4.7 Article

An optimal quantum error-correcting procedure using quantifier elimination

Journal

QUANTUM INFORMATION PROCESSING
Volume 20, Issue 5, Pages -

Publisher

SPRINGER
DOI: 10.1007/s11128-021-03109-w

Keywords

Quantum error correction; Quantifier elimination; Complexity

Funding

  1. National Natural Science Foundation of China [61832015, 62072176, 11871221]
  2. National Key R&D Program of China [2018YFA0306704]
  3. Research Funds of Happiness Flower ECNU [2020ECNU-XFZH005]
  4. Inria-CAS joint project Quasar

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The aim is to design recovery super-operators to maximize the minimum fidelity through noisy quantum communication channels, a MAX-MIN problem outside the realm of convex optimization. The new method achieves exactness and completeness by reduction to quantifier elimination over real closed fields in a fragment. Lastly, the complexity of the method is shown to be in the EXP class.
Quantum communication channels suffer from various noises, which are mathematically modeled by error super-operators. To combat these errors, it is necessary to design recovery super-operators. We aim to construct the optimal recovery that maximizes the minimum fidelity through the noisy channel. It is typically a MAX-MIN problem, out of the scope of convex optimization. Compared to existing methods, our method is exact and complete by a reduction to quantifier elimination over real closed fields in a fragment of two alternative quantifier blocks. Finally, the complexity is shown to be in EXP.

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