Performance comparison of optimization methods on variational quantum algorithms

Abstract

Variational quantum algorithms (VQAs) offer a promising path toward 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 the experiment.

Published version

References in corpus (5)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• Is the Trotterized UCCSD Ansatz chemically well-defined?
• A Stochastic Approach to Unitary Coupled Cluster
• Quantum Computational Advantage via 60-Qubit 24-Cycle Random Circuit Sampling

Cited by in corpus (31)

• A Review on Quantum Approximate Optimization Algorithm and its Variants
• Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
• Benchmarking of Different Optimizers in the Variational Quantum Algorithms for Applications in Quantum Chemistry
• An Empirical Comparison of Optimizers for Quantum Machine Learning with SPSA-based Gradients
• Surrogate-based optimization for variational quantum algorithms
• Transfer learning of optimal QAOA parameters in combinatorial optimization
• Analyzing variational quantum landscapes with information content
• Mitigated barren plateaus in the time-nonlocal optimization of analog quantum-algorithm protocols
• Dissipative variational quantum algorithms for Gibbs state preparation
• Quantum autoencoders for image classification
• Resource frugal optimizer for quantum machine learning
• Efficient and Robust Parameter Optimization of the Unitary Coupled-Cluster Ansatz
• A Novel Quantum Realization of Jet Clustering in High-Energy Physics Experiments
• Towards Optimizations of Quantum Circuit Simulation for Solving Max-Cut Problems with QAOA
• Solving Fractional Differential Equations on a Quantum Computer: A Variational Approach
• Distributed Evolution Strategies with Multi-Level Learning for Large-Scale Black-Box Optimization
• Application of quantum-inspired generative models to small molecular datasets
• Parameter Setting Heuristics Make the Quantum Approximate Optimization Algorithm Suitable for the Early Fault-Tolerant Era
• On Optimizing Hyperparameters for Quantum Neural Networks
• Application of Quantum Tensor Networks for Protein Classification
• Scalability Challenges in Variational Quantum Optimization under Stochastic Noise
• Iteration Complexity of Variational Quantum Algorithms
• BCQQ: Batch-Constraint Quantum Q-Learning with Cyclic Data Re-uploading
• Stabilizer configuration interaction: Finding molecular subspaces with error detection properties
• The Lie Algebra of XY-mixer Topologies and Warm Starting QAOA for Constrained Optimization
• Regularizing quantum loss landscapes by noise injection
• Transformation-free generation of a quasi-diabatic representation from the state-average orbital-optimized variational quantum eigensolver
• Learning Density Functionals from Noisy Quantum Data
• Harmonic Oscillator based Particle Swarm Optimization
• Variational Quantum Generative Modeling by Sampling Expectation Values of Tunable Observables
• Nonlinear path-following via the asymptotic numerical method on a quantum processor