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

• Published in: New journal of physics Vol. 24; no. 2; pp. 23019 - 23045
• Main Authors: Wang, Dong-Sheng, Wang, Yun-Jiang, Cao, Ningping, Zeng, Bei, Laflamme, Raymond
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01-02-2022
• Subjects: Codes; Error correction; Fault tolerance; Physics; quantum computation; Quantum computing; quantum error correction; Qubits (quantum computing); symmetry-protected topological order
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ac4737

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.