Feynman's clock, a new variational principle, and parallel-in-time quantum dynamics

TL;DR

This paper introduces a novel variational principle inspired by Feynman's quantum clock, enabling quantum dynamics to be formulated as a ground state problem and facilitating parallelized quantum simulation.

Contribution

It presents a new discrete-time variational principle that connects quantum dynamics with ground state methods and introduces an algorithm for parallel-in-time quantum simulation.

Findings

Demonstrated parallel speedup in quantum simulations of molecules.

Applied the method to a Hydrogen molecule and an inorganic compound.

Analyzed basis approximation errors in quantum dynamics.

Abstract

We introduce a new 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 new 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 the new variational principle to examine the error of basis approximations in quantum dynamics.