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

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.

Comments are welcome

References in corpus (15)

• Non-Abelian Anyons and Topological Quantum Computation
• The density-matrix renormalization group in the age of matrix product states
• Quantum Computing
• Surface codes: Towards practical large-scale quantum computation
• Generalized Global Symmetries
• Restrictions on Transversal Encoded Quantum Gate Sets
• A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Fault-tolerant logical gates in quantum error-correcting codes
• On topological phases of spin chains
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• Anyons in Multichannel Kondo Systems
• Entanglement in an SU(n) Valence-Bond-Solid State
• Quantum Circuits for Measuring Levin-Wen Operators
• Quantum Computing with sine-Gordon Qubits

Cited by in corpus (9)

• Near-optimal covariant quantum error-correcting codes from random unitaries with symmetries
• Approximate symmetries and quantum error correction
• A comparative study of universal quantum computing models: towards a physical unification
• A prototype of quantum von Neumann architecture
• Complexity and order in approximate quantum error-correcting codes
• Quantum error correction meets continuous symmetries: fundamental trade-offs and case studies
• Quantum resource theory of coding for error correction
• A family of quantum von Neumann architecture
• An additive refinement of quantum channel capacities