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Efficient Simulation of Quantum Error Correction Under Coherent Error Based on the Nonunitary Free-Fermionic

Yasunari Suzuki1,2, Keisuke Fujii1,2,3, Masato Koashi1,2

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We developed an efficient method to calculate quantum error thresholds under non-Clifford noise. Fully coherent noise reduces the error threshold to one-third, providing a benchmark for fault-tolerant quantum computation.

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Computational Physics

Background:

  • Fault-tolerant quantum computation requires precise error threshold evaluation under realistic noise.
  • Non-Clifford noise, prevalent in quantum experiments, poses significant challenges for efficient threshold analysis.
  • Existing methods struggle to efficiently handle the complexities of non-Clifford noise in quantum error correction.

Purpose of the Study:

  • To construct an efficient scheme for estimating the error threshold of quantum codes under non-Clifford noise.
  • To investigate the impact of noise coherence on the error threshold without approximations.
  • To provide accurate benchmark results for non-Clifford noise analysis in quantum computing.

Main Methods:

  • Utilized the nonunitary free-fermionic formalism for efficient simulation of the 1D quantum repetition code.
  • Employed this formalism to analyze coherent noise effects on the error threshold.
  • Performed a leading-order analysis of noise coherence effects on the noise map.

Main Results:

  • Demonstrated that fully coherent noise reduces the error threshold to one-third for the 1D quantum repetition code.
  • Showed the applicability of the developed scheme to surface codes under specific coherent noise models.
  • Established a clear dependence of the error threshold on noise coherence.

Conclusions:

  • The developed scheme provides an accurate and efficient method for evaluating error thresholds under non-Clifford noise.
  • Noise coherence significantly impacts the error threshold, a finding explained through theoretical analysis.
  • The results serve as a crucial benchmark for approximate and heuristic methods in quantum error correction research.