Title

Hamiltonian quantum cellular automata in one dimension

Authors

Authors

D. Nagaj;P. Wocjan

Comments

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Abbreviated Journal Title

Phys. Rev. A

Keywords

COMPUTATION; Optics; Physics, Atomic, Molecular & Chemical

Abstract

We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of ten-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process. We only require the ability to prepare an initial computational basis state that encodes both the quantum circuit and its input. The computational process is then carried out by the autonomous Hamiltonian time evolution. After a time polynomially long in the size of the quantum circuit has passed, the result of the computation is obtained with high probability by measuring a few qudits in the computational basis. This result also implies that there cannot exist efficient classical simulation methods for generic translationally invariant nearest-neighbor Hamiltonians on qudit chains, unless quantum computers can be efficiently simulated by classical computers (or, put in complexity theoretic terms, unless BPP=BQP).

Journal Title

Physical Review A

Volume

78

Issue/Number

3

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

14

WOS Identifier

WOS:000259689400041

ISSN

1050-2947

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