Optimization by a quantum reinforcement algorithm

Abstract

A reinforcement algorithm solves a classical optimization problem by introducing a feedback to the system which slowly changes the energy landscape and converges the algorithm to an optimal solution in the configuration space. Here, we use this strategy to concentrate (localize) preferentially the wave function of a quantum particle, which explores the configuration space of the problem, on an optimal configuration. We examine the method by solving numerically the equations governing the evolution of the system, which are similar to the nonlinear Schrödinger equations, for small problem sizes. In particular, we observe that reinforcement increases the minimal energy gap of the system in a quantum annealing algorithm. Our numerical simulations and the latter observation show that such kind of quantum feedbacks might be helpful in solving a computationally hard optimization problem by a quantum reinforcement algorithm.

14 pages, 5 figures

References in corpus (22)

• Quantum Mechanics helps in searching for a needle in a haystack
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Quantum Amplitude Amplification and Estimation
• Quantum random walks - an introductory overview
• Quantum Computation and Decision Trees
• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• A Quantum Random Walk Search Algorithm
• Universal computation by quantum walk
• Shortcuts to adiabaticity by counter-diabatic driving
• Feedback-control of quantum systems using continuous state-estimation
• Quantum reinforcement learning
• Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems
• Anderson localization casts clouds over adiabatic quantum optimization
• Quantum Adiabatic Brachistochrone
• Learning by message-passing in networks of discrete synapses
• Understanding Quantum Tunneling through Quantum Monte Carlo Simulations
• Modernizing Quantum Annealing using Local Searches
• Nonstoquastic Hamiltonians and Quantum Annealing of an Ising Spin Glass
• Efficient Quantum State Estimation by Continuous Weak Measurement and Dynamical Control
• The many-body localized phase of the quantum random energy model
• Relation between quantum fluctuations and the performance enhancement of quantum annealing in a nonstoquastic Hamiltonian
• Quantum search using non-Hermitian adiabatic evolution

Cited by in corpus (7)

• A high-bias, low-variance introduction to Machine Learning for physicists
• Quantum annealing with longitudinal bias fields
• Enhancing the efficiency of quantum annealing via reinforcement: A path-integral Monte Carlo simulation of the quantum reinforcement algorithm
• Modernizing Quantum Annealing II: Genetic algorithms with the Inference Primitive Formalism
• Quantum annealing sampling with a bias field
• Quantum walk in a reinforced free-energy landscape: Quantum annealing with reinforcement
• Noise tolerance via reinforcement: Learning a reinforced quantum dynamics