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IEEE International Conference on Rebooting Computing (ICRC)

Accelerating VQE Algorithm via Parameters and Measurement Reuse

Xinpeng Li, Ji Liu, Ethan H. Hansen, Shuai Xu, Paul Hovland, Vipin Chaudhary

Published Dec 5, 2023• 1 citation
Publisher

Abstract

The Variational Quantum Eigensolver (VQE), a quantum-classical hybrid algorithm, holds significant potential for advancements in quantum chemistry and optimization tasks. Our study focuses on accelerating the VQE in combinatorial optimization tasks such as Max-Cut, k-Clique, and k-SAT, while addressing the challenges of scalability and measurement overhead in quantum devices. Notably, while solving one problem, it allows us to concurrently compute essential information like expectation values and gradients for multiple other problems. This capability is made feasible because combinatorial optimization problems often share the same measurement basis. Drawing inspiration from this insight, we introduce a method that efficiently solves multiple problems by appropriately selecting their initial points. Subsequently, we propose two selection strategies for the method. Employing these strategies can, to some extent, help avoid the issue of becoming trapped in local optima, thus leading to improved accuracy. Our tests on 5-node and 10-node graphs for Max-Cut and k-Clique show that, in some cases, our method outperforms random initialization in terms of both accuracy and number of iterations.

DOI
10.1109/icrc60800.2023.10386370

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The Variational Quantum Eigensolver (VQE), a quantum-classical hybrid algorithm, holds significant potential for advancements in quantum chemistry and optimization tasks. Our study focuses on accelerating the VQE in combinatorial optimization tasks such as Max-Cut, k-Clique, and k-SAT, while addressing the challenges of scalability and measurement overhead in quantum devices. Notably, while solving one problem, it allows us to concurrently compute essential information like expectation values and gradients for multiple other problems. This capability is made feasible because combinatorial optimization problems often share the same measurement basis. Drawing inspiration from this insight, we introduce a method that efficiently solves multiple problems by appropriately selecting their initial points. Subsequently, we propose two selection strategies for the method. Employing these strategies can, to some extent, help avoid the issue of becoming trapped in local optima, thus leading to improved accuracy. Our tests on 5-node and 10-node graphs for Max-Cut and k-Clique show that, in some cases, our method outperforms random initialization in terms of both accuracy and number of iterations.
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.
ABSTRACT: Even if the quantum computing popularity has recently grown, the currently-available technology is not ready for a fundamental revolution of informatics. In this transition phase, hybrid quantum-classical algorithms can help in understanding the real power that this novel paradigm can reach in the future. In this work, we tested the capability of two such algorithms to solve combinatorial optimization problems: the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We used them to solve max-cut problems, consisting of separating the vertices of an undirected graph in two sub-groups so that the number of edges connecting vertices of different sub-groups is maximal. To do that, we mapped the problem into a quantum system, using the Ising formalism. In particular, we investigated the effect of changing the number of measurements of the quantum circuit associated with the system on the algorithms convergence. A large number of measurements (or shots) allows a better knowledge of the quantum state, but on the other hand, increases the convergence time, making the algorithms less competitive compared to classical techniques. The results showed that VQE needs a mínimum number of measurements to start converging towards the optimal problem solution. Once this threshold is overcome, the solution improves as 1/√shots. QAOA, on the other hand, does not seem to converge, independently of the number of shots.
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.
A variational quantum eigensolver (VQE) optimizes parametrized eigenstates of a Hamiltonian on a quantum processor by updating parameters with a classical computer. Such a hybrid quantum-classical optimization serves as a practical way to leverage classical algorithms in exploiting the power of near-term quantum devices. Here, aiming to solve a group of Hamiltonians more efficiently, we develop an extension of the conventional VQE. A snake algorithm is incorporated to couple optimizing processes for VQEs of different Hamiltonians by gradient descent. Such a so-called collective VQE (CVQE) is applied to simulate molecules with varied bond lengths for demonstration. Numeral simulations show that the CVQE exhibits clear collective behavior in the optimization process of updating parameters. Remarkably, the CVQE tends to avoid a single VQE task to be trapped in the local minimum. The collective optimization utilizes intrinsic relations between related tasks and may inspire advanced hybrid quantum-classical algorithms for solving practical problems with current quantum technologies.
This paper investigates the potential of quantum computing to accelerate combinatorial optimization algorithms. Traditional combinatorial optimization problems, such as the Traveling Salesperson Problem (TSP) and the Integer Linear Programming (ILP), often require exponential time to solve with classical algorithms. We propose a framework leveraging quantum algorithms, specifically the Variational Quantum Eigensolver (VQE), to tackle these problems. The core idea involves mapping the optimization problem into a quantum circuit, where the VQE algorithm iteratively refines a quantum state to find the optimal solution. We explore the theoretical underpinnings of this approach, focusing on the challenges and opportunities associated with quantum state preparation, measurement, and error mitigation. The paper provides a conceptual outline of the methodology and discusses potential improvements and future research directions. We demonstrate the feasibility of applying quantum computing to combinatorial optimization and highlight the potential for significant speedups compared to classical methods, especially as quantum hardware matures.
Abstract Even a minor boost in solving combinatorial optimization problems can greatly benefit multiple industries. Quantum computers, with their unique information processing capabilities, hold promise for delivering such enhancements. The filtering variational quantum eigensolver (F-VQE) is a variational hybrid quantum algorithm designed to solve combinatorial optimization problems on existing quantum computers with limited qubit number, connectivity, and fidelity. In this work we employ instantaneous quantum polynomial circuits as our parameterized quantum circuits. We propose a hardware-efficient implementation that respects limited qubit connectivity and show that they halve the number of circuits necessary to evaluate the gradient with the parameter-shift rule. To assess the potential of this protocol in the context of combinatorial optimization, we conduct extensive numerical analysis. We compare the performance against three classical baseline algorithms on weighted MaxCut and the asymmetric traveling salesperson problem (ATSP). We employ noiseless simulators for problems encoded on 13–29 qubits, and up to 37 qubits on the IBMQ real quantum devices. The ATSP encoding employed reduces the number of qubits and avoids the need of constraints compared to the standard quadratic unconstrained binary optimization/Ising model. Despite some observed positive signs, we conclude that significant development is necessary for a practical advantage with F-VQE.