Quantum Model-Discovery

• URL: http://arxiv.org/abs/2111.06376v1
• Date: Thu, 11 Nov 2021 18:45:52 GMT
• Title: Quantum Model-Discovery
• Authors: Niklas Heim, Atiyo Ghosh, Oleksandr Kyriienko, Vincent E. Elfving
• Abstract summary: Quantum algorithms for solving differential equations have shown a provable advantage in the fault-tolerant quantum computing regime. We extend the applicability of near-term quantum computers to more general scientific machine learning tasks. Our results show a promising path to Quantum Model Discovery (QMoD) on the interface between classical and quantum machine learning approaches.
• Score: 19.90246111091863
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 near-term quantum computers to more general scientific machine learning tasks, including the discovery of differential equations from a dataset of measurements. We use differentiable quantum circuits (DQCs) to solve equations parameterized by a library of operators, and perform regression on a combination of data and equations. Our results show a promising path to Quantum Model Discovery (QMoD), on the interface between classical and quantum machine learning approaches. We demonstrate successful parameter inference and equation discovery using QMoD on different systems including a second-order, ordinary differential equation and a non-linear, partial differential equation.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Quantum Circuit Learning on NISQ Hardware [0.0]
  Current quantum computers are small and error-prone systems. Fault-tolerant quantum computers are not expected to be available in the near future. We show that exemplary QCL circuits with up to three qubits are executable on the IBM quantum computer.
  arXiv  Detail & Related papers  (2024-05-03T13:00:32Z)
• Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations [0.0]
  Chebyshevs have shown significant promise as an efficient tool for both classical and quantum neural networks to solve differential equations. We adapt and generalize this framework in a quantum machine learning setting for a variety of problems. Results indicate a promising approach to the near-term evaluation of differential equations on quantum devices.
  arXiv  Detail & Related papers  (2023-12-14T18:46:35Z)
• QNEAT: Natural Evolution of Variational Quantum Circuit Architecture [95.29334926638462]
  We focus on variational quantum circuits (VQC), which emerged as the most promising candidates for the quantum counterpart of neural networks. Although showing promising results, VQCs can be hard to train because of different issues, e.g., barren plateau, periodicity of the weights, or choice of architecture. We propose a gradient-free algorithm inspired by natural evolution to optimize both the weights and the architecture of the VQC.
  arXiv  Detail & Related papers  (2023-04-14T08:03:20Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• D-CIPHER: Discovery of Closed-form Partial Differential Equations [80.46395274587098]
  We propose D-CIPHER, which is robust to measurement artifacts and can uncover a new and very general class of differential equations. We further design a novel optimization procedure, CoLLie, to help D-CIPHER search through this class efficiently.
  arXiv  Detail & Related papers  (2022-06-21T17:59:20Z)
• Quantum Kernel Methods for Solving Differential Equations [21.24186888129542]
  We propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are represented.
  arXiv  Detail & Related papers  (2022-03-16T18:56:35Z)
• Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
  Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
  arXiv  Detail & Related papers  (2021-07-08T17:59:55Z)
• Quantum Algorithms for Solving Ordinary Differential Equations via Classical Integration Methods [1.802439717192088]
  We explore utilizing quantum computers for the purpose of solving differential equations. We devise and simulate corresponding digital quantum circuits, and implement and run a 6$mathrmth$ order Gauss-Legendre collocation method. As promising future scenario, the digital arithmetic method could be employed as an "oracle" within quantum search algorithms for inverse problems.
  arXiv  Detail & Related papers  (2020-12-17T09:49:35Z)
• Solving nonlinear differential equations with differentiable quantum circuits [21.24186888129542]
  We propose a quantum algorithm to solve systems of nonlinear differential equations. We use automatic differentiation to represent function derivatives in an analytical form as differentiable quantum circuits. We show how this approach can implement a spectral method for solving differential equations in a high-dimensional feature space.
  arXiv  Detail & Related papers  (2020-11-20T13:21:11Z)
• Quantum Geometric Machine Learning for Quantum Circuits and Control [78.50747042819503]
  We review and extend the application of deep learning to quantum geometric control problems. We demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.
  arXiv  Detail & Related papers  (2020-06-19T19:12:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.