The Variational Quantum Eigensolver (VQE) algorithm is gaining interest for its potential use in near-term quantum devices. In the VQE algorithm, parameterized quantum circuits (PQCs) are employed to prepare quantum states, which are then utilized to compute the expectation value of a given Hamiltonian. Designing efficient PQCs is crucial for improving convergence speed. In this study, we introduce problem-specific PQCs tailored for optimization problems by dynamically generating PQCs that incorporate problem constraints. This approach reduces a search space by focusing on unitary transformations that benefit the VQE algorithm, and accelerate convergence. Our experimental results demonstrate that the convergence speed of our proposed PQCs outperforms state-of-the-art PQCs, highlighting the potential of problem-specific PQCs in optimization problems.
The Variational Quantum Eigensolver (VQE) algorithm is gaining interest for its potential use in near-term quantum devices. In the VQE algorithm, parameterized quantum circuits (PQCs) are employed to prepare quantum states, which are then utilized to compute the expectation value of a given Hamiltonian. Designing efficient PQCs is crucial for improving convergence speed. In this study, we introduce problem-specific PQCs tailored for optimization problems by dynamically generating PQCs that incorporate problem constraints. This approach reduces a search space by focusing on unitary transformations that benefit the VQE algorithm, and accelerate convergence. Our experimental results demonstrate that the convergence speed of our proposed PQCs outperforms state-of-the-art PQCs, highlighting the potential of problem-specific PQCs in optimization problems.
The Variational Quantum Eigensolver (VQE) algorithm is attracting much attention to utilize current limited quantum devices. The VQE algorithm requires a quantum circuit with parameters, called an entangler circuit, to prepare a quantum state, and calculates the expectation value of a given Hamiltonian. Creating sophisticated entangler circuits is important from the perspective of the convergence speed. Thus, we propose problem-specific entangler circuits of the VQE algorithm for optimization problems. Our idea is to dynamically create an entangler circuit that reflects constraints of an optimization problem. With a problem-specific entangler circuit, it is possible to reduce a search space by restricting unitary transformations in favor of the VQE algorithm. As a result, we can speed up the convergence of the VQE algorithm. Experimental results show that the convergence speed of the proposed method is significantly faster than that of the state-of-the-art method.
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 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.
The variational quantum eigensolver (VQE) is a hybrid algorithm to find the minimum eigenvalue/vector of the given Hamiltonian by optimizing a parameterized quantum circuit (PQC) using a classical computer. Sequential optimization methods, which are often used in quantum circuit tensor networks, are popular for optimizing the parameterized gates of PQCs. In this paper, we focus on the case where the components to be optimized are single-qubit gates, in which the analytic optimization of a single-qubit gate is sequentially performed. The analytical solution is given by diagonalization of a matrix whose elements are computed from the expectation values of observables specified by a set of predetermined parameters, which we refer to as the parameter configurations. In this paper, we first show that the optimization accuracy significantly depends on the choice of parameter configurations owing to the statistical errors in the expectation values. We then identify a metric that quantifies the optimization accuracy of a parameter configuration for all possible statistical errors, named configuration overhead/cost or C-cost. We theoretically provide the lower bound of C-cost and show that, for the minimum size of parameter configurations, the lower bound is achieved if and only if the parameter configuration satisfies the so-called equiangular line condition. Finally, we provide numerical experiments demonstrating that the optimal parameter configuration exhibits the best result in several VQE problems. We hope that this general statistical methodology will enhance the efficacy of sequential optimization of PQCs for solving practical problems with near-term quantum devices.
Abstract Variational Quantum Eigensolver (VQE) addresses challenges that conventional computation struggles to overcome. However, VQE lacks the ability to autonomously trend towards the direction of quantum advantage, leading to unnecessary consumption of time and resources during parameter optimization. In this work, we present a Simulating Dynamic VQE (D-VQE) that incorporates time evolution for achieving desired simulation accuracy and parameter optimization. Introducing causal cones for Parameterized Quantum Circuits (PQC) and establishing dynamic judgment rules. Consequently, we can reduce the overstacking of components in PQC ansatz. Based on the requirements of precision and circuit scale, a reasonable operator pool is set to deal with the parameters. Through numerical experiments, our method effectively simulates the search for the ground state in the transverse-field Ising model, achieving a relative energy error below 10^(-3) and improving ground state approximation capability. Moreover, in the context of optimized Boltzmann machine learning, the Kullback-Leibler divergence (KLD) value converges to 0.03. These results prove that our work provides an effective and feasible consideration for the improvement of variational quantum algorithms.
Despite the advantage quantum computers are expected to deliver when performing simulations compared to their classical counterparts, the current noisy intermediate-scale quantum (NISQ) devices remain limited in their capabilities. The training of parameterized quantum circuits (PQCs) remains a significant practical challenge, exacerbated by the requirement of shallow circuit depth necessary for their hardware implementation. Hybrid methods employing classical computers alongside quantum devices, such as the Variational Quantum Eigensolver (VQE), have proven useful for analyzing the capabilities of NISQ devices to solve relevant optimization problems. Still, in the simulation of complex structures involving the many-body problem in quantum mechanics, major issues remain about the representation of the system and obtaining results which clearly outperform classical computational devices. In this research contribution we propose the use of parameterized Tensor Networks (TNs) to attempt an improved performance of the VQE algorithm. A joint approach is presented where the Hamiltonian of a system is encapsulated into a Matrix Product Operator (MPO) within a parameterized unitary TN hereby splitting up the optimization task between the TN and the VQE. We show that the hybrid TN-VQE implementation improves the convergence of the algorithm in comparison to optimizing randomly-initialized quantum circuits via VQE.