Spatial search and the Dirac equation
| dc.creator | Childs, Andrew M. | |
| dc.creator | Goldstone, Jeffrey | |
| dc.date | 2004-05-20 | |
| dc.date.accessioned | 2026-07-07T06:09:46Z | |
| dc.date.available | 2026-07-07T06:09:46Z | |
| dc.description | 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. | |
| dc.description | 5 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0405120 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0405120 | |
| dc.identifier | Phys. Rev. A 70, 042312 (2004) | |
| dc.identifier | doi:10.1103/PhysRevA.70.042312 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/92071 | |
| dc.subject | Quantum Physics | |
| dc.title | Spatial search and the Dirac equation | |
| dc.type | text |