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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
1Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
Physical Review Letters
|December 9, 2017
Summary
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.
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.
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