Optimal complexity correction of correlated errors in the surface code

Abstract

The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that are capable of implementing a universal set of gates with error rates below approximately 1%, requirements compatible with experimental reality. Consequently, a number of authors are attempting to squeeze additional performance out of the surface code. We describe an optimal complexity error suppression algorithm, parallelizable to O(1) given constant computing resources per unit area, and provide evidence that this algorithm exploits correlations in the error models of each gate in an asymptotically optimal manner.

6 pages, 9 figures

Cited by in corpus (27)

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• Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
• Low-distance Surface Codes under Realistic Quantum Noise
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
• Ultrahigh Error Threshold for Surface Codes with Biased Noise
• Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
• Focus beyond quadratic speedups for error-corrected quantum advantage
• Machine-learning-assisted correction of correlated qubit errors in a topological code
• Density-matrix simulation of small surface codes under current and projected experimental noise
• A Fault-Tolerant Honeycomb Memory
• Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
• Analysing correlated noise on the surface code using adaptive decoding algorithms
• Decoding algorithms for surface codes
• Benchmarking the Planar Honeycomb Code
• Multi-path Summation for Decoding 2D Topological Codes
• A scalable and fast artificial neural network syndrome decoder for surface codes
• Stability Experiments: The Overlooked Dual of Memory Experiments
• Cosmic-ray-induced correlated errors in superconducting qubit array
• A Scalable Decoder Micro-architecture for Fault-Tolerant Quantum Computing
• Convolutional neural network based decoders for surface codes
• Detrimental non-Markovian errors for surface code memory
• Error correcting power of small topological codes
• Resource optimization for fault-tolerant quantum computing
• Resource comparison of two surface code implementations of small angle Z rotations
• Generalizing the matching decoder for the Chamon code
• Channel Polarization of Two-dimensional-input Quantum Symmetric Channels