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

References in corpus (3)

• Simulated Quantum Computation of Molecular Energies
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Ab initio quantum dynamics using coupled-cluster

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• Clock Quantum Monte Carlo: an imaginary-time method for real-time quantum dynamics
• Variational dynamics as a ground-state problem on a quantum computer
• Adiabatic quantum optimization in presence of discrete noise: Reducing the problem dimensionality
• Feynman's Clock for open quantum systems
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• Parallel-in-time optical simulation of history states
• Categorical Semantics for Schrödinger's Equation
• Path Integrals from Spacetime Quantum Actions
• Emergent dynamics from entangled mixed states
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• History states of one-dimensional quantum walks
• Unifying framework for quantum simulation algorithms for time-dependent Hamiltonian dynamics
• Categorical Quantum Dynamics
• An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum States