Spatial search and the Dirac equation

Details Spatial search and the Dirac equation Spatial search and the Dirac equation

2004-05-20

arxiv.org/abs/quant-ph/0405120v1

Phys. Rev. A 70, 042312 (2004)

Physics

Quantum Physics

5 pages, 1 figure

Scientific paper

10.1103/PhysRevA.70.042312

We consider the problem of searching a d-dimensional lattice of N sites for a single marked location. We present a Hamiltonian that solves this problem in time of order sqrt(N) for d>2 and of order sqrt(N) log(N) in the critical dimension d=2. This improves upon the performance of our previous quantum walk search algorithm (which has a critical dimension of d=4), and matches the performance of a corresponding discrete-time quantum walk algorithm. The improvement uses a lattice version of the Dirac Hamiltonian, and thus requires the introduction of spin (or coin) degrees of freedom.

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