This paper introduces a novel quantum-enhanced iterative algorithm for Monte Carlo simulations. We propose a hybrid approach combining the strengths of quantum annealing and QAOA to accelerate the exploration of the solution space and improve the accuracy of results. The algorithm systematically explores the solution space, leveraging quantum fluctuations to guide the search process and mitigate the effects of local optima. We demonstrate the effectiveness of this approach through simulations across a range of problems, highlighting its potential to significantly enhance the efficiency and reliability of Monte Carlo methods. The core mechanism centers around the quantum annealing process for initial exploration and the QAOA optimization loop for refinement. This research contributes to the development of more robust and faster simulations, offering a promising step towards broader applicability in various scientific and engineering disciplines.This paper introduces a novel quantum-enhanced iterative algorithm for Monte Carlo simulations. We propose a hybrid approach combining the strengths of quantum annealing and QAOA to accelerate the exploration of the solution space and improve the accuracy of results. The algorithm systematically explores the solution space, leveraging quantum fluctuations to guide the search process and mitigate the effects of local optima. We demonstrate the effectiveness of this approach through simulations across a range of problems, highlighting its potential to significantly enhance the efficiency and reliability of Monte Carlo methods. The core mechanism centers around the quantum annealing process for initial exploration and the QAOA optimization loop for refinement. This research contributes to the development of more robust and faster simulations, offering a promising step towards broader applicability in various scientific and engineering disciplines.

Aug 31, 20260 citations

INVESTIGATIONS IN QUANTUM MONTE CARLO

Matthew Clifford Wilson

Feb 2, 20070 citations

Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians

Jacob Bringewatt, W. Dorland, Stephen P. Jordan +1 more

Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX- $k$ -SAT problems, use $k$ -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved $n$ -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-$k$-SAT problems, use $k$-local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved $n$-body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

arXiv:1709.03971Physical Review AFeb 15, 201812 citations

Quadratic Speed-up in Infinite Variance Quantum Monte Carlo

José Blanchet, Márió Szegedy, Guanyang Wang

In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing heavy-tailed distributions, which are commonly encountered in various scientific and engineering fields. Our quantum algorithm efficiently estimates means for variables with a finite $(1+δ)^{\text{th}}$ moment, where $δ$ lies between 0 and 1. It provides a quadratic speedup over the classical Monte Carlo method in both the accuracy parameter $ε$ and the specified moment of the distribution. We establish both classical and quantum lower bounds, showcasing the near-optimal efficiency of our algorithm among quantum methods. Our work focuses not on creating new algorithms, but on analyzing the execution of existing algorithms with available additional information about the random variable. Additionally, we categorize these scenarios and demonstrate a hierarchy in the types of supplementary information that can be provided.In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing heavy-tailed distributions, which are commonly encountered in various scientific and engineering fields. Our quantum algorithm efficiently estimates means for variables with a finite $(1+δ)^{\text{th}}$ moment, where $δ$ lies between 0 and 1. It provides a quadratic speedup over the classical Monte Carlo method in both the accuracy parameter $ε$ and the specified moment of the distribution. We establish both classical and quantum lower bounds, showcasing the near-optimal efficiency of our algorithm among quantum methods. Our work focuses not on creating new algorithms, but on analyzing the execution of existing algorithms with available additional information about the random variable. Additionally, we categorize these scenarios and demonstrate a hierarchy in the types of supplementary information that can be provided.

arXiv:2401.07497Jan 15, 20240 citations

METHODS IN QUANTUM MONTE CARLO

Malvin H. Kalos, G.A. Mikhailov

De Gruyter eBooksDec 31, 19870 citations

k

-SAT problems, use

k

-local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved

n

-body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

(1+δ)^{\text{th}}

moment, where

δ

lies between 0 and 1. It provides a quadratic speedup over the classical Monte Carlo method in both the accuracy parameter

ε

and the specified moment of the distribution. We establish both classical and quantum lower bounds, showcasing the near-optimal efficiency of our algorithm among quantum methods. Our work focuses not on creating new algorithms, but on analyzing the execution of existing algorithms with available additional information about the random variable. Additionally, we categorize these scenarios and demonstrate a hierarchy in the types of supplementary information that can be provided.