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Feynman wasn’t joking: Modeling quantum dynamics with ground state wavefunctions

Posted October 21, 2013

Amongst the late Richard Feynman’s many prolific and profound contributions to quantum mechanics, the eponymous Feynman clock is perhaps one of the more innovative. Conceived as a solution to the problem of quantum simulation, the Feynman clock proposes using quantum computers to simulate quantum systems – and in so doing, conjectures that if a quantum system moves stepwise forward and then backward in time in equal increments, it would necessarily return to its original state. While originally a linear concept, scientists at Harvard University and the University of Notre Dame recently generalized the proposition to construct a more flexible discrete-time variational principle that leads to a parallel-in-time algorithm. (A variational principle is a scientific principle, used within the calculus of variations, which develops general methods for finding functions which minimize or maximize the value of quantities that depend upon those functions.) The researchers then used that algorithm to describe time-based quantum system evolution as a ground state eigenvalue problem – that is, the quantum system’s lowest energy state – which led them to realize that the solution of the quantum dynamics problem could also be obtained by applying the traditional ground state variational principle.

Feynman wasn’t joking: Modeling quantum dynamics with ground state wavefunctions
A schematic representation of the action of the clock Hamiltonian on the history state with three discrete times and a Hilbert space of three states. Each block is a matrix with dimension of the physical system. Credit: Copyright © PNAS, doi:10.1073/pnas.1308069110

Researcher Jarrod R. McClean discussed with the research that he and his colleagues, Profs. John A. Parkhill and Alán Aspuru-Guzik, conducted. “In solving quantum dynamical problems prior to our findings, the large dimension and complexity of models in quantum mechanics make it very computationally expensive tS

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