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GALIC: hybrid multi-qubitwise pauli grouping for quantum computing measurement

quantum SCIENCE AND TECHNOLOGY 2025年第1期10卷

作者： Burns, Matthew X. Liu, Chenxu Stein, Samuel Peng, Bo Kowalski, Karol Li, Ang Pacific Northwest Natl Lab Phys & Computat Sci 902 Battelle Blvd Richland WA 99352 USA Univ Rochester Dept Elect & Comp Engn 500 Comp Studies Bldg POB 270231 Rochester NY 14627 USA UNIV WASHINGTON Dept Elect & Comp Engn 1410 NE Campus Pkwy Seattle WA 98195 USA

Observable estimation is a core primitive in NISQ-era algorithms targeting quantum chemistry applications. To reduce the state preparation overhead required for accurate estimation, recent works have proposed various simultaneous measurement schemes to lower estimator variance. Two primary grouping schemes have been proposed: full commutativity (FC) and qubit-wise commutativity (QWC), with no compelling means of interpolation. In this work we propose a generalized framework for designing and analyzing context-aware hybrid FC/QWC commutativity relations. We use our framework to propose a noise-and-connectivity aware grouping strategy: Generalized backend-Aware pauLI Commutation (GALIC). We demonstrate how GALIC interpolates between FC and QWC, maintaining estimator accuracy in Hamiltonian estimation while lowering variance by an average of 20% compared to QWC. We also explore the design space of near-term quantum devices using the GALIC framework, specifically comparing device noise levels and connectivity. We find that error suppression has a more than 10 x larger impact on device-aware estimator variance than qubit connectivity with even larger correlation differences in estimator biases.

关键词： quantum computing quantum measurement quantum chemistry variational quantum algorithms pauli grouping observable expectation qwc

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Self-adaptive physics-informed quantum machine learning for solving differential equations

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MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2025年第1期6卷

作者： Setty, Abhishek Abdusalamov, Rasul Motzoi, Felix Rhein Westfal TH Aachen Dept Continuum Mech D-52062 Aachen Germany Forschungszentrum Julich Inst Quantum Control PGI 8 D-52425 Julich Germany Univ Cologne Inst Theoret Phys D-50937 Cologne Germany

Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations (DEs). In this work, we adapt and generalize this framework in a quantum machine learning setting for a variety of problems, including the 2D Poisson's equation, second-order linear DE, system of DEs, nonlinear Duffing and Riccati equation. In particular, we propose in the quantum setting a modified Self-Adaptive Physics-Informed Neural Network approach, where self-adaptive weights are applied to problems with multi-objective loss functions. We further explore capturing correlations in our loss function using a quantum-correlated measurement, resulting in improved accuracy for initial value problems. We analyse also the use of entangling layers and their impact on the solution accuracy for second-order DEs. The results indicate a promising approach to the near-term evaluation of DEs on quantum devices.

关键词： quantum machine learning physics-informed neural networks variational quantum algorithms differential equations

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A qubit-efficient variational selected configuration-interaction method

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quantum SCIENCE AND TECHNOLOGY 2025年第1期10卷

作者： Yoffe, Daniel Entin, Noga Natan, Amir Makmal, Adi Tel Aviv Univ Dept Phys Elect IL-69978 Tel Aviv Israel Bar Ilan Univ Engn Fac IL-52900 Ramat Gan Israel Bar Ilan Univ Dept Math IL-52900 Ramat Gan Israel Bar Ilan Univ Ctr Quantum Entanglement Sci & Technol IL-52900 Ramat Gan Israel

Finding the ground-state energy of molecules is an important and challenging computational problem for which quantum computing can potentially find efficient solutions. The variational quantum eigensolver (VQE) is a quantum algorithm that tackles the molecular groundstate problem and is regarded as one of the flagships of quantum computing. Yet, to date, only very small molecules were computed via VQE, due to high noise levels in current quantum devices. Here we present an alternative variational quantum scheme that requires significantly less qubits than VQE. The reduction in the qubit number allows for shallower circuits to be sufficient, rendering the method more resistant to noise. The proposed algorithm, termed variational quantum selected-configuration-interaction (VQ-SCI), is based on: (a) representing the target groundstate as a superposition of Slater determinant configurations, encoded directly upon the quantum computational basis states;and (b) selecting a-priory only the most dominant configurations. This is demonstrated through a set of groundstate calculations of the H-2, LiH, BeH2, H2O, NH3 and C2H4 molecules in the sto-3g basis set, performed on IBM quantum devices. We show that the VQ-SCI reaches the full configuration interaction energy within chemical accuracy using the lowest number of qubits reported to date. Moreover, when the SCI matrix is generated 'on the fly', the VQ-SCI requires exponentially less memory than classical SCI methods. This offers a potential remedy to a severe memory bottleneck problem in classical SCI calculations. Finally, the proposed scheme is general and can be straightforwardly applied for finding the groundstate of any Hermitian matrix, outside the chemical context.

关键词： variational quantum algorithms variational quantum eigensolver qubit-efficient electronic structure configuration interaction first quantization selected configuration interaction

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Development of variational quantum deep neural networks for image recognition

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NEUROCOMPUTING 2022年 501卷 566-582页

作者： Wang, Yunqian Wang, Yufeng Chen, Chao Jiang, Runcai Huang, Wei Nanchang Univ Sch Math & Comp Sci Nanchang 330031 Jiangxi Peoples R China

Parametrized quantum circuits are widely used for supervised learning tasks such as image classification in the noisy intermediate scale quantum era. However, normally, it can only handle low-dimensional data. This study presented a variational quantum deep neural network (VQDNN) model for various scale image recognition tasks. Three classifiers were designed to verify the classification performance of the proposed VQDNN model. In the first classifier, to accommodate the limitations of qubits in both simulation hardware and real quantum hardware - we adopted hybrid principal component analysis - VQDNN architecture. Moreover, the amplitude encoding scheme and the rotation angle coding scheme were employed in the subsequent two classifiers to handle large-size images. Finally, we used the classical neural network and VQDNN model to conduct a comparative experiment of the ten-label classification learning task on the same dataset. The quantum numerical experiment was implemented on two benchmark datasets: the MNIST and UCI databases of handwritten digits. The simulation results showed that the proposed VQDNN classified the two datasets with an accuracy of 100% for the two-class classification task, while the UCI dataset has an accuracy of 90.87% for the ten-label classification task. The proposed VQDNN achieved better classification accuracy than the original classical neural network even under a limited number of qubits available in current hardware, indicating the promising application potential of VQDNN in image recognition. (c) 2022 Elsevier B.V. All rights reserved.

关键词： quantum computation variational quantum algorithms Parametrized quantum circuit quantum deep neural network quantum machine learning

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variational quantum recurrent neural networks for multi-feature forecasting

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INTERNATIONAL JOURNAL OF quantum INFORMATION 2024年第7期22卷

作者： Huang, Rui Yi, Haibo Li, Pak Hon Shenzhen Polytech Univ Sch Artificial Intelligence Shenzhen 518055 Guangdong Peoples R China Sage Hill Sch 20402 Newport Coast Dr Newport Beach CA USA

Recurrent neural networks are a kind of recursion which takes sequence data as input and carries on the evolution of temporal dependency data. variational quantum algorithms use classical computers as the quantum optimizer to update the circuit parameters. In this work, we propose a variational quantum algorithm of the recurrent neural network, which we dub VQRNN, to find approximate optima in the time series forecasting. Motivated by the variational quantum algorithms, we train classical activation functions to assist quantum computing. Here, unlike the quantum tensor networks (QTN) algorithm that predicts a single output feature with a single time step, our algorithm can forecast multi-output features by adjusting the recurrent hidden state. Finally, we deploy the QTN and VQRNN algorithms on the Origin quantum platform with the numerical simulator backends using the Meteorological data set. Experimental results show that the atmospheric pressure prediction accuracy of VQRNN is 99.8864% in multi-feature forecasting tasks. In addition, we conclude that the variation-based model has an excellent performance in multi-feature output forecasting.

关键词： quantum machine learning variational quantum algorithms recurrent neural networks

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Expressivity of variational quantum Machine Learning on the Boolean Cube

IEEE TRANSACTIONS ON QUANTUM ENGINEERING

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IEEE TRANSACTIONS ON quantum ENGINEERING 2023年第1期4卷 1页

作者： Herman, Dylan Raymond, Rudy Li, Muyuan Robles, Nicolas Mezzacapo, Antonio Pistoia, Marco JPMorgan Chase Global Technol Appl Res New York NY 10017 USA IBM Res Tokyo IBM Quantum Tokyo 1038510 Japan Keio Univ Quantum Comp Ctr Yokohama Kanagawa 2238522 Japan IBM T J Watson Res Ctr IBM Quantum Yorktown Hts NY 10598 USA

Categorical data play an important part in machine learning research and appears in a variety of applications. Models that can express large classes of real-valued functions on the Boolean cube are useful for problems involving discrete-valued data types, including those which are not Boolean. To this date, the commonly used schemes for embedding classical data into variational quantum machine learning models encode continuous values. Here, we investigate quantum embeddings for encoding Boolean-valued data into parameterized quantum circuits used for machine learning tasks. We narrow down representability conditions for functions on the n-dimensional Boolean cube with respect to previously known results, using two quantum embeddings: a phase embedding and an embedding based on quantum random access codes. We show that for any real-valued function on the n-dimensional Boolean cube, there exists a variational linear quantum model based on a phase embedding using n qubits that can represent it and an ensemble of such models using d < n qubits that can express any function with degree at most d. Additionally, we prove that variational linear quantum models that use the quantum random access code embedding can express functions on the Boolean cube with degree d <= [n/3] using [n/3] qubits, and that an ensemble of such models can represent any function on the Boolean cube with degree d <= [n/3]. Furthermore, we discuss the potential benefits of each embedding and the impact of serial repetitions. Finally, we demonstrate the use of the embeddings presented by performing numerical simulations and experiments on IBM quantum processors using the Qiskit machine learning framework.

关键词： Qubit Machine learning Task analysis Data models Computational modeling Analytical models Supervised learning Boolean cube expressivity Fourier analysis quantum machine learning variational quantum algorithms

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variational quantum Algorithm Landscape Reconstruction by Low-Rank Tensor Completion 5

Variational Quantum Algorithm Landscape Reconstruction by Lo...

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2024 International Conference on quantum Computing and Engineering

作者： Hao, Tianyi He, Zichang Shaydulin, Ruslan Pistoia, Marco Tannu, Swamit Univ Wisconsin Madison Dept Comp Sci Madison WI 53706 USA JPMorganChase Global Technol Appl Res New York NY 10017 USA

ISBN: (纸本)9798331541378

variational quantum algorithms (VQAs) are a broad class of algorithms with many applications in science and industry. Applying a VQA to a problem involves optimizing a parameterized quantum circuit by maximizing or minimizing a cost function. A particular challenge associated with VQAs is understanding the properties of associated cost functions. Having the landscapes of VQA cost functions can greatly assist in developing and testing new variational quantum algorithms, but they are extremely expensive to compute. Reconstructing the landscape of a VQA using existing techniques requires a large number of cost function evaluations, especially when the dimension or the resolution of the landscape is high. To address this challenge, we propose a low-rank tensor-completion-based approach for local landscape reconstruction. By leveraging compact low-rank representations of tensors, our technique can overcome the curse of dimensionality and handle high-resolution landscapes. We demonstrate the power of landscapes in VQA development by showcasing practical applications of analyzing penalty terms for constrained optimization problems and examining the probability landscapes of certain basis states.

关键词： variational quantum algorithms Landscape Reconstruction Tensor Networks quantum Optimization

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Efficient Discrete Feature Encoding for variational quantum Classifier

Efficient Discrete Feature Encoding for Variational Quantum ...

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IEEE International Conference on quantum Computing and Engineering (QCE)

作者： Yano, Hiroshi Suzuki, Yudai Raymond, Rudy Yamamoto, Naoki Keio Univ Dept Informat & Comp Sci Kohoku Ku Hiyoshi 3-14-1 Yokohama Kanagawa 2238522 Japan Keio Univ Dept Mech Engn Kohoku Ku Hiyoshi 3-14-1 Yokohama Kanagawa 2238522 Japan IBM Res Tokyo Chuo Ku 19-21 Nihonbashi Tokyo 1038510 Japan Keio Univ Quantum Comp Ctr Kohoku Ku Hiyoshi 3-14-1 Yokohama Kanagawa 2238522 Japan Keio Univ Dept Appl Phys & Phys Informat Kohoku Ku Hiyoshi 3-14-1 Yokohama Kanagawa 2238522 Japan

ISBN: (纸本)9781728189697

Recent days have witnessed significant interests in applying quantum-enhanced techniques for solving machine learning tasks in, e.g., classification, regression, and recommender systems. variational methods that use quantum resources of imperfect quantum devices with the help of classical computing techniques are popular for supervised learning. variational quantum Classification (VQC) is one of such variational methods with possible quantum advantage in using quantum-enhanced features that are hard to compute by classical methods. Its performance depends on the mapping of classical features into quantum-enhanced feature space. Although there have been many quantum-mapping functions proposed so far, there is little discussion on efficient mapping of discrete features, such as, race, gender, marriage status and others that are often significant for classifying datasets of interest. We first introduce the use of quantum Random Access Coding (QRAC) to map such discrete features efficiently into limited number of qubits for VQC. We numerically show that QRAC can help speeding up the training of VQC by reducing its parameters via reduction on the number of qubits for the mapping. We confirm the effectiveness of the QRAC in VQC by experimenting on classification of healthcare datasets with both simulators and real quantum devices.

关键词： quantum machine learning variational quantum algorithms discrete features supervised learning quantum random access coding

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VAQEM: A variational Approach to quantum Error Mitigation 28

VAQEM: A Variational Approach to Quantum Error Mitigation

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28th Annual IEEE International Symposium on High-Performance Computer Architecture (HPCA)

作者： Ravi, Gokul Subramanian Smith, Kaitlin N. Gokhale, Pranav Mari, Andrea Earnest, Nathan Javadi-Abhari, Ali Chong, Frederic T. Univ Chicago Chicago IL 60637 USA Supertech Washington DC USA Unitary Fund Washington DC USA IBM TJ Watson Res Ctr IBM Quantum Yorktown Hts NY USA

ISBN: (纸本)9781665420273

variational quantum algorithms (VQA) are one of the most promising candidates for near-term quantum advantage. Traditionally, these algorithms are parameterized by rotational gate angles whose values are tuned over iterative execution on quantum machines. The iterative tuning of these gate angle parameters make VQAs more robust to a quantum machine's noise profile. However, the effect of noise is still a significant detriment to VQA's target estimations on real quantum machines - they are far from ideal. Thus, it is imperative to employ effective error mitigation strategies to improve the fidelity of these quantum algorithms on near-term machines. While existing error mitigation techniques built from theory do provide substantial gains, the disconnect between theory and real machine execution characteristics limit the scope of these improvements. Thus, it is critical to optimize mitigation techniques to explicitly suit the target application as well as the noise characteristics of the target machine. We propose VAQEM, which dynamically tailors existing error mitigation techniques to the actual, dynamic noisy execution characteristics of VQAs on a target quantum machine. We do so by tuning specific features of these mitigation techniques similar to the traditional rotation angle parameters by targeting improvements towards a specific objective function which represents the VQA problem at hand. In this paper, we target two types of error mitigation techniques which are suited to idle times in quantum circuits: single qubit gate scheduling and the insertion of dynamical decoupling sequences. We gain substantial improvements to VQA objective measurements a mean of over 3x across a variety of VQA applications, run on IBM quantum machines. More importantly, while we study two specific error mitigation techniques, the proposed variational approach is general and can be extended to many other error mitigation techniques whose specific configurations are hard to select a pri

关键词： quantum computing noisy intermediate-scale quantum variational quantum algorithms variational quantum eigensolver error mitigation dynamic decoupling gate scheduling

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Warm-Start variational quantum Policy Iteration 5

Warm-Start Variational Quantum Policy Iteration

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2024 International Conference on quantum Computing and Engineering

作者： Meyer, Nico Murauer, Jakob Popov, Alexander Ufrecht, Christian Plinge, Axel Mutschler, Christopher Scherer, Daniel D. Fraunhofer Inst Integrated Circuits IIS Fraunhofer IIS Nurnberg Germany Friedrich Alexander Univ Erlangen Nurnberg Pattern Recognit Lab Erlangen Germany

ISBN: (纸本)9798331541378

Reinforcement learning is a powerful framework aiming to determine optimal behavior in highly complex decision-making scenarios. This objective can be achieved using policy iteration, which requires to solve a typically large linear system of equations. We propose the variational quantum policy iteration (VarQPI) algorithm, realizing this step with a NISQ-compatible quantum-enhanced subroutine. Its scalability is supported by an analysis of the structure of generic reinforcement learning environments, laying the foundation for potential quantum advantage with utility-scale quantum computers. Furthermore, we introduce the warm-start initialization variant (WS-VarQPI) that significantly reduces resource overhead. The algorithm solves a large FrozenLake environment with an underlying 256 x 256-dimensional linear system, indicating its practical robustness.

关键词： quantum computing quantum reinforcement learning policy iteration variational quantum algorithms quantum linear algebra

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