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arXiv:1907.00707

Quantum-Assisted Genetic Algorithm

James A. King, Masoud Mohseni, William Bernoudy, Alexandre Fréchette, Sadeghi, Hossein, Sergei V. Isakov, Hartmut Neven, M. H. S. Amin

Published Jun 24, 2019• 19 citations
arXivHTMLPDF

Abstract

Genetic algorithms, which mimic evolutionary processes to solve optimization problems, can be enhanced by using powerful semi-local search algorithms as mutation operators. Here, we introduce reverse quantum annealing, a class of quantum evolutions that can be used for performing families of quasi-local or quasi-nonlocal search starting from a classical state, as novel sources of mutations. Reverse annealing enables the development of genetic algorithms that use quantum fluctuation for mutations and classical mechanisms for the crossovers -- we refer to these as Quantum-Assisted Genetic Algorithms (QAGAs). We describe a QAGA and present experimental results using a D-Wave 2000Q quantum annealing processor. On a set of spin-glass inputs, standard (forward) quantum annealing finds good solutions very quickly but struggles to find global optima. In contrast, our QAGA proves effective at finding global optima for these inputs. This successful interplay of non-local classical and quantum fluctuations could provide a promising step toward practical applications of Noisy Intermediate-Scale Quantum (NISQ) devices for heuristic discrete optimization.

DOI
10.48550/arxiv.1907.00707

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Genetic algorithms, which mimic evolutionary processes to solve optimization problems, can be enhanced by using powerful semi-local search algorithms as mutation operators. Here, we introduce reverse quantum annealing, a class of quantum evolutions that can be used for performing families of quasi-local or quasi-nonlocal search starting from a classical state, as novel sources of mutations. Reverse annealing enables the development of genetic algorithms that use quantum fluctuation for mutations and classical mechanisms for the crossovers -- we refer to these as Quantum-Assisted Genetic Algorithms (QAGAs). We describe a QAGA and present experimental results using a D-Wave 2000Q quantum annealing processor. On a set of spin-glass inputs, standard (forward) quantum annealing finds good solutions very quickly but struggles to find global optima. In contrast, our QAGA proves effective at finding global optima for these inputs. This successful interplay of non-local classical and quantum fluctuations could provide a promising step toward practical applications of Noisy Intermediate-Scale Quantum (NISQ) devices for heuristic discrete optimization.
A genetic algorithm (GA) is a search-based optimization technique based on the principles of Genetics and Natural Selection. We present an algorithm which enhances the classical GA with input from quantum annealers. As in a classical GA, the algorithm works by breeding a population of possible solutions based on their fitness. However, the population of individuals is defined by the continuous couplings on the quantum annealer, which then give rise via quantum annealing to the set of corresponding phenotypes that represent attempted solutions. This introduces a form of directed mutation into the algorithm that can enhance its performance in various ways. Two crucial enhancements come from the continuous couplings having strengths that are inherited from the fitness of the parents (so-called nepotism) and from the annealer couplings allowing the entire population to be influenced by the fittest individuals (so-called quantum-polyandry). We find our algorithm to be significantly more powerful on several simple problems than a classical GA.
Based on the quantum-assisted genetic algorithm (QAGA) [11] and related approaches we introduce several modifications of QAGA to search for more promising solvers on (at least) graph coloring problems, knapsack problems, Boolean satisfiability problems, and an equal combination of these three. We empirically test the efficiency of these algorithmic changes on a purely classical version of the algorithm (simulated-annealing-assisted genetic algorithm, SAGA) and verify the benefit of selected modifications when using quantum annealing hardware. Our results point towards an inherent benefit of a simpler and more flexible algorithm design.
Abstract Quantum-assisted algorithms are expected to improve the computing performance of classical computers. A quantum genetic algorithm utilizes the advantages of quantum computation by combining the truncation selection in a classical genetic algorithm with the quantum Grover’s algorithm. The parallelism of evaluation can create global search and reduce the need of crossover and mutation in a conventional genetic algorithm. In this work, we aim to demonstrate and simulate the performance of an implementable quantum-assisted genetic algorithm. The algorithm was tested by using quadratic unconstrained binary optimization (QUBO) for 100 iterations; and the results were compared with those from a classical counterpart for 2000 iterations, where both simulations were performed over 100 repetitions. The results showed that the quantum algorithm converges to the optimal solution faster. While the variance is higher at early stage, it quickly and greatly reduces as the algorithm converges. The histograms of possible solutions consistently exhibits this behavior.
Abstract Quantum annealing, a method of computing where optimization and machine learning problems are mapped to physically implemented energy landscapes subject to quantum fluctuations, allows for these fluctuations to be used to assist in finding the solution to some of the world’s most challenging computational problems. Recently, this field has attracted much interest because of the construction of large-scale flux-qubit based quantum annealing devices. These devices have since implemented a technique known as reverse annealing which allows the solution space to be searched locally, and algorithms based on these techniques have been tested. In this paper, I develop a formalism for algorithmic design in quantum annealers, which I call the ‘inference primitive’ formalism. This formalism naturally lends itself to expressing algorithms which are structurally similar to genetic algorithms, but where the annealing processor performs a combined crossover/mutation step. I demonstrate how these methods can be used to understand the algorithms which have already been implemented and the compatibility of such controls with a wide variety of other current efforts to improve the performance of quantum annealers.
Genetic algorithms are widely used for solving optimization problems. As the search space of the problem is augmented, the probability of falling into local minima will be augmented as well. Previous works showed that the adjusted phase (i.e. required modification per generation), may enhance badly the optimality reaching. Moreover, the search for suitable probabilities on crossover and mutation results in huge computational complexity. Recent developments in quantum technology have shown that quantum computers can provide a dramatic advantage over classical computers. This paper will be oriented toward computer scientists interested in the quantum genetic algorithm (QGA). Therefore, we will present a discussion, of the pros, and cons of classical GA. We survey the “state of the art” of the most known techniques for evolving evolutionary algorithms and quantum computing. We intend in this work to help researchers and application developers in gaining insights into the power of quantum computing mechanisms. This science can inherently treat the balance between exploration and exploitation of the search space. This property is due to the use of Q-bits. The orientation toward the best solution is due to the use of Q-gates.
This paper presents a novel approach to complex optimization problems utilizing a hybrid Genetic Algorithm (GA) enhanced with quantum computing techniques. Classical GAs often struggle with slow convergence rates in high-dimensional search spaces. This research addresses this limitation by integrating quantum superposition and interference into the core operations of the GA, specifically crossover and mutation. The proposed method, termed Quantum-Enhanced Genetic Algorithm (Q-GA), aims to significantly accelerate the optimization process by exploring the solution space more efficiently. The core idea is to represent potential solutions within a quantum state, allowing for parallel exploration facilitated by superposition. We detail the architecture of the Q-GA, outlining the integration of classical GA components with quantum algorithms. The performance of the Q-GA is theoretically analyzed, focusing on the potential speedup achievable through quantum computation. The results presented demonstrate the promise of this hybrid approach for tackling computationally intensive optimization problems where classical GAs fall short.