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.

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

References in corpus (5)

• Effective fault-tolerant quantum computation with slow measurements
• Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
• Extended flag gadgets for low-overhead circuit verification
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits
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Cited by in corpus (7)

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• 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