Quantum Model-Discovery
Niklas Heim, Atiyo Ghosh, Oleksandr Kyriienko, Vincent E. Elfving

TL;DR
This paper introduces Quantum Model Discovery (QMoD), a method leveraging near-term quantum computers and differentiable quantum circuits to identify and infer differential equations from data, bridging classical and quantum machine learning.
Contribution
It extends quantum algorithms for PDEs to the discovery of differential equations from data using differentiable quantum circuits, enabling new scientific machine learning applications.
Findings
Successful parameter inference on differential equations
Equation discovery demonstrated on PDEs and ODEs
Promising approach for quantum-assisted scientific modeling
Abstract
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization. Many problems appearing in science and engineering can be rewritten as a set of differential equations. Quantum algorithms for solving differential equations have shown a provable advantage in the fault-tolerant quantum computing regime, where deep and wide quantum circuits can be used to solve large linear systems like partial differential equations (PDEs) efficiently. Recently, variational approaches to solving non-linear PDEs also with near-term quantum devices were proposed. One of the most promising general approaches is based on recent developments in the field of scientific machine learning for solving PDEs. We extend the applicability of…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Neural Networks and Reservoir Computing
MethodsSPEED: Separable Pyramidal Pooling EncodEr-Decoder for Real-Time Monocular Depth Estimation on Low-Resource Settings
