The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum optimization technique used for solving combinatorial optimization problems. However, in constrained binary optimization, QAOA’s reliance on equal initial probabilities for all solutions can lead to suboptimal outcomes. To enhance the performance of QAOA in this context, we propose a novel approach that combines QAOA with genetic algorithms. In this hybrid approach, the results obtained from QAOA serve as the initial population for a genetic algorithm. We apply this methodology to address the k-heaviest subgraph problem, a critical challenge in quantum computing research. Our experiments, conducted on benchmark datasets, demonstrate a significant improvement in solution quality.
The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum optimization technique used for solving combinatorial optimization problems. However, in constrained binary optimization, QAOA’s reliance on equal initial probabilities for all solutions can lead to suboptimal outcomes. To enhance the performance of QAOA in this context, we propose a novel approach that combines QAOA with genetic algorithms. In this hybrid approach, the results obtained from QAOA serve as the initial population for a genetic algorithm. We apply this methodology to address the k-heaviest subgraph problem, a critical challenge in quantum computing research. Our experiments, conducted on benchmark datasets, demonstrate a significant improvement in solution quality.
The Quantum Approximate Optimization Algorithm (QAOA) is emerging as a key method in quantum optimization. Operating within the framework of variational quantum circuits, QAOA entails training a parameterized quantum circuit through classical optimizers to effectively address combinatorial optimization problems. In this context, evolutionary algorithms such as genetic algorithms are emerging as suitable methodologies to search the optimal parameters for QAOA circuits. However, unfortunately, the training process results in a computationally intensive task, and, as a consequence, it is crucial to explore innovative strategies to address this issue. This work introduces a novel approach based on Fuzzy C-means algorithm to opportunely initialize the population of the genetic algorithms employed as optimizers for QAOA and, as a consequence, enhance the training. Experimental results demonstrate that the proposed approach significantly improves the performance of genetic algorithms-based training for QAOA.
Quantum computing is an emerging field on the multidisciplinary interface between physics, engineering, and computer science with the potential to make a large impact on computational intelligence (CI). The aim of this paper is to introduce quantum approximate optimization methods to the CI community because of direct relevance to solving combinatorial problems. We introduce quantum computing and variational quantum algorithms (VQAs). VQAs are an effective method for the near-term implementation of quantum solutions on noisy intermediate-scale quantum (NISQ) devices with less reliable qubits and early-stage error correction. Then, we explain Farhi et al.'s quantum approximate optimization algorithm (Farhi's QAOA, to prevent confusion). This VQA is generalized by Hadfield et al. to the quantum alternating operator ansatz (QAOA), which is a nature-inspired (particularly, adiabatic) quantum metaheuristic for approximately solving combinatorial optimization problems on gate-based quantum computers. We discuss connections of QAOA to relevant domains, such as computational learning theory and genetic algorithms, discussing current techniques and known results regarding hybrid quantum-classical intelligence systems. We present a schematic of how QAOA is constructed, and also discuss how CI techniques can be used to improve QAOA. We conclude with QAOA implementations for the well-known maximum cut, maximum bisection, and traveling salesperson problems, which can serve as templates for CI practitioners interested in using QAOA.
Quantum computing is a promising technology that may provide breakthrough solutions to today’s difficult problems such as breaking encryption and solving large-scale combinatorial optimization problems. A class of algorithms referred to as Quantum Approximate Optimization Algorithm (QAOA) have been recently proposed. QAOA attempts to approximately solve hard problems using a protocol know as bang-bang. The technique is based on the unitary evolution using a Hamiltonian encoding of the objective function of the combinatorial optimization problem. QAOA has been explored in the context of several optimization problems such as Max-Cut problem, variational Eigenvalue problem etc. Recently, attempts have been made to create QAOA for the Traveling Salesman Problem (TSP). Due to small node size and limited solution capability of the currently available Quantum computers and/or simulators, we develop a hybrid approach where subgraphs of a TSP tour are executed on a Quantum computer and the results from the quantum optimization are combined in further optimization of the whole tour. Since the local optimization of a subgraph is prone to getting stuck in a local minima, we overcome this problem by using a parallel Ant Colony Optimization Algorithm with periodic pheromone exchange between colonies. Our results are encouraging and yield optimum results for benchmarks with less than 50 nodes, and usually within 1% of the optimal solution for benchmarks with around 200 nodes.
The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical algorithm to solve binary-variable optimization problems. Due to its expected robustness to systematic errors and the short circuit depth, it is one of the promising candidates likely to run on near-term quantum devices. We project the performance of QAOA applied to the Max-Cut problem and compare it with some of the best classical alternatives, both for exact or approximate solution. When comparing approximate solvers, their performance is characterized by the computational time taken to achieve a given quality of solution. Since QAOA is based on sampling, we introduce performance metrics based on the probability of observing a sample above a certain quality. In addition, we show that the QAOA performance varies significantly with the graph type. By selecting a suitable optimizer for the variational parameters and reducing the number of function evaluations, QAOA performance improves by up to 2 orders of magnitude compared to previous estimates. Especially for 3-regular random graphs, this setting decreases the performance gap with classical alternatives.
Test case optimization (TCO) reduces the software testing cost while preserving its effectiveness. However, to solve TCO problems for large-scale and complex software systems, substantial computational resources are required. Quantum approximate optimization algorithms (QAOAs) are promising combinatorial optimization algorithms that rely on quantum computational resources, with the potential to offer increased efficiency compared to classical approaches. Several proof-of-concept applications of QAOAs for solving combinatorial problems, such as portfolio optimization, energy optimization in power systems, and job scheduling, have been proposed. Given the lack of investigation into QAOA's application for TCO problems, and motivated by the computational challenges of TCO problems and the potential of QAOAs, we present IGDec-QAOA to formulate a TCO problem as a QAOA problem and solve it on both ideal and noisy quantum computer simulators, as well as on a real quantum computer. To solve bigger TCO problems that require many qubits, which are unavailable these days, we integrate a problem decomposition strategy with the QAOA. We performed an empirical evaluation with five TCO problems and four publicly available industrial datasets from ABB, Google, and Orona to compare various configurations of IGDec-QAOA, assess its decomposition strategy of handling large datasets, and compare its performance with classical algorithms (i.e., Genetic Algorithm (GA) and Random Search). Based on the evaluation results achieved on an ideal simulator, we recommend the best configuration of our approach for TCO problems. Also, we demonstrate that our approach can reach the same effectiveness as GA and outperform GA in two out of five test case optimization problems we conducted. In addition, we observe that, on the noisy simulator, IGDec-QAOA achieved similar performance to that from the ideal simulator. Finally, we also demonstrate the feasibility of IGDec-QAOA on a real quantum computer in the presence of noise.
Quantum Genetic Algorithms (QGA) integrate genetic programming and quantum computing to address search and optimization problems. The standard strategy of the hybrid QGA approach is to add quantum resources to classical genetic algorithms (GA), thus improving their efficacy (i.e., quantum optimization of a classical algorithm). However, the extent of such improvements is still unclear. Conversely, Reduced Quantum Genetic Algorithm (RQGA) is a fully quantum algorithm that reduces the GA search for the best fitness in a population of potential solutions to running Grover's algorithm. Unfortunately, RQGA finds the best fitness value and its corresponding chromosome (i.e., the solution or one of the solutions of the problem) in exponential runtime, [[EQUATION]], where [[EQUATION]] is the number of qubits in the individuals' quantum register. This paper introduces a novel QGA optimization strategy, namely a classical optimization of a fully quantum algorithm, to address the Reduced Quantum Genetic Algorithm (RQGA) complexity problem. Accordingly, we control the complexity of theReduced Quantum Genetic Algorithm (RQGA) algorithm by selecting a limited number of qubits in the individuals' register and fixing the remaining ones as classical values of '0' and '1' with a genetic algorithm. We also improve the performance of RQGA by discarding unfit solutions and bounding the search only in the area of valid individuals. As a result, our Hybrid Quantum Algorithm with Genetic Optimization (HQAGO) solves search problems in [[EQUATION]] oracle queries, where [[EQUATION]] is the number of fixed classical bits in the individuals' register.