Ability of stabilizer quantum error correction to protect itself from its own imperfection

Abstract

The theory of stabilizer quantum error correction allows us to actively stabilize quantum states and simulate ideal quantum operations in a noisy environment. It is critical is to correctly diagnose noise from its syndrome and nullify it accordingly. However, hardware that performs quantum error correction itself is inevitably imperfect in practice. Here, we show that stabilizer codes possess a built-in capability of correcting errors not only on quantum information but also on faulty syndromes extracted by themselves. Shor's syndrome extraction for fault-tolerant quantum computation is naturally improved. This opens a path to realizing the potential of stabilizer quantum error correction hidden within an innocent looking choice of generators and stabilizer operators that have been deemed redundant.

arXiv comment9 pages, 3 tables, final accepted version for publication in Physical Review A (v2: improved main theorem, slightly expanded each section, reformatted for readability, v3: corrected an error and typos in the proof of Theorem 2, v4: edited language)

References in corpus (7)

• Mixed State Entanglement and Quantum Error Correction
• Good Quantum Error-Correcting Codes Exist
• Multiple Particle Interference and Quantum Error Correction
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Quantum Computing with Very Noisy Devices
• Fault-Tolerant Error Correction with Efficient Quantum Codes
• Active stabilisation, quantum computation and quantum state synthesis

Cited by in corpus (21)

• Degenerate Quantum LDPC Codes With Good Finite Length Performance
• Bias-preserving gates with stabilized cat qubits
• A theory of single-shot error correction for adversarial noise
• Linear Programming Bounds for Entanglement-Assisted Quantum Error-Correcting Codes by Split Weight Enumerators
• Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
• Higher-dimensional quantum hypergraph-product codes
• Beyond single-shot fault-tolerant quantum error correction
• Pauli channels can be estimated from syndrome measurements in quantum error correction
• Single-shot decoding of good quantum LDPC codes
• Fault-tolerant Preparation of Stabilizer States for Quantum CSS Codes by Classical Error-Correcting Codes
• Learning logical Pauli noise in quantum error correction
• Decoding of Quantum Data-Syndrome Codes via Belief Propagation
• Efficient Preparation of Large Block Code Ancilla States for Fault-tolerant Quantum Computation
• Minimal distances for certain quantum product codes and tensor products of chain complexes
• Optimal noise estimation from syndrome statistics of quantum codes
• Quantum convolutional data-syndrome codes
• Generalized quantum data-syndrome codes and belief propagation decoding for phenomenological noise
• Robust projective measurements through measuring code-inspired observables
• Single-shot quantum error correction with the three-dimensional subsystem toric code
• Probabilistic bounds on the trapping redundancy of linear codes
• Robust Syndrome Extraction via BCH Encoding