Feynman’s clock, a new variational principle, and parallel-in-time quantum dynamics
Significance Methodology for studying quantum ground-state problems is currently more mature than what is available for quantum dynamical problems. Moreover, modern computing architectures demand that new algorithms be able to make use of parallel processing. We introduce a construction inspired by quantum computation that allows one to use virtually any model for a ground-state wavefunction to model quantum many-body dynamics and formulate it in a way that naturally leads to a parallel-in-time algorithm. We show how the elementary ground-state variational principle maps onto a new time-dependent variational principle and demonstrate practical examples of its use. 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.