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

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.

Researcher Jarrod R. McClean discussed with Phys.org 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 to perform dynamics simulations," McClean tells Phys.org. "This means that only very short time scales can be examined with high accuracy. Moreover," he points out, "previous attempts to utilize modern parallel computers have been hindered by strong spatial interactions within quantum systems."

"One usually thinks of quantum information as a field that leads to the development of quantum computers," Harvard's Aspuru-Guzik notes. "It turns out that classical computing can benefit and learn from the ideas of quantum information. This application of Feynman's clock to the challenging problem of time evolution is an example of this."

Traditional algorithms utilize parallelization in space, in which a supercomputer comprising many processors spatially distributes and advances the problem in single temporal increments. "What is less natural," McClean continues, "is to think about the possibility of setting up a calculation that is parallel in time." This means that the simulation at different points in time has to be simultaneously calculated on many processors. "That's the focal point of our study," McClean stresses. "We exploit the clock construction, which was originally designed to think about quantum computing for use in parallel computers."

McClean notes the importance of demonstrating their proposal's accuracy convergence by applying the configuration interaction method – a linear variational method for solving the nonrelativistic Schrödinger equation. "We wanted to show that the convergence of configuration interaction in spacetime has similar properties to its usual application in ground state chemistry," he explains. "To do this, we had to find a system of interest where we could also control the importance of two-body and one-body interactions."