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arXiv · 2105.14777

Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes

Dong-Sheng Wang·Yun-Jiang Wang·Ningping Cao·Bei Zeng·Raymond Laflamme
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Abstract

In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes ("quasi codes"). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The model of QEQ computation lies in between the two well-known ones: the usual noisy quantum computation without error correction and the usual fault-tolerant quantum computation, but closer to the later. Many notions of exact quantum codes need to be adjusted for the quasi setting. Here we develop quasi error-correction theory using quantum instrument, the notions of quasi universality, quasi code distances, and quasi thresholds, etc. We find a wide class of quasi codes which are called valence-bond-solid codes, and we use them as concrete examples to demonstrate QEQ computation.

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Dong-Sheng Wang, Yun-Jiang Wang, Ningping Cao, Bei Zeng, Raymond Laflamme. 2021-05-31. Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes. https://doi.org/10.1088/1367-2630%2Fac4737

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