Stochastic noise can be helpful for variational quantum algorithms

Abstract

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided for example by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms.

15 pages, presentation improved, proofs extended

References in corpus (29)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Characterizing Quantum Supremacy in Near-Term Devices
• Evaluating analytic gradients on quantum hardware
• The Variational Quantum Eigensolver: a review of methods and best practices
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices
• Training variational quantum algorithms is NP-hard
• Non-convex Optimization for Machine Learning
• Stochastic gradient descent for hybrid quantum-classical optimization
• Computational advantage of quantum random sampling
• Entanglement Devised Barren Plateau Mitigation
• The statistics of critical points of Gaussian fields on large-dimensional spaces
• Capacity and quantum geometry of parametrized quantum circuits
• Evaluating the noise resilience of variational quantum algorithms
• Representation Learning via Quantum Neural Tangent Kernels
• Analytic theory for the dynamics of wide quantum neural networks
• Noise-Resilient Variational Hybrid Quantum-Classical Optimization
• Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm
• Impact of quantum noise on the training of quantum Generative Adversarial Networks
• Variational Quantum Algorithms for Semidefinite Programming
• Bayesian Learning of Parameterised Quantum Circuits
• Laziness, Barren Plateau, and Noise in Machine Learning

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• Regularizing quantum loss landscapes by noise injection
• Assessing Projected Quantum Kernels for the Classification of IoT Data
• From barren plateaus through fertile valleys: Conic extensions of parameterised quantum circuits