Performance comparison of optimization methods on variational quantum algorithms

• URL: http://arxiv.org/abs/2111.13454v2
• Date: Tue, 14 Dec 2021 12:46:26 GMT
• Title: Performance comparison of optimization methods on variational quantum algorithms
• Authors: Xavier Bonet-Monroig, Hao Wang, Diederick Vermetten, Bruno Senjean, Charles Moussa, Thomas B\"ack, Vedran Dunjko, Thomas E. O'Brien
• Abstract summary: Variational quantum algorithms (VQAs) offer a promising path towards using near-term quantum hardware for applications in academic and industrial research. We study the performance of four commonly used gradient-free optimization methods: SLSQP, COBYLA, CMA-ES, and SPSA.
• Score: 2.690135599539986
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Variational quantum algorithms (VQAs) offer a promising path towards using near-term quantum hardware for applications in academic and industrial research. These algorithms aim to find approximate solutions to quantum problems by optimizing a parametrized quantum circuit using a classical optimization algorithm. A successful VQA requires fast and reliable classical optimization algorithms. Understanding and optimizing how off-the-shelf optimization methods perform in this context is important for the future of the field. In this work we study the performance of four commonly used gradient-free optimization methods: SLSQP, COBYLA, CMA-ES, and SPSA, at finding ground-state energies of a range of small chemistry and material science problems. We test a telescoping sampling scheme (where the accuracy of the cost-function estimate provided to the optimizer is increased as the optimization converges) on all methods, demonstrating mixed results across our range of optimizers and problems chosen. We further hyperparameter tune two of the four optimizers (CMA-ES and SPSA) across a large range of models, and demonstrate that with appropriate hyperparameter tuning, CMA-ES is competitive with and sometimes outperforms SPSA (which is not observed in the absence of hyperparameter tuning). Finally, we investigate the ability of an optimizer to beat the `sampling noise floor', given by the sampling noise on each cost-function estimate provided to the optimizer. Our results demonstrate the necessity for tailoring and hyperparameter-tuning known optimization techniques for inherently-noisy variational quantum algorithms, and that the variational landscape that one finds in a VQA is highly problem- and system-dependent. This provides guidance for future implementations of these algorithms in experiment.

Related papers

• Bayesian Parameterized Quantum Circuit Optimization (BPQCO): A task and hardware-dependent approach [49.89480853499917]
  Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems. In this paper, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems. We also study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers.
  arXiv  Detail & Related papers  (2024-04-17T11:00:12Z)
• Efficient and Robust Parameter Optimization of the Unitary Coupled-Cluster Ansatz [4.607081302947026]
  We propose sequential optimization with approximate parabola (SOAP) for parameter optimization of unitary coupled-cluster ansatz on quantum computers. Numerical benchmark studies on molecular systems demonstrate that SOAP achieves significantly faster convergence and greater robustness to noise. SOAP is further validated through experiments on a superconducting quantum computer using a 2-qubit model system.
  arXiv  Detail & Related papers  (2024-01-10T03:30:39Z)
• Randomized Benchmarking of Local Zeroth-Order Optimizers for Variational Quantum Systems [65.268245109828]
  We compare the performance of classicals across a series of partially-randomized tasks. We focus on local zeroth-orders due to their generally favorable performance and query-efficiency on quantum systems.
  arXiv  Detail & Related papers  (2023-10-14T02:13:26Z)
• QAOA Performance in Noisy Devices: The Effect of Classical Optimizers and Ansatz Depth [0.32985979395737786]
  The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum algorithm for Near-term Intermediate-Scale Quantum computers (NISQ) This paper presents an investigation into the impact realistic noise on the classical vectors. We find that while there is no significant difference in the performance of classicals in a state simulation, the Adam and AMSGrads perform best in the presence of shot noise.
  arXiv  Detail & Related papers  (2023-07-19T17:22:44Z)
• Quantum approximate optimization via learning-based adaptive optimization [5.399532145408153]
  Quantum approximate optimization algorithm (QAOA) is designed to solve objective optimization problems. Our results demonstrate that the algorithm greatly outperforms conventional approximations in terms of speed, accuracy, efficiency and stability. This work helps to unlock the full power of QAOA and paves the way toward achieving quantum advantage in practical classical tasks.
  arXiv  Detail & Related papers  (2023-03-27T02:14:56Z)
• An Empirical Evaluation of Zeroth-Order Optimization Methods on AI-driven Molecule Optimization [78.36413169647408]
  We study the effectiveness of various ZO optimization methods for optimizing molecular objectives. We show the advantages of ZO sign-based gradient descent (ZO-signGD) We demonstrate the potential effectiveness of ZO optimization methods on widely used benchmark tasks from the Guacamol suite.
  arXiv  Detail & Related papers  (2022-10-27T01:58:10Z)
• Bilevel Optimization: Convergence Analysis and Enhanced Design [63.64636047748605]
  Bilevel optimization is a tool for many machine learning problems. We propose a novel stoc-efficientgradient estimator named stoc-BiO.
  arXiv  Detail & Related papers  (2020-10-15T18:09:48Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA [68.11912614360878]
  Hybrid quantum-classical algorithms such as Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical parameter to find better parameters more easily and hence results in an improved performance.
  arXiv  Detail & Related papers  (2020-03-11T13:52:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.