We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between… Expand

Quantum annealing is a generic name of quantum algorithms that use quantum-mechanical fluctuations to search for the solution of an optimization problem. It shares the basic idea with quantum… Expand

We study the statistical properties of an NP-complete problem, the subset sum, using the methods and concepts of statistical mechanics. The problem is a generalization of the number partitioning… Expand

A statistical-mechanical formulation for image restoration and error-correcting codes is developed and it is proved that the quality of restoration/decoding is maximized at a specific set of parameter values determined by the source and channel properties.Expand

This work introduces antiferromagnetic quantum fluctuations into quantum annealing in addition to the conventional transverse-field term and finds that there exists a quantum path to reach the final ground state from the trivial initial state that avoids first-order transitions for intermediate values of p.Expand

This perspectives article first gives a brief introduction to the concept of quantum annealing, and then highlights new pathways that may clear the way towards feasible and large scale quantumAnnealing.Expand

Analytical studies of Hamiltonians with infinite-range non-random as well as random interactions from the perspective of possible enhancement of the efficiency of quantum annealing or adiabatic quantum computing show that multi-body transverse interactions render the Hamiltonian non-stoquastic and reduce a first-order quantum phase transition in the simple transverse-field case to a second-order transition.Expand

We study the performance of quantum annealing for systems with ground-state degeneracy by directly solving the Schrodinger equation for small systems and quantum Monte Carlo simulations for larger… Expand