Universal quantum computation by discontinuous quantum walk

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.042304· OSTI ID:21450722

Underwood, Michael S; Feder, David L ^[1]

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1. Institute for Quantum Information Science, University of Calgary, Calgary, Alberta T2N 1N4 (Canada)

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum ''walker'' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This ''discontinuous'' quantum walk employs perfect quantum-state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one time step apart.

• OSTI ID: 21450722
• Journal Information: Physical Review. A, Vol. 82, Issue 4; Other Information: DOI: 10.1103/PhysRevA.82.042304; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
COMPUTERIZED SIMULATION
EVOLUTION
GRAPH THEORY
HAMILTONIANS
MATRICES
QUANTUM COMPUTERS
QUANTUM MECHANICS
QUANTUM STATES
QUBITS
RANDOMNESS
COMPUTERS
INFORMATION
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
QUANTUM INFORMATION
QUANTUM OPERATORS
SIMULATION