Between Shor and Steane: A unifying construction for measuring error syndromes

Abstract

Fault-tolerant quantum error correction requires the measurement of error syndromes in a way that minimizes correlated errors on the quantum data. Steane and Shor ancilla are two well-known methods for fault-tolerant syndrome extraction. In this paper, we find a unifying construction that generates a family of ancilla blocks that interpolate between Shor and Steane. This family increases the complexity of ancilla construction in exchange for reducing the rounds of measurement required to fault-tolerantly measure the error. We then apply this construction to the toric code of size $L\times L$ and find that blocks of size $m\times m$ can be used to decode errors in $O(L/m)$ rounds of measurements. Our method can be applied to any Calderbank-Shor-Steane codes and presents a new direction for optimizing fault-tolerant quantum computation.

References in corpus (27)

• Fault-tolerant quantum computation by anyons
• Surface codes: Towards practical large-scale quantum computation
• Good Quantum Error-Correcting Codes Exist
• Topological quantum memory
• Quantum Computing with Very Noisy Devices
• Quantum Error Correction and Orthogonal Geometry
• Topological Quantum Distillation
• High threshold universal quantum computation on the surface code
• Overhead and noise threshold of fault-tolerant quantum error correction
• Fault-Tolerant Error Correction with Efficient Quantum Codes
• Active stabilisation, quantum computation and quantum state synthesis
• Single-qubit quantum memory exceeding $10$-minute coherence time
• Quantum error correction with only two extra qubits
• Topological and subsystem codes on low-degree graphs with flag qubits
• Single-shot fault-tolerant quantum error correction
• Effective fault-tolerant quantum computation with slow measurements
• Flag fault-tolerant error correction with arbitrary distance codes
• Fault-tolerant quantum computation with few qubits
• A theory of single-shot error correction for adversarial noise
• The surface code with a twist
• Flag fault-tolerant error correction for any stabilizer code
• Fault-Tolerant Weighted Union-Find Decoding on the Toric Code
• Fault Tolerance with Bare Ancillae for a [[7,1,3]] Code
• Direct measurement of Bacon-Shor code stabilizers
• Fault-tolerant Compass Codes
• Efficient Preparation of Large Block Code Ancilla States for Fault-tolerant Quantum Computation
• Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes