Proof of finite surface code threshold for matching

Abstract

The field of quantum computation currently lacks a formal proof of experimental feasibility. Qubits are fragile and sophisticated quantum error correction is required to achieve reliable quantum computation. The surface code is a promising quantum error correction code, requiring only a physically reasonable 2-D lattice of qubits with nearest neighbor interactions. However, existing proofs that reliable quantum computation is possible using this code assume the ability to measure four-body operators and, despite making this difficult to realize assumption, require that the error rate of these operator measurements is less than 10^-9, an unphysically low target. High error rates have been proved tolerable only when assuming tunable interactions of strength and error rate independent of distance, which is also unphysical. In this work, given a 2-D lattice of qubits with only nearest neighbor two-qubit gates, and single-qubit measurement, initialization, and unitary gates, all of which have error rate p, we prove that arbitrarily reliable quantum computation is possible provided p<7.4x10^-4, a target that many experiments have already achieved. This closes a long-standing open problem, formally proving the experimental feasibility of quantum computation under physically reasonable assumptions.

5 pages, 4 figures, published version

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• Early Fault-Tolerant Quantum Computing
• Coping with qubit leakage in topological codes
• Cellular-automaton decoders with provable thresholds for topological codes
• Holonomic Surface Codes for Fault-Tolerant Quantum Computation
• Errors and pseudo-thresholds for incoherent and coherent noise
• Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation
• Simulation of rare events in quantum error correction
• Resource-efficient and fault-tolerant topological quantum computation with hybrid entanglement of light
• Fully tunable longitudinal spin-photon interactions in Si and Ge quantum dots
• Benchmarking near-term devices with quantum error correction
• Practical Topological Cluster State Quantum Computing Requires Loss Below 1%
• Energy-Consumption Advantage of Quantum Computation
• Logical Error Rate Scaling of the Toric Code
• Analytic asymptotic performance of topological codes
• High-fidelity two-qubit gates of hybrid superconducting-semiconducting singlet-triplet qubits
• Fidelity Threshold of the Surface Code Beyond Single-Qubit Error Models
• Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes
• Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons
• The role of entropy in topological quantum error correction
• Active error correction for Abelian and non-Abelian anyons
• Color code decoder with improved scaling for correcting circuit-level noise
• Error correction of transversal CNOT gates for scalable surface code computation
• Error models in quantum computation: an application of model selection
• Topological Dynamical Decoupling
• Continuous error correction for Ising anyons
• Engineering autonomous error correction in stabilizer codes at finite temperature
• Decoding the Projective Transverse Field Ising Model
• What determines the ultimate precision of a quantum computer?
• Fault-tolerant quantum speedup from constant depth quantum circuits
• Quantum computer error structure probed by quantum error correction syndrome measurements
• Resource optimization for fault-tolerant quantum computing
• Almost Linear Decoder for Optimal Geometrically Local Quantum Codes
• Single-shot quantum error correction with the three-dimensional subsystem toric code
• Robust Syndrome Extraction via BCH Encoding
• Symmetry in Multi-Qubit Correlated Noise Errors Enhances Surface Code Thresholds
• All-to-all connectivity of Rydberg-atom-based quantum processors with messenger qubits
• Channel Polarization of Two-dimensional-input Quantum Symmetric Channels
• Decoder Dependence in Surface-Code Threshold Estimation under Digitized Hybrid Continuous-Variable and Discrete Noise
• Overflow-Safe Polylog-Time Parallel Minimum-Weight Perfect Matching Decoder: Toward Experimental Demonstration