Accuracy threshold for concatenated error detection in one dimension

Abstract

Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical systems that are candidates for quantum computing possess this property. Here we study the performance of a concatenated error-detection code in a system that permits only nearest-neighbor interactions in one dimension. We make use of a new message-passing scheme that maximizes the number of errors that can be reliably corrected by the code. Our numerical results indicate that arbitrarily accurate universal quantum computation is possible if the probability of failure of each elementary physical operation is below approximately 10^{-5}. This threshold is three orders of magnitude lower than the highest known.

7 pages, 4 figures, now with error bars

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• Fault-tolerant thresholds for quantum error correction with the surface code
• Blind topological measurement-based quantum computation
• Fault tolerant architectures for superconducting qubits
• A logical qubit in a linear array of semiconductor quantum dots
• High-threshold topological quantum error correction against biased noise
• Fault-tolerant qubit from a constant number of components
• One-dimensional quantum computing with a 'segmented chain' is feasible with today's gate fidelities
• Threshold error rates for the toric and surface codes
• Optimal correction of concatenated fault-tolerant quantum codes
• Measurement-Based Quantum Computation on Two-Body Interacting Qubits with Adiabatic Evolution
• Transitions in the quantum computational power
• Long-distance entanglement generation with scalable and robust two-dimensional quantum network
• Structured Error Recovery for Codeword-Stabilized Quantum Codes
• Resource optimization for fault-tolerant quantum computing
• Performance and Error Analysis of Knill's Postselection Scheme in a Two-Dimensional Architecture
• Fault-tolerant fidelity based on few-qubit codes: Parity-check circuits for biased error channels