Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 110, Issue 41, Pages E3901-E3909Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1308069110
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Funding
- Department of Energy Computational Science Graduate Fellowship [DE-FG02-97ER25308]
- National Science Foundation [CHE-1152291]
- Hughes Research Laboratories [M1144-201167-DS]
- University of California, San Diego [FA9550-12-1-0046]
- US Department of Defense
- Corning Foundation
- Camille and Henry Dreyfus Foundation
- Alfred P. Sloan Foundation
- Direct For Mathematical & Physical Scien
- Division Of Chemistry [1152291] Funding Source: National Science Foundation
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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.
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