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The Journal of Physical Chemistry A

Quantum Thermal Annealing with Renormalization: Application to a Frustrated Model Protein

Yong-Han Lee, B. J. Berne

Published Dec 8, 2000• 23 citations
Publisher

Abstract

A renormalization approach is introduced in quantum thermal annealing. This new global optimization algorithm (QTAR) is applied to a highly frustrated BLN model protein with 46 residues. The underlying quantum sampling algorithms utilized are primitive and staging path integral Monte Carlo. The current method enables us to achieve significant improvement in the success rate for locating the global minimum of this protein, while using much less computational effort, compared to previous schemes used. Further applications and possible enhancements of the algorithm are also discussed.

DOI
10.1021/jp002589u

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A renormalization approach is introduced in quantum thermal annealing. This new global optimization algorithm (QTAR) is applied to a highly frustrated BLN model protein with 46 residues. The underlying quantum sampling algorithms utilized are primitive and staging path integral Monte Carlo. The current method enables us to achieve significant improvement in the success rate for locating the global minimum of this protein, while using much less computational effort, compared to previous schemes used. Further applications and possible enhancements of the algorithm are also discussed.
The details of an efficient global optimization approach, quantum thermal annealing with renormalization (QTAR) (Y. H. Lee and B. J. Berne, J. Phys. Chem. A, in press (2000)) are presented in this paper. This method is based on the application of the Migdal-Kadanoff method for decimating Trotter time slices in the staging and primitive algorithms for sampling path integrals using Monte Carlo methods. In a nutshell, one starts in a strong quantum regime where the number of Trotter beads representing each quantum particle and the value of Planck's constant are large, thereby allowing for efficient tunneling through the barriers of a rough energy landscape typical in the folding of proteins, and anneals the system methodically to the classical limit where the values of the aforementioned quantities are 1 and 0, respectively. Global optimization of the system is achieved through the iterative use of such quantum-to-classical annealing cycles. The QTAR algorithm applied to a highly frustrated BLN model protein with 46 residues more efficiently locates the global energy minimum than established methods like simulated annealing.
Abstract The details of an efficient global optimization approach, quantum thermal annealing with renormalization (QTAR) (Y. H. Lee and B. J. Berne, J. Phys. Chem. A, in press (2000)) are presented in this paper. This method is based on the application of the Migdal‐Kadanoff method for decimating Trotter time slices in the staging and primitive algorithms for sampling path integrals using Monte Carlo methods. In a nutshell, one starts in a strong quantum regime where the number of Trotter beads representing each quantum particle and the value of Planck's constant are large, thereby allowing for efficient tunneling through the barriers of a rough energy landscape typical in the folding of proteins, and anneals the system methodically to the classical limit where the values of the aforementioned quantities are 1 and 0, respectively. Global optimization of the system is achieved through the iterative use of such quantum‐to‐classical annealing cycles. The QTAR algorithm applied to a highly frustrated BLN model protein with 46 residues more efficiently locates the global energy minimum than established methods like simulated annealing.
Quantum annealing was recently found experimentally in a disordered spin-12\frac{1}{2}21​ magnet to be more effective than its classical, thermal counterpart. We use the random two-dimensional Ising model as a test example and perform on it both classical and quantum (path-integral) Monte Carlo annealing. A systematic study of the dependence of the final residual energy on the annealing Monte Carlo time quantitatively demonstrates the superiority of quantum relative to classical annealing in this system. In order to determine the parameter regime for optimal efficiency of the quantum annealing procedure we explore a range of values of Trotter slice number P and temperature T. This identifies two different regimes of freezing with respect to efficiency of the algorithm, and leads to useful guidelines for the optimal choice of quantum annealing parameters.
Finding the global minimum of a potential energy surface is a fundamental challenge in materials science, with applications ranging from protein folding to cluster physics and, more broadly, to systems in which the number of (meta)stable configurations grows prohibitively large. In recent decades, quantum annealing (QA) has emerged as a promising global optimization strategy, exploiting quantum fluctuations in contrast to the thermal fluctuations that drive its classical counterpart. Here, we introduce a novel implementation of QA based on path-integral molecular dynamics, an efficient and well-established framework for sampling the quantum nuclear density without the need to manipulate many-body wavefunctions explicitly. While retaining the flexibility and simplicity of molecular dynamics simulations, this quantum-annealing protocol delivers strong performance across a wide range of atomic systems, simulated by either empirical force fields or machine-learning interatomic potentials. The method can be used either as a global optimizer of the potential-energy surface, or as a quantum-informed structure-search strategy in which nuclear quantum effects are included directly in the optimization workflow -- a feature particularly relevant for materials such as high-pressure hydrides.
This article considers quantum annealing in the Ising framework for solving combinatorial optimization problems. The path-integral Monte Carlo simulation approach is often used to approximate quantum annealing and implement the approximation by classical computers, which refers to simulated quantum annealing (SQA). In this article, we introduce a data augmentation scheme into SQA and develop a new algorithm for its implementation. The proposed algorithm reveals new insights on the sampling behaviors in SQA. Theoretical analyses are established to justify the algorithm, and numerical studies are conducted to check its performance and to confirm the theoretical findings. Supplementary materials for this article are available online.
A new unbiased global optimization approach is proposed, based on quantum staging path integral Monte Carlo sampling and local minimization of individual imaginary time slices. This algorithm uses the quantum tunneling effect to speed up the crossing of energy barriers. This method differs in important ways from previous work on quantum annealing and is able to find all the global minima of Lennard-Jones clusters of size up to N=100, except for N=76, 77, and 98. The comparison between this new algorithm and several other classes of algorithms is presented.