An Empirical Comparison of Optimizers for Quantum Machine Learning with SPSA-based Gradients

Abstract

VQA have attracted a lot of attention from the quantum computing community for the last few years. Their hybrid quantum-classical nature with relatively shallow quantum circuits makes them a promising platform for demonstrating the capabilities of NISQ devices. Although the classical machine learning community focuses on gradient-based parameter optimization, finding near-exact gradients for VQC with the parameter-shift rule introduces a large sampling overhead. Therefore, gradient-free optimizers have gained popularity in quantum machine learning circles. Among the most promising candidates is the SPSA algorithm, due to its low computational cost and inherent noise resilience. We introduce a novel approach that uses the approximated gradient from SPSA in combination with state-of-the-art gradient-based classical optimizers. We demonstrate numerically that this outperforms both standard SPSA and the parameter-shift rule in terms of convergence rate and absolute error in simple regression tasks. The improvement of our novel approach over SPSA with stochastic gradient decent is even amplified when shot- and hardware-noise are taken into account. We also demonstrate that error mitigation does not significantly affect our results.

References in corpus (26)

• Adam: A Method for Stochastic Optimization
• Quantum Computing in the NISQ era and beyond
• Quantum algorithm for solving linear systems of equations
• Variational Quantum Algorithms
• A Quantum Approximate Optimization Algorithm
• On the Convergence of Adam and Beyond
• Error mitigation for short-depth quantum circuits
• Evaluating analytic gradients on quantum hardware
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Extending the computational reach of a noisy superconducting quantum processor
• Scalable Quantum Simulation of Molecular Energies
• Efficient variational quantum simulator incorporating active error minimisation
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Quantum Error Mitigation
• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
• Cloud Quantum Computing of an Atomic Nucleus
• Scalable error mitigation for noisy quantum circuits produces competitive expectation values
• On Empirical Comparisons of Optimizers for Deep Learning
• Performance comparison of optimization methods on variational quantum algorithms
• A Comparison of Various Classical Optimizers for a Variational Quantum Linear Solver
• Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition
• Quantum computing of the ${}^6$Li nucleus via ordered unitary coupled clusters
• Benchmarking of Different Optimizers in the Variational Quantum Algorithms for Applications in Quantum Chemistry
• Gradient Estimation with Constant Scaling for Hybrid Quantum Machine Learning
• Quantum Reinforcement Learning for Solving a Stochastic Frozen Lake Environment and the Impact of Quantum Architecture Choices
• Towards solving the BCS Hamiltonian gap in Near-Term Quantum Computers

Cited by in corpus (8)

• Quantum Machine Learning in Drug Discovery: Applications in Academia and Pharmaceutical Industries
• Guided-SPSA: Simultaneous Perturbation Stochastic Approximation assisted by the Parameter Shift Rule
• Quantum Natural Policy Gradients: Towards Sample-Efficient Reinforcement Learning
• Variational Quantum Algorithms for Differential Equations on a Noisy Quantum Computer
• BCQQ: Batch-Constraint Quantum Q-Learning with Cyclic Data Re-uploading
• Exploring new variational quantum circuit ansatzes for solving $SU(2)$ matrix models
• Qiskit-Torch-Module: Fast Prototyping of Quantum Neural Networks
• CutReg: A loss regularizer for enhancing the scalability of QML via adaptive circuit cutting