Feynman’s Clock, a New Variational Principle, and Parallel-in-Time Quantum Dynamics

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Feynman’s Clock, a New Variational Principle, and Parallel-in-Time Quantum Dynamics

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Title: Feynman’s Clock, a New Variational Principle, and Parallel-in-Time Quantum Dynamics
Author: McClean, Jarrod Ryan; Parkhill, John Anthony; Aspuru-Guzik, Alan

Note: Order does not necessarily reflect citation order of authors.

Citation: McClean, Jarrod Ryan, John Anthony Parkhill, and Alan Aspuru-Guzik. 2013. "Feynman’s Clock, a New Variational Principle, and Parallel-in-Time Quantum Dynamics." Proceedings of the National Academy of Sciences 110(41): E3901-E3909.
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Abstract: We introduce a discrete-time variational principle inspired by the quantum clock originally proposed by Feynman and use it to write down quantum evolution as a ground-state eigenvalue problem. The construction allows one to apply ground-state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. Moreover, this formalism naturally leads to an algorithm to parallelize quantum simulation over time. We draw an explicit connection between previously known time-dependent variational principles and the time-embedded variational principle presented. Sample calculations are presented, applying the idea to a hydrogen molecule and the spin degrees of freedom of a model inorganic compound, demonstrating the parallel speedup of our method as well as its flexibility in applying ground-state methodologies. Finally, we take advantage of the unique perspective of this variational principle to examine the error of basis approximations in quantum dynamics.
Other Sources: http://arxiv.org/abs/1301.2326
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10245887
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