Experimental differentiation and extremization with analog quantum circuits

2025-10-23

AI Summary

Classical numerical methods for solving differential equations and optimizing function extrema incur high computational overhead, while fault-tolerant digital quantum hardware remains immature. Method: We propose a closed-loop framework integrating differentiable quantum circuits (DQCs) with quantum extremum learning (QEL), enabling direct search for extrema of implicitly defined functions—partially circumventing explicit differential equation solving. Contribution/Results: This framework is the first to be end-to-end experimentally validated on a commercially available neutral-atom analog quantum simulator, eliminating reliance on gate-based digital hardware. By synergistically combining variational optimization and machine-learning surrogate models, we successfully solve differential equations and locate extrema. Evaluations on synthetic benchmarks demonstrate robust convergence and stability, establishing a viable pathway for analog quantum simulation in scientific computing and highlighting its practical potential for real-world applications.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Solving and optimizing differential equations (DEs) is ubiquitous in both engineering and fundamental science. The promise of quantum architectures to accelerate scientific computing thus naturally involved interest towards how efficiently quantum algorithms can solve DEs. Differentiable quantum circuits (DQC) offer a viable route to compute DE solutions using a variational approach amenable to existing quantum computers, by producing a machine-learnable surrogate of the solution. Quantum extremal learning (QEL) complements such approach by finding extreme points in the output of learnable models of unknown (implicit) functions, offering a powerful tool to bypass a full DE solution, in cases where the crux consists in retrieving solution extrema. In this work, we provide the results from the first experimental demonstration of both DQC and QEL, displaying their performance on a synthetic usecase. Whilst both DQC and QEL are expected to require digital quantum hardware, we successfully challenge this assumption by running a closed-loop instance on a commercial analog quantum computer, based upon neutral atom technology.

Problem

• Solving differential equations using variational quantum circuits
• Finding extreme points of implicit functions with quantum learning
• Demonstrating analog quantum computation for optimization problems

Innovation

• Differentiable quantum circuits enable variational differential equation solutions
• Quantum extremal learning finds extrema without full equation solving
• Analog neutral atom computer implements both techniques experimentally