Fault-tolerant Holonomic Quantum Computation in Surface Codes

Abstract

We show that universal holonomic quantum computation (HQC) can be achieved fault-tolerantly by adiabatically deforming the gapped stabilizer Hamiltonian of the surface code, where quantum information is encoded in the degenerate ground space of the system Hamiltonian. We explicitly propose procedures to perform each logical operation, including logical state initialization, logical state measurement, logical CNOT, state injection and distillation,etc. In particular, adiabatic braiding of different types of holes on the surface leads to a topologically protected, non-Abelian geometric logical CNOT. Throughout the computation, quantum information is protected from both small perturbations and low weight thermal excitations by a constant energy gap, and is independent of the system size. Also the Hamiltonian terms have weight at most four during the whole process. The effect of thermal error propagation is considered during the adiabatic code deformation. With the help of active error correction, this scheme is fault-tolerant, in the sense that the computation time can be arbitrarily long for large enough lattice size. It is shown that the frequency of error correction and the physical resources needed can be greatly reduced by the constant energy gap.

26 pages, 18 figures, 2 tables, comments welcomed. v4:published version, more details of Hadmard

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• Surface codes: Towards practical large-scale quantum computation
• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological Quantum Distillation
• Topological fault-tolerance in cluster state quantum computation
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Experimental Realization of Universal Geometric Quantum Gates with Solid-State Spins
• Simple proof of equivalence between adiabatic quantum computation and the circuit model
• On thermalization in Kitaev's 2D model
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Improved magic states distillation for quantum universality
• Towards Fault Tolerant Adiabatic Quantum Computation
• Abelian and non-Abelian geometric phases in adiabatic open quantum systems
• Fault-tolerant holonomic quantum computation
• On the stability of quantum holonomic gates
• Scheme for fault-tolerant holonomic computation on stabilizer codes

Cited by in corpus (1)

• Nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases