
• Pauli channels can be estimated from syndrome measurements in quantum error correction
• Sparse Quantum Codes from Quantum Circuits
• On maximum-likelihood decoding with circuit-level errors
• Optimal noise estimation from syndrome statistics of quantum codes
• Efficient diagnostics for quantum error correction
• On the Cleaning Lemma of Quantum Coding Theory
• Efficiently computing logical noise in quantum error correcting codes

Cited by in corpus (9)

• Data-driven decoding of quantum error correcting codes using graph neural networks
• A generalized cycle benchmarking algorithm for characterizing mid-circuit measurements
• Quantum computer error structure probed by quantum error correction syndrome measurements
• Fault-tolerant compiling of classically hard IQP circuits on hypercubes
• Efficient self-consistent learning of gate set Pauli noise
• Error mitigation and circuit division for early fault-tolerant quantum phase estimation
• Characterizing physical and logical errors in a transversal CNOT via cycle error reconstruction
• Quantum subspace verification for error correction codes
• Disambiguating Pauli noise in quantum computers