Fidelity Threshold of the Surface Code Beyond Single-Qubit Error Models

Abstract

The surface code is one the most promising alternatives for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attrative features. We develop an exact formulation for the fidelity of the surface code that allows us to probe much further on this promise of strong protection. This formulation goes beyond the stochastic single-qubit error model approximation and can take into account both correlated errors and inhomogeneities in the coupling between physical qubits and the environment. For the case of a bit-flipping environment, we map the complete evolution after one quantum error correction cycle onto the problem of computing correlation functions of a two-dimensional Ising model with boundary fields. Exact results for the fidelity threshold of the surface code are then obtained for several relevant types of noise. Analytical predictions for a representative case are confirmed by Monte Carlo simulations.

12 pages, 6 figures; revised and extended version

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Cited by in corpus (14)

• Low-distance Surface Codes under Realistic Quantum Noise
• Quantum memories at finite temperature
• Multiqubit Spectroscopy of Gaussian Quantum Noise
• Fault-tolerant error correction with the gauge color code
• Analysing correlated noise on the surface code using adaptive decoding algorithms
• Limitations in quantum computing from resource constraints
• Comparison of a quantum error correction threshold for exact and approximate errors
• Spatial Coherence of Light in Collective Spontaneous Emission
• Numerical and analytical bounds on threshold error rates for hypergraph-product codes
• Correcting non-independent and non-identically distributed errors with surface codes
• Topological quantum error correction in the Kitaev honeycomb model
• Surface code fidelity at finite temperatures
• Long-time efficacy of the surface code in the presence of a superohmic environment
• Decoding Quantum Error Correction Codes with Local Variation