Monte Carlo studies of quantum and classical annealing on a double-well
arXiv:cond-mat/0512064 · doi:10.1103/PhysRevB.73.144302
Abstract
We present results for a variety of Monte Carlo annealing approaches, both classical and quantum, benchmarked against one another for the textbook optimization exercise of a simple one-dimensional double-well. In classical (thermal) annealing, the dependence upon the move chosen in a Metropolis scheme is studied and correlated with the spectrum of the associated Markov transition matrix. In quantum annealing, the Path-Integral Monte Carlo approach is found to yield non-trivial sampling difficulties associated with the tunneling between the two wells. The choice of fictitious quantum kinetic energy is also addressed. We find that a ``relativistic'' kinetic energy form, leading to a higher probability of long real space jumps, can be considerably more effective than the standard one.
arXiv comment15 pages, 10 figures, REVTex 4
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- Simulated quantum annealing as a simulator of non-equilibrium quantum dynamics
- Direct comparison of quantum and simulated annealing on a fully-connected Ising ferromagnet
- Quantum annealing speedup over simulated annealing on random Ising chains
- Simulated quantum annealing of double-well and multi-well potentials
- Quantum annealing of an Ising spin-glass by Green's function Monte Carlo
- Understanding Quantum Tunneling using Diffusion Monte Carlo Simulations
- Thermal, quantum and simulated quantum annealing: analytical comparisons for simple models
- Quantum Monte Carlo simulation of BEC-impurity tunneling