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Quantum annealing in the transverse Ising model
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…
Statistical Physics of Spin Glasses and Information Processing
- H. Nishimori
- 19 July 2001
Mathematical foundation of quantum annealing
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…
Internal Energy, Specific Heat and Correlation Function of the Bond-Random Ising Model
- H. Nishimori
- 1 October 1981
Statistical Mechanics of an NP-complete Problem: Subset Sum
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…
Statistical mechanics of image restoration and error-correcting codes.
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.
Quantum annealing with antiferromagnetic fluctuations.
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.
Perspectives of quantum annealing: Methods and implementations.
- P. Hauke, H. Katzgraber, W. Lechner, H. Nishimori, W. Oliver
- PhysicsReports on progress in physics. Physical Society
- 15 March 2019
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.
Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stoquastic Hamiltonians
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.
Ground-state statistics from annealing algorithms: quantum versus classical approaches
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…