Efficient classical simulation of spin networks

In general, quantum systems are believed to be exponentially hard to simulate using classical computers. It is in these hard cases where we hope to find quantum algorithms that provide speed up over classical algorithms. In the paradigm of quantum adiabatic computation, instances of spin networks with 2-local interactions could hopefully efficiently compute certain problems in NP-complete. Thus, we are interested in the adiabatic evolution of spin networks. There are analytical solutions to specific Hamiltonians for 1D spin chains. However, analytical solutions to networks of higher dimensionality are unknown. The dynamics of Cayley trees (three binary trees connected at the root) at zero temperature are unknown. The running time of the adiabatic evolution of Cayley trees could provide an insight into the dynamics of more complicated spin networks. Matrix Product States (MPS) define a wavefunction anzatz that approximates slightly entangled quantum systems using poly(n) parameters. The MPS representation is exponentially smaller than the exact representation, which involves 0(2n) parameters. The MPS Algorithm evolves states in the MPS representation.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Physics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Sylvester, Igor Andrade

Advisor dc:contributor.advisor

• Edward Farhi.

• Physics.

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/1721.1/36112

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/36112