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

• URL: http://arxiv.org/abs/2105.14777v1
• Date: Mon, 31 May 2021 08:17:30 GMT
• Title: Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• Authors: Dong-Sheng Wang, Yun-Jiang Wang, Ningping Cao, Bei Zeng, Raymond Laflamme
• Abstract summary: We develop the theory of quasi-exact fault-tolerant quantum computation, which uses qubits encoded into quasi-exact quantum error-correction codes ("quasi codes") The model of QEQ lies in between the two well-known ones: the usual noisy quantum universality without error correction and the usual fault-tolerant quantum computation, but closer to the later.
• Score: 3.6192409729339223
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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