Quantum Analytic Descent

Abstract

Variational algorithms have particular relevance for near-term quantum computers but require non-trivial parameter optimisations. Here we propose Analytic Descent: Given that the energy landscape must have a certain simple form in the local region around any reference point, it can be efficiently approximated in its entirety by a classical model -- we support these observations with rigorous, complexity-theoretic arguments. One can classically analyse this approximate function in order to directly `jump' to the (estimated) minimum, before determining a more refined function if necessary. We derive an optimal measurement strategy and generally prove that the asymptotic resource cost of a `jump' corresponds to only a single gradient vector evaluation.

22 pages, 9 figures

References in corpus (12)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Variational Quantum Algorithms
• Many body localization and thermalization in quantum statistical mechanics
• Noisy intermediate-scale quantum (NISQ) algorithms
• Strong quantum computational advantage using a superconducting quantum processor
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• The effect of data encoding on the expressive power of variational quantum machine learning models
• Hybrid quantum-classical algorithms and quantum error mitigation
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• Virtual Distillation for Quantum Error Mitigation
• Exponential Error Suppression for Near-Term Quantum Devices
• The Dominant Eigenvector of a Noisy Quantum State

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• Universal Effectiveness of High-Depth Circuits in Variational Eigenproblems
• Quantum Error Mitigated Classical Shadows
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• Biased Estimator Channels for Classical Shadows
• Weighted Approximate Quantum Natural Gradient for Variational Quantum Eigensolver
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