Experimental differentiation and extremization with analog quantum circuits

2025/10/23 by Evan Philip, Julius de Hond, Philip, Evan +19
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Neural and Evolutionary Computing (cs.NE) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.2510.20713

openalex publication_date 2025/10/23 · openalex created_date 2025/10/25 · openalex updated_date 2026/07/28

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.

Citations

• Continuous operation of a coherent 3,000-qubit system
• Evaluation of derivatives using approximate generalized parameter shift rule
• Addressing the Readout Problem in Quantum Differential Equation Algorithms with Quantum Scientific Machine Learning
• Quantum Computing for nonlinear differential equations and turbulence
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• The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?
• B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
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