Physics-Informed Neural Networks for an optimal counterdiabatic quantum computation
University of Valencia（瓦伦西亚大学）；Kipu Quantum（Kipu量子公司）
Antonio Ferrer-Sánchez, Carlos Flores-Garrigos, Carlos Hernani-Morales, José J. Orquín-Marqués, Narendra N. Hegade, Alejandro Gomez Cadavid, Iraitz Montalban, E… 展开作者
Antonio Ferrer-Sánchez, Carlos Flores-Garrigos, Carlos Hernani-Morales, José J. Orquín-Marqués, Narendra N. Hegade, Alejandro Gomez Cadavid, Iraitz Montalban, Enrique Solano, Yolanda Vives-Gilabert, José D. Martín-Guerrero
我们引入了一种新方法，利用物理信息神经网络（PINNs）的优势来解决由 $N_{Q}$ 量子比特系统组成的量子电路优化中的反绝热（CD）协议。主要目标是利用受物理启发的深度学习技术，准确求解量子系统内不同物理可观测量的时间演化。为实现此目标，我们将必要的物理信息嵌入底层神经网络中以有效解决问题。具体而言，我们对所有物理可观测量施加厄米性条件，并利用最小作用量原理，从而保证基于底层物理获取最合适的反绝热项。所提方法为解决 CD 驱动问题提供了可靠替代方案，摆脱了以往依赖经典数值近似的方法中常遇到的限制。该方法提供了一个通用框架，可从与问题相关的物理可观测量中获得最优结果，包括称为调度函数的时间外部参数化、涉及非绝热项的规范势或算子，以及系统能级的时间演化等。该方法的主要应用对象是 $\mathrm{H_{2}}$ 和 $\mathrm{LiH}$ 分子，分别由采用 STO-3G 基组的 2 量子比特和 4 量子比特系统表示。所呈现的结果证明，成功导出了非绝热项的理想分解，该分解通过利用 Pauli 算子的线性组合实现。这一特性为其在量子计算算法中的实际实现赋予了显著优势。
英文摘要：
We introduce a novel methodology that leverages the strength of Physics-Informed Neural Networks (PINNs) to address the counterdiabatic (CD) protocol in the optimization of quantum circuits comprised of systems with $N_{Q}$ qubits. The primary objective is to utilize physics-inspired deep learning techniques to accurately solve the time evolution of the different physical observables within the quantum system. To accomplish this objective, we embed the necessary physical information into an underlying neural network to effectively tackle the problem. In particular, we impose the hermiticity condition on all physical observables and make use of the principle of least action, guaranteeing the acquisition of the most appropriate counterdiabatic terms based on the underlying physics. The proposed approach offers a dependable alternative to address the CD driving problem, free from the constraints typically encountered in previous methodologies relying on classical numerical approximations. Our method provides a general framework to obtain optimal results from the physical observables relevant to the problem, including the external parameterization in time known as scheduling function, the gauge potential or operator involving the non-adiabatic terms, as well as the temporal evolution of the energy levels of the system, among others. The main applications of this methodology have been the $\mathrm{H_{2}}$ and $\mathrm{LiH}$ molecules, represented by a 2-qubit and 4-qubit systems employing the STO-3G basis. The presented results demonstrate the successful derivation of a desirable decomposition for the non-adiabatic terms, achieved through a linear combination utilizing Pauli operators. This attribute confers significant advantages to its practical implementation within quantum computing algorithms.
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SVKM’s Dwarkadas J. Sanghvi College of Engineering（SVKM德瓦卡达斯·J·桑格维工程学院）；New York University Abu Dhabi (NYUAD)（纽约大学阿布扎比分校）；NYUAD Research Institute（纽约大学阿布扎比分校研究院）；The Maersk Mc-Kinney Moller Institute（马士基麦克-金尼·莫勒研究所）；University of Southern Denmark（南丹麦大学）
Physics-Informed Neural Network Surrogate Models for River Stage Prediction
Graz Technical University of Technology（格拉茨技术大学）；University of New Orleans（新奥尔良大学）；US Army Corps of Engineers（美国陆军工程兵团）；Naval Research Laboratory（海军研究实验室）
SPINONet: Scalable Spiking Physics-informed Neural Operator for Computational Mechanics Applications
Department of Applied Mechanics（应用力学系）；Indian Institute of Technology Delhi（德里印度理工学院）；Institute of Structural Mechanics and Dynamics in Aerospace Engineering（航空航天工程中的结构力学与动力学研究所）；Faculty of Aerospace Engineering and Geodesy（航空航天工程与大地测量学系）；University of Stuttgart（斯图加特大学）；Experimental Hepatobiliary Surgery Group（肝胆外科实验小组）；Department of Hepatobiliary Surgery and Visceral Transplantation（肝胆外科与内脏移植部）；University of Leipzig Medical Center（莱比锡大学医学中心）；Department of Civil and Systems Engineering（土木与系统工程系）；Johns Hopkins University（约翰霍普金斯大学）；Data Science and AI Institute（数据科学与人工智能研究所）；Yardi School of Artificial Intelligence (YScAI)（Yardi人工智能学院（YScAI））
Revisiting Heat Flux Analysis of Tungsten Monoblock Divertor on EAST using Physics-Informed Neural Network
School of Computer Science and Technology, Anhui University（安徽大学计算机科学与技术学院）；Tongling University（铜陵大学）；Institute of Plasma Physics, Chinese Academy of Sciences（中国科学院等离子体物理研究所）
Simulating Three-dimensional Turbulence with Physics-informed Neural Networks
Institution for Foundation of Data Science, Yale University（数据科学基础研究所，耶鲁大学）；Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania（机械工程与应用力学系，宾夕法尼亚大学）；Sibley School of Mechanical and Aerospace Engineering, Cornell University（机械与航空航天工程学院，康奈尔大学）；Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory（先进计算、数学和数据部门，太平洋西北国家实验室）
Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks
Tsinghua University（清华大学）；Bauhaus-Universität Weimar（魏玛包豪斯大学）；CNPC Engineering Technology RD Company Limited（中国石油集团工程技术研究院有限公司）；Queensland University of Technology（昆士兰科技大学）；Leibniz University Hannover（汉诺威莱布尼茨大学）
A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks
Université de Toulouse（图卢兹大学）；INP-ENSEEIHT（国立图卢兹应用科学学院-国立高等电子、电工、计算机、水力与电信学院）；IRIT（图卢兹计算机研究所）；CERFACS（欧洲科学计算高级研究中心）；BRLi（BRLi公司）；Université de Lyon（里昂大学）；INRIA（法国国家信息与自动化研究所）；ENSL（里昂高等师范学院）；UCBL（里昂第一大学）；CNRS（法国国家科学研究中心）；University of Namur（那慕尔大学）
Droplet-LNO: Physics-Informed Laplace Neural Operators for Accurate Prediction of Droplet Spreading Dynamics on Complex Surfaces
Department of Mechanical Engineering, IIT Kharagpur（印度克里希纳加尔帕大学机械工程系）；Department of Computer Science & Engineering, IIT Kharagpur（印度克里希纳加尔帕大学计算机科学与工程系）
Advancing Physics Data Analysis through Machine Learning and Physics-Informed Neural Networks
Institute of Informatics and Telecommunications, National Centre for Scientific Research “Demokritos”（德谟克里特国家科学研究中心信息学与电信研究所）；School of Rural, Surveying and Geoinformatics Engineering, National Technical University of Athens（雅典国立技术大学农村、测量与地理信息工程学院）
Hybrid thermal modeling of additive manufacturing processes using physics-informed neural networks for temperature prediction and parameter identification
