Clock Quantum Monte Carlo: an imaginary-time method for real-time quantum dynamics

Abstract

In quantum information theory, there is an explicit mapping between general unitary dynamics and Hermitian ground state eigenvalue problems known as the Feynman-Kitaev Clock. A prominent family of methods for the study of quantum ground states are quantum Monte Carlo methods, and recently the full configuration interaction quantum Monte Carlo (FCIQMC) method has demonstrated great promise for practical systems. We combine the Feynman-Kitaev Clock with FCIQMC to formulate a new technique for the study of quantum dynamics problems. Numerical examples using quantum circuits are provided as well as a technique to further mitigate the sign problem through time-dependent basis rotations. Moreover, this method allows one to combine the parallelism of Monte Carlo techniques with the locality of time to yield an effective parallel-in-time simulation technique.

References in corpus (10)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Universal computation by multi-particle quantum walk
• Quantum Monte Carlo method using phase-free random walks with Slater determinants
• Linear-scaling and parallelizable algorithms for stochastic quantum chemistry
• The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method
• Interacting boson problems are QMA-hard
• The sign problem in full configuration interaction quantum Monte Carlo: Linear and sub-linear representation regimes for the exact wave function
• The effect of quantization on the FCIQMC sign problem
• Feynman's clock, a new variational principle, and parallel-in-time quantum dynamics
• Feynman's Clock for open quantum systems

Cited by in corpus (15)

• Variational ansatz-based quantum simulation of imaginary time evolution
• Easing the Monte Carlo sign problem
• TurboRVB: a many-body toolkit for {\it ab initio} electronic simulations by quantum Monte Carlo
• The HANDE-QMC project: open-source stochastic quantum chemistry from the ground state up
• A driven-dissipative quantum Monte Carlo method for open quantum systems
• History state formalism for Dirac's theory
• System-time entanglement in a discrete time model
• History states of systems and operators
• Fully quantum embedding with density functional theory for full configuration interaction quantum Monte Carlo
• Variational dynamics as a ground-state problem on a quantum computer
• Improved walker population control for full configuration interaction quantum Monte Carlo
• Parallel-in-time optical simulation of history states
• Path Integrals from Spacetime Quantum Actions
• History states of one-dimensional quantum walks
• Sampling and the complexity of nature