A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Computing Minimum-Weight Perfect Matchings
INFORMS Journal on Computing
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Noise threshold for a fault-tolerant two-dimensional lattice architecture
Quantum Information & Computation
Surface code quantum error correction incorporating accurate error propagation
Quantum Information & Computation
Graphical algorithms and threshold error rates for the 2d color code
Quantum Information & Computation
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The planar code scheme for quantum computation features a 2d array of nearest-neighborcoupled qubits yet claims a threshold error rate approaching 1% [1]. This result wasobtained for the toric code, from which the planar code is derived, and surpasses allother known codes restricted to 2d nearest-neighbor architectures by several orders ofmagnitude. We describe in detail an error correction procedure for the toric and planarcodes, which is based on polynomial-time graph matching techniques and is efficientlyimplementable as the classical feed-forward processing step in a real quantum computer.By applying one and two qubit depolarizing errors of equal probability p, we determinethe threshold error rates for the two codes (differing only in their boundary conditions)for both ideal and non-ideal syndrome extraction scenarios. We verify that the toriccode has an asymptotic threshold of pth = 15.5% under ideal syndrome extraction, and pth = 7.8×10-3 for the non-ideal case, in agreement with [1]. Simulations of the planarcode indicate that the threshold is close to that of the toric code.