Quantum DeepONet: Neural operators accelerated by quantum computing

Abstract

In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as deep operator network (DeepONet), which learn mappings between infinite-dimensional function spaces, promise efficient computation of PDE solutions for a new condition in a single forward pass. However, classical DeepONet entails quadratic complexity concerning input dimensions during evaluation. Given the progress in quantum algorithms and hardware, here we propose to utilize quantum computing to accelerate DeepONet evaluations, yielding complexity that is linear in input dimensions. Our proposed quantum DeepONet integrates unary encoding and orthogonal quantum layers. We benchmark our quantum DeepONet using a variety of PDEs, including the antiderivative operator, advection equation, and Burgers' equation. We demonstrate the method's efficacy in both ideal and noisy conditions. Furthermore, we show that our quantum DeepONet can also be informed by physics, minimizing its reliance on extensive data collection. Quantum DeepONet will be particularly advantageous in applications in outer loop problems which require exploring parameter space and solving the corresponding PDEs, such as uncertainty quantification and optimal experimental design.

29 pages, 9 figures

References in corpus (30)

• Quantum Machine Learning
• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Quantum algorithm for solving linear systems of equations
• Variational Quantum Algorithms
• Quantum support vector machine for big data classification
• Quantum Circuit Learning
• Quantum principal component analysis
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
• Physics-informed neural networks for inverse problems in nano-optics and metamaterials
• Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks
• Quantum Data Fitting
• Benchmarking an 11-qubit quantum computer
• Quantum-enhanced machine learning
• Quantum Boltzmann Machine
• Dying ReLU and Initialization: Theory and Numerical Examples
• Collapse of Deep and Narrow Neural Nets
• Barren Plateaus in Variational Quantum Computing
• DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks
• Physics-Informed Neural Operator for Learning Partial Differential Equations
• Modelling and Simulating the Noisy Behaviour of Near-term Quantum Computers
• Quantum Methods for Neural Networks and Application to Medical Image Classification
• Towards provably efficient quantum algorithms for large-scale machine-learning models
• Transformer for Partial Differential Equations' Operator Learning
• GNOT: A General Neural Operator Transformer for Operator Learning
• Non-trivial symmetries in quantum landscapes and their resilience to quantum noise
• PPDONet: Deep Operator Networks for Fast Prediction of Steady-State Solutions in Disk-Planet Systems
• Effects of noise on the overparametrization of quantum neural networks
• Realization of a quantum neural network using repeat-until-success circuits in a superconducting quantum processor
• Emergence of noise-induced barren plateaus in arbitrary layered noise models