Global Optimization:  Quantum Thermal Annealing with Path Integral Monte Carlo

Lee, Yong-Han; Berne, B. J.

doi:10.1021/jp991868i

Cited by 71 publications

(85 citation statements)

References 54 publications

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“…Lemma 1 (Lower bound on the transition probability) The elements of the transition matrix defined by (2.1), (3.5) and (3.6) have the following lower bound: 16) and…”

Section: Convergence Theorem For Qa-pimcmentioning

confidence: 99%

Convergence theorems for quantum annealing

Morita

Nishimori²

2006

J. Phys. A: Math. Gen.

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Abstract. We prove several theorems to give sufficient conditions for convergence of quantum annealing, which is a protocol to solve generic optimization problems by quantum dynamics. In particular the property of strong ergodicity is proved for the path-integral Monte Carlo implementation of quantum annealing for the transverse Ising model under a power decay of the transverse field. This result is to be compared with the much slower inverse-log decay of temperature in the conventional simulated annealing. Similar results are proved for the Green's function Monte Carlo approach. Optimization problems in continuous space of particle configurations are also discussed.

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“…Lemma 1 (Lower bound on the transition probability) The elements of the transition matrix defined by (2.1), (3.5) and (3.6) have the following lower bound: 16) and…”

Section: Convergence Theorem For Qa-pimcmentioning

confidence: 99%

Convergence theorems for quantum annealing

Morita

Nishimori²

2006

J. Phys. A: Math. Gen.

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“…Some amount of success was obtained in several cases, notably in the folding of off-lattice polymer models 5,6 , in the 2D random Ising model annealing 7,8 , in the Lennard-Jones clusters optimization 9,10 , and in the Traveling Salesman Problem 11 . Despite these successes -mostly obtained by PathIntegral Monte Carlo (PIMC) implementations of QA -there is no general theory addressing and even less predicting the performance of a QA algorithm.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo studies of quantum and classical annealing on a double well

2006

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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.

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“…Subsequent studies 28,29,30,31,32 illustrated that the 46-mer system exhibits a high degree of frustration and its energy landscape is very rugged. That is, there are many local minima with energies close to that of the native state, and it is very difficult to find the global minimum 7,8,10,33 .…”

Section: Introductionmentioning

confidence: 99%

Conformational space annealing and an off-lattice frustrated model protein

Kim

Lee

2003

The Journal of Chemical Physics

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A global optimization method, conformational space annealing (CSA), is applied to study a 46-residue protein with the sequence B 9 N 3 (LB) 4 N 3 B 9 N 3 (LB) 5 L, where B, L and N designate hydrophobic, hydrophilic, and neutral residues, respectively. The 46-residue BLN protein is folded into the native state of a four-stranded β-barrel. It has been a challenging problem to locate the global minimum of the 46-residue BLN protein since the system is highly frustrated and consequently its energy landscape is quite rugged. The CSA successfully located the global minimum of the 46-mer for all 100 independent runs. The CPU time for CSA is about seventy times less than that for simulated annealing (SA), and its success rate (100%) to find the global minimum is about eleven times higher. The amount of computational efforts used for CSA is also about ten times less than that of the best global optimization method yet applied to the 46-residue BLN protein, the quantum thermal annealing with renormalization. The 100 separate CSA runs produce the global minimum 100 times as well as other 5950 final conformations corresponding to a total of 2361 distinct local minima of the protein. Most of the final conformations have relatively small RMSD values from the global minimum, independent of their diverse energy values. Very close to the global minimum, there exist quasi-global-minima which are frequently obtained as one of the final answers from SA runs. We find that there exist two largest energy gaps between the quasi-global-minima and the other local minima. Once a SA run is trapped in one of these quasiglobal-minima, it cannot be folded into the global minimum before crossing over the two large energy barriers, clearly demonstrating the reason for the poor success rate of SA.2

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Global Optimization: Quantum Thermal Annealing with Path Integral Monte Carlo

Cited by 71 publications

References 54 publications

Convergence theorems for quantum annealing

Convergence theorems for quantum annealing

Monte Carlo studies of quantum and classical annealing on a double well

Conformational space annealing and an off-lattice frustrated model protein

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