Experimental demonstration and exploration of quantum lattice gas algorithms

Recently, it has been suggested that an array of small quantum information processors sharing classical information can be used to solve selected computational problems, referred to as a type-II quantum computer. The first concrete implementation demonstrated here solves the diffusion equation, and it provides a test example from which to probe the strengths and limitations of this new computation paradigm. The NMR experiment consists of encoding a mass density onto an array of 16 two-qubit quantum information processors and then following the computation through 7 time steps of the algorithm. The results show a good agreement with the analytic solution for diffusive dynamics. From the numerical simulations of the NMR implementations, we explore two major error sources (1) the systematic error in the collision operator and (2) the linear approximation in the initialization. Since the mass density evolving under the Burgers equation develops sharp features over time, this is a stronger test of liquid state NMR implementations of type-II quantum computers than the previous example using the diffusion equation. Small systematic errors in the collision operator accumulate and swamp all other errors. We propose, and demonstrate, that the accumulation of this error can be avoided to a large extent by replacing the single collision operator with a set of operators, that have random errors and similar fidelities.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Nuclear Engineering

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2005

Author dc:creator

• Chen, Zhiying, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• David G. Cory.

• Nuclear Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/34435

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34435