Diego de Falco and Dario Tamascelli 2004 J. Phys. A: Math. Gen. 37 909 doi:10.1088/0305-4470/37/3/025
Diego de Falco and Dario Tamascelli
Show affiliationsWe 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.
03.67.Lx Quantum computation architectures and implementations
03.67.Mn Entanglement measures, witnesses, and other characterizations
60G50 Sums of independent random variables; random walks
81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
Issue 3 (23 January 2004)
Received 19 March 2003
Published 7 January 2004
Diego de Falco and Dario Tamascelli 2004 J. Phys. A: Math. Gen. 37 909
Grigorii B Malykin 2006 Phys.-Usp. 49 837
Abhay Ashtekar et al 2003 Class. Quantum Grav. 20 L11
K De'Bell and D Imeson 1997 J. Phys.: Condens. Matter 9 5719
Qiu Xue-Qiong et al 2008 Chinese Phys. Lett. 25 536
C A Clarkson and A A Coley 2001 Class. Quantum Grav. 18 1305
P Y Chu et al 1992 Eur. J. Phys. 13 17
Guo Hong-Kai and Fang Hai-Ping 2005 Chinese Phys. Lett. 22 787
R L Dixon and K E Ekstrand 1974 Phys. Med. Biol. 19 196
J Zimányi et al 2005 J. Phys. G: Nucl. Part. Phys. 31 711