Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Adiabatic quantum optimization with the wrong Hamiltonian

Adiabatic quantum optimization with the wrong Hamiltonian Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement these Hamiltonians will be imperfect and limited in its precision. Even small perturbations and imprecisions can have profound effects on the nature of the ground state. Here we consider an imperfect implementation of adiabatic quantum optimization and show that, for a widely applicable random control noise model, quantum stabilizer encodings are able to reduce the effective noise magnitude and thus improve the likelihood of a successful computation or simulation. This reduction builds upon two design principles: summation of equivalent logical operators to increase the energy scale of the encoded optimization problem, and the inclusion of a penalty term comprising the sum of the code stabilizer elements. We illustrate our findings with an Ising ladder and show that classical repetition coding drastically increases the probability that the ground state of a perturbed model is decodable to that of the unperturbed model, while using only realistic two-body interaction. Finally, we note that the repetition encoding is a special case of quantum stabilizer encodings, and show that this in principle allows us to generalize our results to many types of analog quantum information processing, albeit at the expense of many-body interactions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Adiabatic quantum optimization with the wrong Hamiltonian

Physical Review A , Volume 88 (6) – Dec 11, 2013
7 pages

Loading next page...
 
/lp/american-physical-society-aps/adiabatic-quantum-optimization-with-the-wrong-hamiltonian-5IQlF5urim

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
American Physical Society (APS)
Copyright
©2013 American Physical Society
ISSN
1050-2947
DOI
10.1103/PhysRevA.88.062314
Publisher site
See Article on Publisher Site

Abstract

Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement these Hamiltonians will be imperfect and limited in its precision. Even small perturbations and imprecisions can have profound effects on the nature of the ground state. Here we consider an imperfect implementation of adiabatic quantum optimization and show that, for a widely applicable random control noise model, quantum stabilizer encodings are able to reduce the effective noise magnitude and thus improve the likelihood of a successful computation or simulation. This reduction builds upon two design principles: summation of equivalent logical operators to increase the energy scale of the encoded optimization problem, and the inclusion of a penalty term comprising the sum of the code stabilizer elements. We illustrate our findings with an Ising ladder and show that classical repetition coding drastically increases the probability that the ground state of a perturbed model is decodable to that of the unperturbed model, while using only realistic two-body interaction. Finally, we note that the repetition encoding is a special case of quantum stabilizer encodings, and show that this in principle allows us to generalize our results to many types of analog quantum information processing, albeit at the expense of many-body interactions.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Dec 11, 2013

There are no references for this article.