2014/11/30 by Yi-Cong Zheng, Todd A. Brun
Computer Science · Mathematics · Physics and Astronomy · #Adiabatic quantum computation #Algorithm #Classical mechanics #Computer science #Holonomic #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum computer #Quantum mechanics #Statistical physics #quant-ph
paper · pdf · doi:10.1103/physreva.91.022302
published as Phys. Rev. A 91, 022302 (2015) · 26 pages, 18 figures, 2 tables, comments welcomed. v4:published version, more details of Hadmard
arxiv created 2015/02/04 · openalex publication_date 2015/02/04 · arxiv updated 2015/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We show that universal holonomic quantum computation 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 controlled-not (cnot), state injection, 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.