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Towards solving the BCS Hamiltonian gap in near-term quantum computers

RESULTS IN PHYSICS 2023年 44卷

作者： Sa, Nahum Oliveira, Ivan S. Roditi, Itzhak Ctr Brasileiro Pesquisas Fis Rua Dr Xavier Sigaud 150 BR-22290180 Rio De Janeiro Brazil Swiss Fed Inst Technol Inst Theoret Phys CH-8093 Zurich Switzerland

In this work, using a Noisy Intermediate-Scale quantum (NISQ) framework, we obtain the gap of a Bardeen- Cooper-Schrieffer (BCS) Hamiltonian. This could lead to interesting implications for superconductivity re-search. For such task, we choose to use the variational quantum Deflation and analyze the hardware restrictions that are needed to find the energy spectra on current quantum *** also compare two different kinds of classical optimizers, Constrained Optimization BY Linear Approx-imations (COBYLA) and Simultaneous Perturbation Stochastic Approximation (SPSA), and study the effect of decoherence caused by the presence of noise when using simulations in real devices. We apply our method for an example with both 2 and 5 qubits. Furthermore, we show how to approximate the gap within one standard deviation, even with the presence of noise.

关键词： variational quantum algorithms quantum computing quantum simulation NISQ

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Entanglement-informed construction of variational quantum circuits

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quantum SCIENCE AND TECHNOLOGY 2025年第3期10卷 035032-035032页

作者： Joch, Alina Uhrig, Goetz S. Fauseweh, Benedikt TU Dortmund Univ Condensed Matter Theory Otto Hahn Str 4 D-44227 Dortmund Germany German Aerosp Ctr DLR Inst Software Technol D-51147 Cologne Germany

The variational quantum eigensolver is a promising tool for simulating ground states of quantum many-body systems on noisy quantum computers. Its effectiveness relies heavily on the ansatz, which must be both hardware-efficient for implementation on noisy hardware and problem-specific to avoid local minima and convergence problems. In this article, we explore entanglement-informed ansatz schemes that naturally emerge from specific models, aiming to balance accuracy with minimal use of two-qubit entangling gates. We investigate three models of quasi-1D Hamiltonians focusing on entanglement barriers and long-range interactions. We find that including the entanglement structure in the parameterized quantum circuit reduces the resources necessary to achieve a given accuracy. A better assessment is obtained by analyzing how the ansatz captures the entanglement spectrum. Our comprehensive analysis provides a new perspective on the design of ans & auml;tze based on the expected entanglement structure of the approximated state.

关键词： variational quantum algorithms entanglement spectrum renormalization group

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variational quantum neural networks based on dynamic layerwise strategy

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JOURNAL OF SUPERCOMPUTING 2025年第8期81卷

作者： Qi, Han Zhang, Long Gong, Changqing Por, Lip Yee Gani, Abdullah Shenyang Aerosp Univ Sch Comp Sci Shenyang 110000 Peoples R China Univ Malaya Fac Comp Sci & Informat Technol Jalan Univ Kuala Lumpur 50603 Malaysia

variational quantum algorithms (VQAs) form a category of hybrid quantum-classical approaches designed to harness the computational advantages of quantum devices. Nevertheless, in the NISQ era, these algorithms face considerable hurdles due to the barren plateau (BP) problem. More precisely, as parameterized quantum circuits grow deeper, the loss function's gradient diminishes exponentially. This drastically compromises the effectiveness of gradient-based optimization and complicates the training procedure. To address these issues, we present DL-VQNN, an innovative framework integrating a two-stage learning strategy. Initially, dynamic layerwise learning is implemented. During this phase, the quantum circuit undergoes gradual expansion alongside hierarchical training. This method not only refines initialization and training efficiency but also significantly mitigates the barren plateau issue while boosting the model's trainability. Subsequently, a sequential optimization strategy is adopted to adjust the parameters and optimize the entire network structure. Experimental results demonstrate the efficacy of DL-VQNN. On the NSL-KDD dataset, DL-VQNN achieves improved classification accuracy while reducing training time by up to 46%. Further evaluations across multiple datasets confirm its strong generalization and robustness. These findings suggest that DL-VQNN is a promising framework for scalable quantum machine learning, offering significant improvements in both performance and efficiency.

关键词： variational quantum algorithms Barren plateau Dynamic layerwise

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Recompilation-enhanced simulation of electron-phonon dynamics on IBM quantum computers

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NEW JOURNAL OF PHYSICS 2022年第9期24卷 093017页

作者： Jaderberg, Benjamin Eisfeld, Alexander Jaksch, Dieter Mostame, Sarah Univ Oxford Clarendon Lab Parks Rd Oxford OX1 3PU England Max Planck Inst Phys Komplexer Syst Nothnitztr Str 38 D-01187 Dresden Germany Univ Hamburg Inst Laserphys D-22761 Hamburg Germany IBM TJ Watson Res Ctr IBM Quantum Yorktown Hts NY 10598 USA

Simulating quantum systems is believed to be one of the first applications for which quantum computers may demonstrate a useful advantage. For many problems in physics, we are interested in studying the evolution of the electron-phonon Hamiltonian, for which efficient digital quantum computing schemes exist. Yet to date, no accurate simulation of this system has been produced on real quantum hardware. In this work, we consider the absolute resource cost for gate-based quantum simulation of small electron-phonon systems as dictated by the number of Trotter steps and bosonic energy levels necessary for the convergence of dynamics. We then apply these findings to perform experiments on IBM quantum hardware for both weak and strong electron-phonon coupling. Despite significant device noise, through the use of approximate circuit recompilation we obtain electron-phonon dynamics on current quantum computers comparable to exact diagonalisation. Our results represent a significant step in utilising near term quantum computers for simulation of quantum dynamics and highlight the novelty of approximate circuit recompilation as a tool for reducing noise.

关键词： quantum computing quantum algorithms variational quantum algorithms quantum circuit recompilation quantum simulation electron-phonon

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quantum Architecture Search with Meta-Learning

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ADVANCED quantum TECHNOLOGIES 2022年第8期5卷

作者： He, Zhimin Chen, Chuangtao Li, Lvzhou Zheng, Shenggen Situ, Haozhen Foshan Univ Sch Elect & Informat Engn Foshan 528000 Peoples R China Foshan Univ Sch Mechatron Engn & Automat Foshan 528000 Peoples R China Sun Yat Sen Univ Sch Comp Sci & Engn Inst Quantum Comp & Comp Theory Guangzhou 510006 Peoples R China Peng Cheng Lab Shenzhen 518055 Peoples R China South China Agr Univ Coll Math & Informat Guangzhou 510642 Peoples R China

variational quantum algorithms (VQAs) have been successfully applied to quantum approximate optimization algorithms, variational quantum compiling and quantum machine learning models. The performances of VQAs largely depend on the architecture of parameterized quantum circuits (PQCs). quantum architecture search (QAS) aims to automate the design of PQCs in different VQAs with classical optimization algorithms. However, current QAS algorithms do not use prior experiences and search the quantum architecture from scratch for each new task, which is inefficient and time consuming. In this paper, a meta quantum architecture search (MetaQAS) algorithm is proposed, which learns good initialization heuristics of the architecture (i.e., meta-architecture), along with the meta-parameters of quantum gates from a number of training tasks such that they can adapt to new tasks with fewer gradient updates, which leads to fast learning on new tasks. The proposed MetaQAS can be used with arbitrary gradient-based QAS algorithms. Simulation results on variational quantum compiling (VQC) and quantum approximate optimization algorithm (QAOA) show that the architectures optimized by MetaQAS converge faster than a state-of-the-art gradient-based QAS algorithm, namely DQAS. MetaQAS also achieves a better solution than DQAS after fine-tuning of gate parameters.

关键词： meta-learning quantum architecture search variational quantum algorithms

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A Case for Noisy Shallow Gate-based Circuits in quantum Machine Learning

A Case for Noisy Shallow Gate-based Circuits in Quantum Mach...

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IEEE International Conference on Rebooting Computing (ICRC)

作者： Selig, Patrick Murphy, Niall Sundareswaran, Ashwin R. Redmond, David Caton, Simon Univ Coll Dublin Sch Comp Sci Dublin Ireland Univ Coll Dublin Ctr Quantum Engn Sci & Technol Dublin Ireland Equall Labs Dublin Ireland

ISBN: (纸本)9781665423328

There is increasing interest in the development of gate-based quantum circuits for the training of machine learning models. Yet, little is understood concerning the parameters of circuit design, and the effects of noise and other measurement errors on the performance of quantum machine learning models. In this paper, we explore the practical implications of key circuit design parameters (number of qubits, depth etc.) using several standard machine learning datasets and IBM's Qiskit simulator. In total we evaluate over 6500 unique circuits with n approximate to 120700 individual runs. We find that in general shallow (low depth) wide (more qubits) circuit topologies tend to outperform deeper ones in settings without noise. We also explore the implications and effects of different notions of noise and discuss circuit topologies that are more / less robust to noise for classification machine learning tasks. Based on the findings we define guidelines for circuit topologies that show near-term promise for the realisation of quantum machine learning algorithms using gate-based NISQ quantum computer.

关键词： Qiskit quantum Machine Learning variational quantum algorithms NISQ architecture Noise Gate-based Circuits

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quantum self-supervised learning

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quantum SCIENCE AND TECHNOLOGY 2022年第3期7卷 035005-035005页

作者： Jaderberg, B. Anderson, L. W. Xie, W. Albanie, S. Kiffner, M. Jaksch, D. Univ Oxford Clarendon Lab Parks Rd Oxford OX1 3PU England Univ Oxford Dept Engn Sci Visual Geometry Grp Oxford England Univ Cambridge Dept Engn Cambridge England Natl Univ Singapore Ctr Quantum Technol 3 Sci Dr 2 Singapore 117543 Singapore Univ Hamburg Inst Laserphys D-22761 Hamburg Germany

The resurgence of self-supervised learning, whereby a deep learning model generates its own supervisory signal from the data, promises a scalable way to tackle the dramatically increasing size of real-world data sets without human annotation. However, the staggering computational complexity of these methods is such that for state-of-the-art performance, classical hardware requirements represent a significant bottleneck to further progress. Here we take the first steps to understanding whether quantum neural networks (QNNs) could meet the demand for more powerful architectures and test its effectiveness in proof-of-principle hybrid experiments. Interestingly, we observe a numerical advantage for the learning of visual representations using small-scale QNN over equivalently structured classical networks, even when the quantum circuits are sampled with only 100 shots. Furthermore, we apply our best quantum model to classify unseen images on the ibmq_paris quantum computer and find that current noisy devices can already achieve equal accuracy to the equivalent classical model on downstream tasks.

关键词： variational quantum algorithms quantum machine learning self-supervised learning deep learning quantum neural networks

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Twisted hybrid algorithms for combinatorial optimization

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quantum SCIENCE AND TECHNOLOGY 2022年第4期7卷 045013-045013页

作者： Caha, Libor Kliesch, Alexander Koenig, Robert Tech Univ Munich Zentrum Math Munich Germany Munich Ctr Quantum Sci & Technol Munich Germany

Proposed hybrid algorithms encode a combinatorial cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. Classical processing is typically only used for the choice of variational parameters following gradient descent. As a consequence, these approaches are limited by the descriptive power of the associated states. We argue that for certain combinatorial optimization problems, such algorithms can be hybridized further, thus harnessing the power of efficient non-local classical processing. Specifically, we consider combining a quantum variational ansatz with a greedy classical post-processing procedure for the MaxCut-problem on three-regular graphs. We show that the average cut-size produced by this method can be quantified in terms of the energy of a modified problem Hamiltonian. This motivates the consideration of an improved algorithm which variationally optimizes the energy of the modified Hamiltonian. We call this a twisted hybrid algorithm since the additional classical processing step is combined with a different choice of variational parameters. We exemplify the viability of this method using the quantum approximate optimization algorithm (QAOA), giving analytic lower bounds on the expected approximation ratios achieved by twisted QAOA. We observe that for levels p - 1, ..., 5, these lower bounds are comparable to the known lower bounds on QAOA at level p + 1 for high-girth graphs. This suggests that using twisted QAOA can reduce the circuit depth by 4 and the number of variational parameters by 2.

关键词： quantum algorithms variational quantum algorithms combinatorial optimization approximation algorithms hybrid algorithms MaxCut

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Machine learning in the quantum realm: The state-of-the-art, challenges, and future vision

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EXPERT SYSTEMS WITH APPLICATIONS 2022年第0期194卷 116512-116512页

作者： Houssein, Essam H. Abohashima, Zainab Elhoseny, Mohamed Mohamed, Waleed M. Minia Univ Fac Comp & Informat Al Minya Egypt Nahda Univ Fac Comp Sci Bani Suwayf Egypt Univ Sharjah Sharjah U Arab Emirates Mansoura Univ Fac Comp & Informat Mansoura Egypt

Machine learning has become a ubiquitous and effective technique for data processing and classification. Furthermore, due to the superiority and progress of quantum computing in many areas (e.g., cryptography, machine learning, healthcare), a combination of classical machine learning and quantum information processing has established a new field, called, quantum machine learning. One of the most frequently used applications of quantum computing is machine learning. This paper aims to present a comprehensive review of state-of-the-art advances in quantum machine learning. Besides, this paper outlines recent works on different architectures of quantum deep learning, and illustrates classification tasks in the quantum domain as well as encoding methods and quantum subroutines. Furthermore, this paper examines how the concept of quantum computing enhances classical machine learning. Two methods for improving the performance of classical machine learning are presented. Finally, this work provides a general review of challenges and the future vision of quantum machine learning.

关键词： quantum machine learning quantum computing quantum deep learning quantum inspired Hybrid quantum-classical quantum classification variational quantum algorithms

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Differentiable quantum architecture search

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quantum SCIENCE AND TECHNOLOGY 2022年第4期7卷 045023-045023页

作者： Zhang, Shi-Xin Hsieh, Chang-Yu Zhang, Shengyu Yao, Hong Tsinghua Univ Inst Adv Study Beijing 100084 Peoples R China Tencent Tencent Quantum Lab Shenzhen 518057 Guangdong Peoples R China Tsinghua Univ State Key Lab Low Dimens Quantum Phys Beijing 100084 Peoples R China

quantum architecture search (QAS) is the process of automating architecture engineering of quantum circuits. It has been desired to construct a powerful and general QAS platform which can significantly accelerate current efforts to identify quantum advantages of error-prone and depth-limited quantum circuits in the NISQ era. Hereby, we propose a general framework of differentiable quantum architecture search (DQAS), which enables automated designs of quantum circuits in an end-to-end differentiable fashion. We present several examples of circuit design problems to demonstrate the power of DQAS. For instance, unitary operations are decomposed into quantum gates, noisy circuits are re-designed to improve accuracy, and circuit layouts for quantum approximation optimization algorithm are automatically discovered and upgraded for combinatorial optimization problems. These results not only manifest the vast potential of DQAS being an essential tool for the NISQ application developments, but also present an interesting research topic from the theoretical perspective as it draws inspirations from the newly emerging interdisciplinary paradigms of differentiable programming, probabilistic programming, and quantum programming.

关键词： variational quantum algorithms quantum architecture search quantum simulations

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