Avoiding barren plateaus using classical shadows

Abstract

Variational quantum algorithms are promising algorithms for achieving quantum advantage on near-term devices. The quantum hardware is used to implement a variational wave function and measure observables, whereas the classical computer is used to store and update the variational parameters. The optimization landscape of expressive variational ansätze is however dominated by large regions in parameter space, known as barren plateaus, with vanishing gradients which prevents efficient optimization. In this work we propose a general algorithm to avoid barren plateaus in the initialization and throughout the optimization. To this end we define a notion of weak barren plateaus (WBP) based on the entropies of local reduced density matrices. The presence of WBPs can be efficiently quantified using recently introduced shadow tomography of the quantum state with a classical computer. We demonstrate that avoidance of WBPs suffices to ensure sizable gradients in the initialization. In addition, we demonstrate that decreasing the gradient step size, guided by the entropies allows to avoid WBPs during the optimization process. This paves the way for efficient barren plateau free optimization on near-term devices.

arXiv comment9 pages, 4 figures, comments are welcome; v2: improved readability, added new section and data, added more citations

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• Scalable and Flexible Classical Shadow Tomography with Tensor Networks
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• High Dimensional Quantum Machine Learning With Small Quantum Computers
• A semi-agnostic ansatz with variable structure for quantum machine learning
• Variational thermal quantum simulation of the lattice Schwinger model
• An Alternative Approach to Quantum Imaginary Time Evolution
• Entanglement entropy production in Quantum Neural Networks
• A Performance Study of Variational Quantum Algorithms for Solving the Poisson Equation on a Quantum Computer
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• Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series
• Solution of SAT Problems with the Adaptive-Bias Quantum Approximate Optimization Algorithm
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• Bayesian Learning of Parameterised Quantum Circuits
• Quantum-enhanced neural networks in the neural tangent kernel framework
• Measuring energy by measuring any other observable
• Optimisation-free Classification and Density Estimation with Quantum Circuits
• Twisted hybrid algorithms for combinatorial optimization
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• Quantum Circuit Cutting for Classical Shadows
• Symmetry-based quantum algorithms for open-shop scheduling with hard constraints