Realization of holonomic single-qubit operations

Toyoda, Kenji; Uchida, Kensuke; Noguchi, Atsushi; Haze, Shinsuke; Urabe, Shinji

doi:10.1103/physreva.87.052307

Cited by 69 publications

(49 citation statements)

References 27 publications

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“…A recent experiment has demonstrated GQC using adiabatic evolution in a tripod configuration, where three ground‐state levels couple to an excited stated by use of three resonant laser fields. This experiment realized a universal set of one‐qubit gates based on the adiabatic scheme proposed in [70] resulting from adiabatic transport of this dark energy eigensubspace for a single trapped ion.…”

Section: Quantum Computationmentioning

confidence: 99%

Geometric phases in quantum information

Sjöqvist

2015

Int J of Quantum Chemistry

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The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by focusing on three main themes: the use of GPs to perform robust quantum computation, the development of GP concepts for mixed quantum states, and the discovery of a new type of topological phases for entangled quantum systems. We delineate the theoretical development as well as describe recent experiments related to GPs in the context of quantum information.

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Section: Quantum Computationmentioning

confidence: 99%

Geometric phases in quantum information

Sjöqvist

2015

Int J of Quantum Chemistry

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“…For instance, HQC was realized in the nuclear magnetic resonance (NMR)28, trapped ions29 and superconducting qubit experiments30. DFS has been experimentally demonstrated in NMR31, trapped ions32 and photonic systems33.…”

Section: Resultsmentioning

confidence: 99%

Expedited Holonomic Quantum Computation via Net Zero-Energy-Cost Control in Decoherence-Free Subspace

Pyshkin

Luo

Jing

et al. 2016

Sci Rep

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Holonomic quantum computation (HQC) may not show its full potential in quantum speedup due to the prerequisite of a long coherent runtime imposed by the adiabatic condition. Here we show that the conventional HQC can be dramatically accelerated by using external control fields, of which the effectiveness is exclusively determined by the integral of the control fields in the time domain. This control scheme can be realized with net zero energy cost and it is fault-tolerant against fluctuation and noise, significantly relaxing the experimental constraints. We demonstrate how to realize the scheme via decoherence-free subspaces. In this way we unify quantum robustness merits of this fault-tolerant control scheme, the conventional HQC and decoherence-free subspace, and propose an expedited holonomic quantum computation protocol.

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“…Theoretical and experimental progress in non-Abelian HQC for single-qubit operations has been made recently, through both adiabatic [60] and nonadiabatic evolution [61][62][63][64] on various of physical systems. Applying our scheme to an actual physical system needs local four-body interactions.…”

Section: Discussionmentioning

confidence: 99%

Fault-tolerant holonomic quantum computation in surface codes

Zheng

Brun

2015

Phys. Rev. A

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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.

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Realization of holonomic single-qubit operations

Cited by 69 publications

References 27 publications

Geometric phases in quantum information

Geometric phases in quantum information

Expedited Holonomic Quantum Computation via Net Zero-Energy-Cost Control in Decoherence-Free Subspace

Fault-tolerant holonomic quantum computation in surface codes

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