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variational Quantum algorithm for Solving Quantum Transport Equation in Semiconductor Device

IEEE TRANSACTIONS ON ELECTRON DEVICES 2025年第6期72卷 3265-3273页

作者： Yang, Qimao Guo, Jing Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA

As semiconductor feature sizes continue to shrink, accurate and efficient simulations of quantum transport become increasingly critical in device design and manufacturing. The nonequilibrium Green's function (NEGF) formalism is a widely used method for simulating quantum transport in semiconductor devices, but it is computationally demanding. Quantum computing offers a promising solution, in this work, we pioneer the application of the variational quantum linear solver (VQLS) to the NEGF problem, addressing the challenges associated with handling complex numbers inherent in quantum transport equations. We introduce a new cost function tailored to this framework, demonstrating improved performance over existing approaches. Furthermore, we show that VQLS can efficiently parallelize the computation across different energy levels, significantly reducing computational costs. Our results highlight the potential of variational quantum algorithms (VQAs) in enhancing the scalability and efficiency of quantum transport simulations.

关键词： Mathematical models Cost function Computational modeling Green's function methods Computational efficiency Linear systems Qubit Quantum algorithm Quantum state Vectors Quantum computing quantum transport semiconductor variational algorithm

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Performance analysis of a filtering variational quantum algorithm

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NEW JOURNAL OF PHYSICS 2025年第5期27卷

作者： Marin-Sanchez, Gabriel Amaro, David Quantinuum Partnership HouseCarlisle Pl London SW1P 1BX England

Even a minor boost in solving combinatorial optimization problems can greatly benefit multiple industries. Quantum computers, with their unique information processing capabilities, hold promise for delivering such enhancements. The filtering variational quantum eigensolver (F-VQE) is a variational hybrid quantum algorithm designed to solve combinatorial optimization problems on existing quantum computers with limited qubit number, connectivity, and fidelity. In this work we employ instantaneous quantum polynomial circuits as our parameterized quantum circuits. We propose a hardware-efficient implementation that respects limited qubit connectivity and show that they halve the number of circuits necessary to evaluate the gradient with the parameter-shift rule. To assess the potential of this protocol in the context of combinatorial optimization, we conduct extensive numerical analysis. We compare the performance against three classical baseline algorithms on weighted MaxCut and the asymmetric traveling salesperson problem (ATSP). We employ noiseless simulators for problems encoded on 13-29 qubits, and up to 37 qubits on the IBMQ real quantum devices. The ATSP encoding employed reduces the number of qubits and avoids the need of constraints compared to the standard quadratic unconstrained binary optimization/Ising model. Despite some observed positive signs, we conclude that significant development is necessary for a practical advantage with F-VQE.

关键词： IQP QML quantum optimization variational algorithm

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Engineering a Cost Function for Real-world Implementation of a variational Quantum algorithm

Engineering a Cost Function for Real-world Implementation of...

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IEEE International Conference on Quantum Computing and Engineering (QCE)

作者： Premaratne, Shavindra P. Matsuura, A. Y. Intel Corp Intel Labs Hillsboro OR 97124 USA

ISBN: (纸本)9781728189697

Hybrid quantum-classical variational algorithm execution typically involve the use of quantum processing for state evolution, and classical processing for cost function evaluation and guiding optimization. This paper proposes a new approach for engineering cost functions for a certain class of quantum-classical hybrid variation algorithms, in order to improve performance of these algorithms on today's small qubit systems. In this work, we apply this approach to a variational algorithm that generates thermofield double states (in the transverse field Ising model), which are relevant for studying thermal phase transitions in condensed matter systems. We discuss the benefits and drawbacks of various cost functions, apply our new engineering approach and show that it yields good agreement across the full temperature range.

关键词： NISQ devices thermofield double variational algorithm cost function

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Fast-QTrain: an algorithm for fast training of variational classifiers

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QUANTUM INFORMATION PROCESSING 2022年第5期21卷 1-20页

作者： Dangwal, Siddharth Sharma, Ritvik Bhowmik, Debanjan Indian Inst Technol Delhi Dept Elect Engn Delhi 110016 India Indian Inst Technol Dept Elect Engn Mumbai 400076 Maharashtra India

This work proposes a novel algorithm (Fast-QTrain) that enables fast training of variational classifiers. This training speedup is achieved by processing multiple samples, from a classical data set, in parallel during the training process. The proposed algorithm utilizes a quantum RAM along with other quantum circuits for implementing the forward pass. Besides, instead of computing the loss classically, which is the usual practice, we calculate the loss here using a swap test circuit. As a result, our algorithm reduces the training cost of a variational classifier trained for in epochs from the usual O(mN) (which is also the case with most classical machine learning algorithms) to O(N + m log N) where the data set contains N samples. Ignoring the one-time overhead of loading the N training samples into the qRAM, the time complexity per epoch of training is O(log N) in our proposed algorithm, as opposed to O(N) (which is the case for other variational algorithms and most classical machine learning algorithms). By performing quantum-circuit simulations on the Pennylane package, we show fairly accurate training using our proposed algorithm on a popular, classical data set: Fisher's Iris data set of flowers. While we restrict ourselves to binary classification (of samples from classical data sets) in this paper, our algorithm can be easily generalized to carry out multi-class classification. Our proposed algorithm (Fast-QTrain) can also be adapted for any classification ansatz used in the variational circuit as long as the encoding of the classical data into qubits is non-parameterized.

关键词： Quantum machine learning variational algorithm Supervised learning

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Two-Layer Ocean Circulation Model with variational Control of Turbulent Viscosity Coefficient

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IZVESTIYA ATMOSPHERIC AND OCEANIC PHYSICS 2023年第2期59卷 189-200页

作者： Zalesny, V. B. Russian Acad Sci Marchuk Inst Numer Math Moscow 119333 Russia

The development of a variational method for solving the problem of quasi-geostrophic dynamics in a two-layer periodic channel is considered. The development of the method is as follows. First, the formulation of the variational problem is generalized: the turbulent exchange coefficient of a quasi-geostrophic potential vorticity (QGPV) is included in the control vector. Second, the solution area more accurately describes the size of the Antarctic Circumpolar Current (ACC). Using the selection of linear meridional transport and the expansion of the solution in a Fourier series, the problem is reduced to a nonlinear system of ordinary differential equations (ODEs) in time. The doubly connected domain leads to the fact that the solution of the ODE must satisfy an additional stationary relation that determines the transport of the ACC. The variational algorithm is reduced to solving a system of forward and adjoint equations minimizing the mean squared error of the stationary relation. The QGPV turbulent exchange coefficient is determined in the process of solving the optimal problem. The numerical runs are carried out for a periodic channel simulating the water area of the ACC in the Southern Ocean. The characteristics of stationary current regimes are studied for different values of the model parameters. Sinusoidal circulation in both layers with a linear transfer with the wind, depending on the bottom topography, is typical. In some cases, under the sinusoidal, in the lower layer, a cellular circulation is formed, and sometimes an undercurrent occurs. In this case, the solution of the optimal problem is characterized by a low value of the turbulent viscosity coefficient and a low transport in the lower layer.

关键词： quasi-geostrophic potential vorticity two-layer ocean model variational algorithm turbulent viscosity coefficient

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Community Detection on Social Networks With Sentimental Interaction

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INTERNATIONAL JOURNAL ON SEMANTIC WEB AND INFORMATION SYSTEMS 2024年第1期20卷 1页

作者： Feng, Bingdao Cheng, Fangyu Liu, Yanfei Chang, Xinglong Wang, Xiaobao Jin, Di Tianjin Univ Coll Intelligence & Comp Tianjin Peoples R China Harbin Inst Technol Sch Architecture & Design Harbin Peoples R China Tianjin Univ Tianjin Peoples R China

Many studies on community detection are mainly based on the similarity in friendship between users. Recent studies have started to explore node contents to identify semantically meaningful communities. However, the sentimental interaction information which plays an important role in community detection is often ignored. By analyzing and utilizing the abundant sentimental interaction information, one can not only more precisely identify the communities, but also discover the interesting interactions and conflicts between these communities. Based on this concept, the authors propose a new Community Sentiment Diffusion Detection Model (CSDD), which utilizes sentimental information embedded in forward posts. Furthermore, the authors present an efficient variational algorithm for model inference. The community detection results have been verified on two large Twitter datasets. It is experimentally demonstrated that we can provide a fine-grained view of sentimental interaction between communities and discover the mechanism of sentiment diffusion between communities.

关键词： Community Detection Sentiment Diffusion variational algorithm Bayesian Model Social Networks

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Heterogeneity Analysis on Multi-State Brain Functional Connectivity and Adolescent Neurocognition

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2024年第546期119卷 851-863页

作者： Wang, Shiying Constable, Todd Zhang, Heping Zhao, Yize Yale Univ Dept Biostat New Haven CT 06520 USA Yale Univ Dept Radiol & Biomed Imaging New Haven CT USA

Brain functional connectivity or connectome, a unique measure for brain functional organization, provides a great potential to explain the neurobiological underpinning of behavioral profiles. Existing connectome-based analyses highly concentrate on brain activities under a single cognitive state, and fail to consider heterogeneity when attempting to characterize brain-to-behavior relationships. In this work, we study the complex impact of multi-state functional connectivity on behaviors by analyzing the data from a recent landmark brain development and child health study. We propose a nonparametric, Bayesian supervised heterogeneity analysis to uncover neurodevelopmental subtypes with distinct effect mechanisms. We impose stochastic block structures to identify network-based functional phenotypes and develop a variational expectation-maximization algorithm to facilitate an efficient posterior computation. Through integrating resting-state and task-related functional connectomes, we dissect heterogeneous effect mechanisms on children's fluid intelligence from the functional network phenotypes, including Fronto-parietal Network and Default Mode Network, under different cognitive states. Based on extensive simulations, we further confirm the superior performance of our method on uncovering brain-to-behavior relationships. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work.

关键词： Bayesian modeling Functional connectivity Heterogeneity analysis Stochastic block model variational algorithm

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variational learning algorithms for quantum query complexity

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NEW JOURNAL OF PHYSICS 2024年第3期26卷 033024页

作者： Wu, Zipeng Hou, Shi-Yao Zhang, Chao Li, Lvzhou Zeng, Bei Hong Kong Univ Sci & Technol Dept Phys Kowloon Clear Water Bay Hong Kong Peoples R China Shenzhen SpinQ Technol Co Ltd Shenzhen Peoples R China Sichuan Normal Univ Coll Phys & Elect Engn Ctr Computat Sci Chengdu 610068 Peoples R China Sun Yat Sen Univ Inst Quantum Comp & Comp Theory Sch Comp Sci & Engn Guangzhou 510006 Peoples R China

Quantum query complexity is pivotal in the analysis of quantum algorithms, encompassing well-known examples like search and period-finding algorithms. These algorithms typically involve a sequence of unitary operations and oracle calls dependent on an input variable. In this study, we introduce a variational learning approach to explore quantum query complexity. Our method employs an efficient parameterization of the unitary operations and utilizes a loss function derived from the algorithm's error probability. We apply this technique to various quantum query complexities, notably devising a new algorithm that resolves the 5-bit Hamming modulo problem with four queries, addressing an open question from Cornelissen et al (2021 arXiv:2112.14682). This finding is corroborated by a semidefinite programming (SDP) approach. Our numerical method exhibits superior memory efficiency compared to SDP and can identify quantum query algorithms (QQAs) that require a smaller workspace register dimension, an aspect not optimized by SDP. These advancements present a significant step forward in the practical application and understanding of QQAs.

关键词： quantum query complexity variational algorithm semidefinite programming

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variational quantum algorithms for trace norms and their applications

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Communications in Theoretical Physics 2021年第10期73卷 90-96页

作者： Sheng-Jie Li Jin-Min Liang Shu-Qian Shen Ming Li College of Science China University of Petroleum266580 QingdaoChina School of Mathematical Sciences Capital Normal University100048 BeijingChina

The trace norm of matrices plays an important role in quantum information and quantum computing. How to quantify it in today’s noisy intermediate scale quantum(NISQ) devices is a crucial task for information processing. In this paper, we present three variational quantum algorithms on NISQ devices to estimate the trace norms corresponding to different *** with the previous methods, our means greatly reduce the requirement for quantum resources. Numerical experiments are provided to illustrate the effectiveness of our algorithms.

关键词： quantum algorithm trace norm variational algorithm

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A comparison of various classical optimizers for a variational quantum linear solver

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QUANTUM INFORMATION PROCESSING 2021年第6期20卷 1-14页

作者： Pellow-Jarman, Aidan Sinayskiy, Ilya Pillay, Anban Petruccione, Francesco Univ KwaZulu Natal Univ RdChiltern Hill ZA-3629 Chiltern Hill Westville South Africa Natl Inst Theoret Phys NITheP ZA-4001 Kwa Zulu South Africa Ctr Artificial Intelligence Res CAIR Cape Town South Africa Korea Adv Inst Sci & Technol Sch Elect Engn Daejeon 34141 South Korea

variational hybrid quantum classical algorithms are a class of quantum algorithms intended to run on noisy intermediate-scale quantum (NISQ) devices. These algorithms employ a parameterized quantum circuit (ansatz) and a quantum-classical feedback loop. A classical device is used to optimize the parameters in order to minimize a cost function that can be computed far more efficiently on a quantum device. The cost function is constructed such that finding the ansatz parameters that minimize its value, solves some problem of interest. We focus specifically on the variational quantum linear solver, and examine the effect of several gradient-free and gradient-based classical optimizers on performance. We focus on both the average rate of convergence of the classical optimizers studied, as well as the distribution of their average termination cost values, and how these are affected by noise. Our work demonstrates that realistic noise levels on NISQ devices present a challenge to the optimization process. All classical optimizers appear to be very negatively affected by the presence of realistic noise. If noise levels are significantly improved, there may be a good reason for preferring gradient-based methods in the future, which performed better than the gradient-free methods with only shot-noise present. The gradient-free optimizers, simultaneous perturbation stochastic approximation (SPSA) and Powell's method, and the gradient-based optimizers, AMSGrad and BFGS performed the best in the noisy simulation, and appear to be less affected by noise than the rest of the methods. SPSA appears to be the best performing method. COBYLA, Nelder-Mead and Conjugate-Gradient methods appear to be the most heavily affected by noise, with even slight noise levels significantly impacting their performance.

关键词： variational algorithm Classical optimizer Near-term quantum device NISQ VQLS

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