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Journal of Signal Processing

Fundamental Research on Applying Artificial Bee Colony Algorithm to an Optimizer in Variational Quantum Eigensolver

Kotaro Murayama, Yoshifumi Moriyama, Ichiro Iimura, Shigeru Nakayama

Published Dec 31, 2024• 0 citations
Publisher

Abstract

The variational quantum eigensolver (VQE), a hybrid algorithm combining quantum and classical computing, has attracted significant interest. As an optimizer for VQE, gradient-based methods are frequently used. However, in the presence of complex optimization landscapes, these methods may struggle to search for a globally optimal solution. In this study, we applied the artificial bee colony (ABC) algorithm as an optimizer for VQE, which is a robust swarm intelligence for the optimization of high-dimensional functions. We conducted experiments to investigate the effectiveness of the ABC algorithm in solving number partitioning problems (NPPs) of 4, 5, 6, and 8 sizes. The results showed that an ansatz with fewer blocks yielded superior results for NPPs of these sizes. In this context, “block" refers to a pair of entanglement and rotation layers. The parameters related to the local search in the ABC algorithm, which is the number of iterations to abandon, should be increased in the quantum circuit used in this study. Additionally, the population size should be increased in accordance with the size of the problem to be solved. The objective of this research is to contribute to the selection of optimizers for VQE, with a focus on the problem to be solved, and to contribute to the improvement of VQE performance, which has been a significant area of interest in the noisy intermediate-scale quantum era.

DOI
10.2299/jsp.29.1

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The variational quantum eigensolver (VQE), a hybrid algorithm combining quantum and classical computing, has attracted significant interest. As an optimizer for VQE, gradient-based methods are frequently used. However, in the presence of complex optimization landscapes, these methods may struggle to search for a globally optimal solution. In this study, we applied the artificial bee colony (ABC) algorithm as an optimizer for VQE, which is a robust swarm intelligence for the optimization of high-dimensional functions. We conducted experiments to investigate the effectiveness of the ABC algorithm in solving number partitioning problems (NPPs) of 4, 5, 6, and 8 sizes. The results showed that an ansatz with fewer blocks yielded superior results for NPPs of these sizes. In this context, “block" refers to a pair of entanglement and rotation layers. The parameters related to the local search in the ABC algorithm, which is the number of iterations to abandon, should be increased in the quantum circuit used in this study. Additionally, the population size should be increased in accordance with the size of the problem to be solved. The objective of this research is to contribute to the selection of optimizers for VQE, with a focus on the problem to be solved, and to contribute to the improvement of VQE performance, which has been a significant area of interest in the noisy intermediate-scale quantum era.
In this paper, a novel hybrid Artificial Bee Colony (ABC) and Quantum Evolutionary Algorithm (QEA) is proposed for solving continuous optimization problems. ABC is adopted to increase the local search capacity as well as the randomness of the populations. In this way, the improved QEA can jump out of the premature convergence and find the optimal value. To show the performance of our proposed hybrid QEA with ABC, a number of experiments are carried out on a set of well-known Benchmark continuous optimization problems and the related results are compared with two other QEAs: the QEA with classical crossover operation, and the QEA with 2-crossover strategy. The experimental comparison results demonstrate that the proposed hybrid ABC and QEA approach is feasible and effective in solving complex continuous optimization problems.
Variational quantum algorithms have promising applications in noisy intermediate-scale quantum (NISQ) devices. These algorithms rely on a classical optimization outer loop that minimizes a parameterized quantum circuit function. The optimization in variational quantum eigensolver (VQE) is NP-hard, meaning that finding the optimal solution is infeasible in the worst-case scenario. One way to address this challenge is through parallel optimization of parameters using multiple-parameterized quantum circuits. However, this approach is unsuitable for cloud-based quantum processing unit utilization due to the increased number of quantum circuit executions. Although NISQ devices have limitations in terms of gate depth, their size has been growing in recent years. Therefore, implementing multiple-parameterized quantum circuits in NISQ devices can suppress the increase in the number of executions. In this study, we propose a parallel-VQE, which leverages the parallel execution of parameterized quantum circuits to perform parallel parameter optimization in VQE, achieving convergence to solutions closer to the ground state. We validate the effectiveness of parallel-VQE in solving the random weighted max-cut problem using numerical simulations and a real quantum device. We present the results of running up to six circuits in parallel (120 qubits) and demonstrate the advantages of using multiple units to improve computational accuracy. This study provides a potential method for solving eigenvalue problems and combinatorial optimization problems for future quantum devices.
In the field of finding ground and excited states, where quantum computation holds significant promise, using a variational quantum eigensolver (VQE) is a typical approach. However, the success of this approach is vulnerable to two factors: classical optimization for the ansätz parameters and noise from quantum devices. To address these challenges, we adopted particle swarm optimization (PSO) based on swarm intelligence for VQE and presented its performance. Furthermore, a modified PSO, gradient-based adaptive quantum-behaved particle swarm optimization (GAQPSO), is proposed. This algorithm adaptively upgrades parameters based on gradients or shared information within the swarm, enhancing optimization capability and noise resistance. We tested this algorithm using VQE simulations on several molecular systems with different geometries and found that, when using random initial values, GAQPSO achieves accurate results even in the presence of noise, whereas traditional PSO, QPSO, COBYLA, and gradient-based algorithms (GD and L-BFGS-B) fail. The GAQPSO algorithm presents a novel approach to optimizing VQE, demonstrating superior performance in parameter optimization and noise resilience compared to traditional optimization algorithms. This effectively advances the process of achieving a quantum advantage for quantum computing in quantum chemistry problems.
To enhance the performance of the artificial bee colony optimization by integrating the quantum computing model into bee colony optimization, we present a quantum-inspired bee colony optimization algorithm. In our method, the bees are encoded with the qubits described on the Bloch sphere. The classical bee colony algorithm is used to compute the rotation axes and rotation angles. The Pauli matrices are used to construct the rotation matrices. The evolutionary search is achieved by rotating the qubit about the rotation axis to the target qubit on the Bloch sphere. By measuring with the Pauli matrices, the Bloch coordinates of qubit can be obtained, and the optimization solutions can be presented through the solution space transformation. The proposed method can simultaneously adjust two parameters of a qubit and automatically achieve the best match between two adjustment quantities, which may accelerate the optimization process. The experimental results show that the proposed method is obviously superior to the classical one for some benchmark functions.
Variational Quantum Eigensolver (VQE) has emerged as a prominent hybrid quantum-classical algorithm for near-term quantum computing, particularly in applications like quantum machine learning. However, the performance of VQE is significantly constrained by the limitations of classical optimization methods employed to minimize the expectation value of the Hamiltonian. Traditional VQE approaches often suffer from slow convergence and sensitivity to initial conditions, particularly when dealing with complex, high-dimensional problems encountered in machine learning scenarios. This work introduces a novel adaptive quantum computing framework for VQE optimization, designed to dynamically adjust the quantum circuit parameters during the optimization process. By continuously monitoring the optimization progress and intelligently modifying the parameters, we aim to accelerate convergence and improve the robustness of VQE algorithms for machine learning tasks. The core idea is to shift from a static, fixed-parameter VQE to a dynamic, adaptive one. We explore various adaptive control strategies and demonstrate their potential to significantly reduce the number of iterations required to reach a solution, leading to improved computational efficiency and enabling VQE to tackle more complex machine learning problems within the constraints of current quantum hardware. The research focuses on the theoretical underpinnings and the design principles of this adaptive approach, laying the foundation for future implementations and experimental validation.
Variational quantum algorithms are a promising hybrid framework for solving chemistry and physics problems with broad applicability to optimization as well. They are particularly well suited for noisy intermediate-scale quantum computers. In this paper we describe the unitary block optimization scheme (UBOS) and apply it to two variational quantum algorithms: the variational quantum eigensolver (VQE) and variational time evolution. The goal of VQE is to optimize a classically intractable parameterized quantum wave function to target a physical state of a Hamiltonian or solve an optimization problem. UBOS is an alternative to other VQE optimization schemes with a number of advantages, including fast convergence, less sensitivity to barren plateaus, the ability to tunnel through some local minima, and no hyperparameters to tune. We additionally describe how UBOS applies to real and imaginary time-evolution (TUBOS).