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Spin Glass Patch Planting

Wenlong Wang, Salvatore Mandrà, Helmut G. Katzgraber

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

In this paper, we propose a patch planting method for creating arbitrarily large spin glass instances with known ground states. The scaling of the computational complexity of these instances with various block numbers and sizes is investigated and compared with random instances using population annealing Monte Carlo and the quantum annealing DW2X machine. The method can be useful for benchmarking tests for future generation quantum annealing machines, classical and quantum mechanical optimization algorithms.

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In this paper, we propose a patch planting method for creating arbitrarily large spin glass instances with known ground states. The scaling of the computational complexity of these instances with various block numbers and sizes is investigated and compared with random instances using population annealing Monte Carlo and the quantum annealing DW2X machine. The method can be useful for benchmarking tests for future generation quantum annealing machines, classical and quantum mechanical optimization algorithms.
There has been considerable progress in the design and construction of quantum annealing devices. However, a conclusive detection of quantum speedup over traditional silicon-based machines remains elusive, despite multiple careful studies. In this work we outline strategies to design hard tunable benchmark instances based on insights from the study of spin glasses - the archetypal random benchmark problem for novel algorithms and optimization devices. We propose to complement head-to-head scaling studies that compare quantum annealing machines to state-of-the-art classical codes with an approach that compares the performance of different algorithms and/or computing architectures on different classes of computationally hard tunable spin-glass instances. The advantage of such an approach lies in having to only compare the performance hit felt by a given algorithm and/or architecture when the instance complexity is increased. Furthermore, we propose a methodology that might not directly translate into the detection of quantum speedup, but might elucidate whether quantum annealing has a "`quantum advantage" over corresponding classical algorithms like simulated annealing. Our results on a 496 qubit D-Wave Two quantum annealing device are compared to recently-used state-of-the-art thermal simulated annealing codes.
Population annealing Monte Carlo is an efficient sequential algorithm for simulating kkk-local Boolean Hamiltonians. Because of its structure, the algorithm is inherently parallel and therefore well suited for large-scale simulations of computationally hard problems. Here we present various ways of optimizing population annealing Monte Carlo using 2-local spin-glass Hamiltonians as a case study. We demonstrate how the algorithm can be optimized from an implementation, algorithmic accelerator, as well as scalable parallelization points of view. This makes population annealing Monte Carlo perfectly suited to study other frustrated problems such as pyrochlore lattices, constraint-satisfaction problems, as well as higher-order Hamiltonians commonly found in, e.g., topological color codes.
Spin glasses are disordered magnets with random interactions that are, generally, in conflict with each other. Finding the ground states of spin glasses is not only essential for the understanding of the nature of disordered magnetic and other physical systems, but also useful to solve a broad array of hard combinatorial optimization problems across multiple disciplines. Despite decades-long efforts, an algorithm with both high accuracy and high efficiency is still lacking. Here we introduce DIRAC - a deep reinforcement learning framework, which can be trained purely on small-scale spin glass instances and then applied to arbitrarily large ones. DIRAC displays better scalability than other methods and can be leveraged to enhance any thermal annealing method. Extensive calculations on 2D, 3D and 4D Edwards-Anderson spin glass instances demonstrate the superior performance of DIRAC over existing methods. As many hard combinatorial optimization problems have Ising spin glass formulations, our results suggest a promising tool in solving these hard problems. Moreover, the presented algorithm will help us better understand the nature of the low-temperature spin-glass phase, which is a fundamental challenge in statistical physics.
In the era of quantum technology, benchmarking classical algorithms is necessary for certifying the results given by the quantum device to the optimization problem that is wanted to solve. Here we analyse a new algorithm that gives an upper and a lower bound to the ground state solution of Ising type optimization problems. We test its performance in solution planted problems and compare it with simulated annealing, a common algorithm to solve optimization problems, getting in general more reliable results in the same amount of time. Additionally, we verify the tunable hardness of the planting schemes used to generate the optimization problems.
Spin glasses are disordered magnets with random interactions that are, generally, in conflict with each other. Finding the ground states of spin glasses is not only essential for understanding the nature of disordered magnets and many other physical systems, but also useful to solve a broad array of hard combinatorial optimization problems across multiple disciplines. Despite decades-long efforts, an algorithm with both high accuracy and high efficiency is still lacking. Here we introduce DIRAC - a deep reinforcement learning framework, which can be trained purely on small-scale spin glass instances and then applied to arbitrarily large ones. DIRAC displays better scalability than other methods and can be leveraged to enhance any thermal annealing method. Extensive calculations on 2D, 3D and 4D Edwards-Anderson spin glass instances demonstrate the superior performance of DIRAC over existing methods. The presented framework will help us better understand the nature of the low-temperature spin-glass phase, which is a fundamental challenge in statistical physics. Moreover, the gauge transformation technique adopted in DIRAC builds a deep connection between physics and artificial intelligence. In particular, this opens up a promising avenue for reinforcement learning models to explore in the enormous configuration space, which would be extremely helpful to solve many other hard combinatorial optimization problems.
We are interested in benchmarking both quantum annealing and classical algorithms for minimizing quadratic unconstrained binary optimization (QUBO) problems. Such problems are NP-hard in general, implying that the exact minima of randomly generated instances are hard to find and thus typically unknown. While brute forcing smaller instances is possible, such instances are typically not interesting due to being too easy for both quantum and classical algorithms. In this contribution, we propose a novel method, called posiform planting, for generating random QUBO instances of arbitrary size with known optimal solutions, and use those instances to benchmark the sampling quality of four D-Wave quantum annealers utilizing different interconnection structures (Chimera, Pegasus, and Zephyr hardware graphs) and the simulated annealing algorithm. Posiform planting differs from many existing methods in two key ways. It ensures the uniqueness of the planted optimal solution, thus avoiding groundstate degeneracy, and it enables the generation of QUBOs that are tailored to a given hardware connectivity structure, provided that the connectivity is not too sparse. Posiform planted QUBOs are a type of 2-SAT boolean satisfiability combinatorial optimization problems. Our experiments demonstrate the capability of the D-Wave quantum annealers to sample the optimal planted solution of combinatorial optimization problems with up to 5, 627 qubits.