Fault-tolerant quantum error correction using error weight parities

Abstract

In quantum error correction using imperfect primitives, errors of high weight arising from a few faults are major concerns since they might not be correctable by the quantum error correcting code. Fortunately, some errors of different weights are logically equivalent and the same correction procedure is applicable to all equivalent errors, thus correcting high-weight errors is sometimes possible. In this work, we introduce a technique called weight parity error correction (WPEC) which can correct Pauli error of any weight in some stabilizer codes provided that the parity of the weight of the error is known. We show that the technique is applicable to concatenated codes constructed from the [[7,1,3]] Steane code or the [[23,1,7]] Golay code. We also provide a fault-tolerant error correction protocol using WPEC for the [[49,1,9]] concatenated Steane code which can correct up to 3 faults and requires only 2 ancillas.

arXiv comment13 pages, 6 figures, comments welcome. V2: minor revision. V3: proof of Fact 1 added & minor revision

References in corpus (28)

• Good Quantum Error-Correcting Codes Exist
• Multiple Particle Interference and Quantum Error Correction
• Reliable Quantum Computers
• Overhead and noise threshold of fault-tolerant quantum error correction
• Active stabilisation, quantum computation and quantum state synthesis
• Quantum error correction with only two extra qubits
• Topological and subsystem codes on low-degree graphs with flag qubits
• Effective fault-tolerant quantum computation with slow measurements
• Flag fault-tolerant error correction with arbitrary distance codes
• Fault-tolerant quantum computation with few qubits
• Threshold Accuracy for Quantum Computation
• The surface code with a twist
• Triangular color codes on trivalent graphs with flag qubits
• Flag fault-tolerant error correction for any stabilizer code
• Fault-tolerant magic state preparation with flag qubits
• Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
• Neural network decoder for topological color codes with circuit level noise
• Fault-tolerant preparation of approximate GKP states
• Fault-tolerant quantum error correction for Steane's seven-qubit color code with few or no extra qubits
• Transversality and lattice surgery: exploring realistic routes towards coupled logical qubits with trapped-ion quantum processors
• Overhead analysis of universal concatenated quantum codes
• Flag fault-tolerant error correction, measurement, and quantum computation for cyclic CSS codes
• Fault-tolerant protection of near-term trapped-ion topological qubits under realistic noise sources
• Fault-tolerant Quantum Error Correction on Near-term Quantum Processors using Flag and Bridge Qubits
• Fast fault-tolerant filtering of quantum codewords
• Extended flag gadgets for low-overhead circuit verification
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits
• Error rates and resource overheads of encoded three-qubit gates

Cited by in corpus (7)

• A circuit-level protocol and analysis for twist-based lattice surgery
• Adaptive syndrome measurements for Shor-style error correction
• Achieving fault tolerance on capped color codes with few ancillas
• Decoding Merged Color-Surface Codes and Finding Fault-Tolerant Clifford Circuits Using Solvers for Satisfiability Modulo Theories
• Low-Depth Flag-Style Syndrome Extraction for Small Quantum Error-Correction Codes
• Optimization tools for distance-preserving flag fault-tolerant error correction
• Concatenated Steane code with single-flag syndrome checks