We present an implementation of Grover’s algorithm in the framework of Feynman’s cursor model of a quantum computer. The cursor degrees of freedom act as a quantum clocking mechanism, and allow Grover’s algorithm to be performed using a single, time-independent Hamiltonian. We examine issues of locality and resource usage in implementing such a Hamiltonian. In the familiar language of Heisenberg spin–spin coupling, the clocking mechanism appears as an excitation of a basically linear chain of spins, with occasional controlled jumps that allow for motion on a planar graph: in this sense our model implements the idea of ‘timing’ a quantum algorithm using a continuous-time random walk. In this context we examine some consequences of the entanglement between the states of the input/output register and the states of the quantum clock.

Grover’s algorithm on a Feynman computer / D. de Falco, D. Tamascelli. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - 37:3(2004 Jan 23), pp. 909-930.

Grover’s algorithm on a Feynman computer

D. de Falco
Primo
;
D. Tamascelli
Ultimo
2004

Abstract

We present an implementation of Grover’s algorithm in the framework of Feynman’s cursor model of a quantum computer. The cursor degrees of freedom act as a quantum clocking mechanism, and allow Grover’s algorithm to be performed using a single, time-independent Hamiltonian. We examine issues of locality and resource usage in implementing such a Hamiltonian. In the familiar language of Heisenberg spin–spin coupling, the clocking mechanism appears as an excitation of a basically linear chain of spins, with occasional controlled jumps that allow for motion on a planar graph: in this sense our model implements the idea of ‘timing’ a quantum algorithm using a continuous-time random walk. In this context we examine some consequences of the entanglement between the states of the input/output register and the states of the quantum clock.
Grover's algorithm ; Feynman quantum computer ; quantum clock
Settore MAT/06 - Probabilita' e Statistica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/34864
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