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Performance and scaling analysis of variational quantum simulation

quantum SCIENCE AND TECHNOLOGY 2025年第1期10卷

作者： Ponce, Mario Cope, Thomas de Vega, Ines Leib, Martin IQM Quantum Comp Georg Brauchle Ring 23-25 D-80992 Munich Germany Ludwig Maximilians Univ Munchen Dept Phys Theresienstr 37 D-80333 Munich Germany Ludwig Maximilians Univ Munchen Arnold Sommerfeld Ctr Theoret Phys Theresienstr 37 D-80333 Munich Germany

We present an empirical analysis of the scaling of the minimal quantum circuit depth required for a variational quantum simulation (VQS) method to obtain a solution to the time evolution of a quantum system within a predefined error tolerance. In a comparison against a non-variational method based on Trotterized time evolution, we observe similar scaling behaviours of the depth requirements of VQS and Trotter when the size of the system and the simulated time grow linearly. Results are also put into perspective by discussing the corresponding classical complexity required for VQS. Our results allow us to identify a possible advantage region for VQS over Trotterization.

关键词： variational quantum algorithms time evolution scaling analysis

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quantum surrogate modelling to solve phase field simulation problems in metal solidification

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JOURNAL OF SUPERCOMPUTING 2025年第5期81卷

作者： Eider, Garate-Perez Meritxell, Gomez-Omella Jon, Lambarri Naroa, Martin Tekniker BRTA Intellingent Informat Syst & Adv Mfg Technol Inaki Goenaga St 5 Eibar 20600 Spain Univ Basque Country Fac Informat Manuel Lardizabal Pasealekua 1 Donostia San Sebastian 20018 Spain Univ Carlos III Madrid Madrid St 126 Getafe 28903 Spain

variational quantum algorithms (VQAs) are hybrid algorithms that combine quantum computing capabilities with classical machine learning (ML) tasks, utilizing classical optimizers to train parametrized quantum circuits. This work demonstrates their practical utility by addressing regression tasks in an industrially relevant context: modelling dendritic solidification in metals, a process crucial for determining mechanical properties in additive manufacturing. By comparing a classical surrogate model based on extreme gradient boosting with a hybrid classical-quantum VQA model, this work shows that VQAs can serve as a viable alternative for computationally expensive surrogate modelling. These findings highlight the potential of VQAs to tackle complex physical phenomena in high-cost computational scenarios, advancing their application in real-world industrial ML challenges.

关键词： quantum Machine Learning variational quantum algorithms Surrogate Models Phase Field Problem

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Learning density functionals from noisy quantum data

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MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2025年第2期6卷

作者： Koridon, Emiel Frohnert, Felix Prehn, Eric van Nieuwenburg, Evert Tura, Jordi Polla, Stefano Vrije Univ Theoret Chem Amsterdam Netherlands Leiden Univ aQaL Appl Quantum Algorithms Lorentz Insitute Theo Leiden Netherlands Leiden Univ Leiden Inst Adv Comp Sci Leiden Netherlands

The search for useful applications of noisy intermediate-scale quantum (NISQ) devices in quantum simulation has been hindered by their intrinsic noise and the high costs associated with achieving high accuracy. A promising approach to finding utility despite these challenges involves using quantum devices to generate training data for classical machine learning (ML) models. In this study, we explore the use of noisy data generated by quantum algorithms in training an ML model to learn a density functional for the Fermi-Hubbard model. We benchmark various ML models against exact solutions, demonstrating that a neural-network ML model can successfully generalize from small datasets subject to noise typical of NISQ algorithms. The learning procedure can effectively filter out unbiased sampling noise, resulting in a trained model that outperforms any individual training data point. Conversely, when trained on data with expressibility and optimization error typical of the variational quantum eigensolver, the model replicates the biases present in the training data. The trained models can be applied to solving new problem instances in a Kohn-Sham-like density optimization scheme, benefiting from automatic differentiability and achieving reasonably accurate solutions on most problem instances. Our findings suggest a promising pathway for leveraging NISQ devices in practical quantum simulations, highlighting both the potential benefits and the challenges that need to be addressed for successful integration of quantum computing and ML techniques.

关键词： density functional theory machine learning quantum algorithms NISQ variational quantum algorithms

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A Monte Carlo Tree Search approach to QAOA: finding a needle in the haystack

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NEW JOURNAL OF PHYSICS 2025年第4期27卷 043014-043014页

作者： Agirre, Andoni van Nieuwenburg, Evert Wauters, Matteo M. Donostia Int Phys Ctr DIPC Manuel Lardizabal Pasealekua 4 Donostia San Sebastian 20018 Spain Univ Copenhagen Niels Bohr Inst Ctr Quantum Devices Univ Pk 5 DK-2100 Copenhagen Denmark Univ Basque Country UPV EHU Dept PMAS Phys Chem & Technol Manuel Lardizabal Pasealekua 3 Donostia San Sebastian 20018 Spain Leiden Univ Lorentz Inst POB 9506 NL-2300 RA Leiden Netherlands Leiden Univ Leiden Inst Adv Comp Sci POB 9506 NL-2300 RA Leiden Netherlands Univ Trento CNR INO Pitaevskii BEC Ctr Via Sommar 14 I-38123 Trento Italy Univ Trento Dept Phys Via Sommar 14 I-38123 Trento Italy Trento Inst Fundamental Phys & Applicat INFN TIFPA Via Sommar 14 I-38123 Trento Italy

The search for quantum algorithms to tackle classical combinatorial optimization problems has long been one of the most attractive yet challenging research topics in quantum computing. In this context, variational quantum algorithms (VQAs) are a promising family of hybrid quantum-classical methods tailored to cope with the limited capability of near-term quantum hardware. However, their effectiveness is hampered by the complexity of the classical parameter optimization which is prone to getting stuck either in local minima or in flat regions of the cost-function landscape. The clever design of efficient optimization methods is therefore of fundamental importance for fully leveraging the potential of VQAs. In this work, we approach parameter optimization as a sequential decision-making problem and tackle it with an adaptation of Monte Carlo Tree Search, a powerful artificial intelligence technique designed for efficiently exploring complex decision graphs. We show that leveraging regular parameter patterns deeply affects the decision-tree structure and allows for a flexible and noise-resilient optimization strategy suitable for near-term quantum devices. Our results shed further light on the interplay between artificial intelligence and quantum information and provide a valuable addition to the toolkit of variational quantum circuits.

关键词： variational quantum algorithms quantum optimization artificial intelligence NISQ algorithms

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Improving quantum metrology protocols with programmable photonic circuits

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NANOPHOTONICS 2025年

作者： de las Heras, Alberto Munoz Porras, Diego Gonzalez-Tudela, Alejandro CSIC Inst Fundamental Phys IFF Calle Serrano 113b Madrid 28006 Spain

Photonic quantum metrology enables the measurement of physical parameters with precision surpassing classical limits by using quantum states of light. However, generating states providing a large metrological advantage is hard because standard probabilistic methods suffer from low generation rates. Deterministic protocols using non-linear interactions offer a path to overcome this problem, but they are currently limited by the errors introduced during the interaction time. Thus, finding strategies to minimize the interaction time of these non-linearities is still a relevant question. In this work, we introduce and compare different deterministic strategies based on continuous and programmable Jaynes-Cummings and Kerr-type interactions, aiming to maximize the metrological advantage while minimizing the interaction time. We find that programmable interactions provide a larger metrological advantage than continuous operations at the expense of slightly larger interaction times. We show that while for Jaynes-Cummings non-linearities the interaction time grows with the photon number, for Kerr-type ones it decreases, favoring the scalability to big photon numbers. Finally, we also optimize different measurement strategies for the deterministically generated states based on photon-counting and homodyne detection.

关键词： photonic quantum metrology variational quantum algorithms programmable photonic circuits non-linear optics and photonics

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A quantum Framework for Combinatorial Optimization Problem over Graphs

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DATA SCIENCE AND ENGINEERING 2025年 1-12页

作者： Shi, Meng Wu, Sai Li, Ying Yuan, Gongsheng Yao, Chang Chen, Gang Bangsun Technol Hangzhou Zhejiang Peoples R China

Combinatorial optimization problems over graphs, such as the traveling salesman problem, longest path problem, and maximum independent set problem, are well-known for being computationally costly, some even NP-hard problems. In this paper, we propose a general quantum algorithm framework searching for approximate solutions to combinatorial optimization problems with linear objective functions. Our framework provides APIs (application programming interfaces) that enable developers to encode weighted graph structures onto quantum circuits and utilize variational algorithms to generate approximate solutions. One key advantage of our framework is that it allows developers to design new graph algorithms for the graph problem represented as linear combinations of edge weights without requiring expertise in quantum programming. Besides, it only uses a logarithmic level of quantum bit scale, making our framework work on quantum computers with limited physical resources. Our experimental results demonstrate that our framework can provide good approximations for the traveling salesman problem compared to current quantum algorithm.

关键词： quantum computing variational quantum algorithms Combinatorial optimization problem Traveling salesman problem

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EVOVAQ: EVOlutionary algorithms-based toolbox for variational quantum circuits

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SOFTWAREX 2024年 26卷

作者： Acampora, Giovanni Gutierrez, Carlos Cano Chiatto, Angela Hidalgo, Jose Manuel Soto Vitiello, Autilia Univ Naples Federico II Dept Phys Ettore Pancini Naples Italy Univ Granada Dept Comp Sci & Artificial Intelligence Granada Spain Univ Granada Dept Comp Engn Automat & Robot Granada Spain

Evolutionary algorithms (EAs) are becoming increasingly popular for training variational quantum Circuits (VQCs) due to their ability to conserve quantum resources. However, there is currently a lack of user-friendly tools for implementing this approach. To address this issue, this paper proposes EVOVAQ, a Python-based framework designed to simplify the use of EAs for training VQCs. EVOVAQ seamlessly integrates evolutionary computation with quantum libraries such as Qiskit, making it easy to use for both quantum computing and EAs communities. Furthermore, EVOVAQ's scalability enables the development of customized solutions, promoting innovation in the quantum computing field.

关键词： Evolutionary algorithms Python package quantum computing quantum machine learning variational quantum algorithms

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Learning quantum symmetries with interactive quantum-classical variational algorithms

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2024年第31期57卷 315304-315304页

作者： Lu, Jonathan Z. Bravo, Rodrigo Araiza Hou, Kaiying Dagnew, Gebremedhin A. Yelin, Susanne F. Najafi, Khadijeh Harvard Univ Dept Phys Cambridge MA 02138 USA IBM Quantum IBM TJ Watson Res Ctr Yorktown Hts NY 10598 USA 1QB Informat Technol Inc Vancouver BC Canada MIT Dept Math Cambridge MA USA

A symmetry of a state |psi > is a unitary operator of which |psi > is an eigenvector. When |psi > is an unknown state supplied by a black-box oracle, the state's symmetries provide key physical insight into the quantum system;symmetries also boost many crucial quantum learning techniques. In this paper, we develop a variational hybrid quantum-classical learning scheme to systematically probe for symmetries of |psi > with no a priori assumptions about the state. This procedure can be used to learn various symmetries at the same time. In order to avoid re-learning already known symmetries, we introduce an interactive protocol with a classical deep neural net. The classical net thereby regularizes against repetitive findings and allows our algorithm to terminate empirically with all possible symmetries found. An iteration of the learning algorithm can be implemented efficiently with non-local SWAP gates;we also give a less efficient algorithm with only local operations, which may be more appropriate for current noisy quantum devices. We simulate our algorithm on representative families of states, including cluster states and ground states of Rydberg and Ising Hamiltonians. We also find that the numerical query complexity scales well for up to moderate system sizes.

关键词： quantum machine learning variational quantum algorithms interactive learning quantum symmetries

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quantum-inspired variational algorithms for partial differential equations: application to financial derivative pricing

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QUANTITATIVE FINANCE 2021年第1期24卷 2259954-2259954页

作者： Zhao, Tianchen Sun, Chuhao Cohen, Asaf Stokes, James Veerapaneni, Shravan Univ Michigan Dept Math Ann Arbor MI 48109 USA

variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs);namely, the real- and imaginary time-dependent Schrodinger equation. In this paper, we present a simple generalization of VMC applicable to arbitrary time-dependent PDEs, showcasing the technique in the multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets.

关键词： variational quantum algorithms variational quantum Monte Carlo Multi-asset Black-Scholes PDE

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Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement

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quantum SCIENCE AND TECHNOLOGY 2025年第1期10卷 015008-015008页

作者： Correr, Guilherme Ilario Medina, Ivan Azado, Pedro C. Drinko, Alexandre Soares-Pinto, Diogo O. Univ Sao Paulo Inst Fis Sao Carlos CP 369 BR-13560970 Sao Carlos SP Brazil Univ Helsinki QTF Ctr Excellence FIN-00014 Helsinki Finland Univ Helsinki Dept Phys FIN-00014 Helsinki Finland Trinity Coll Dublin Sch Phys Dublin 2 Ireland

While scalable error correction schemes and fault tolerant quantum computing seem not to be universally accessible in the near sight, the efforts of many researchers have been directed to the exploration of the contemporary available quantum hardware. Due to these limitations, the depth and dimension of the possible quantum circuits are restricted. This motivates the study of circuits with parameterized operations that can be classically optimized in hybrid methods as variational quantum algorithms, enabling the reduction of circuit depth and size. The characteristics of these Parameterized quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application, motivating the study of their intrinsic properties. In this work, we analyse the generation of random states in PQCs under restrictions on the qubits connectivities, justified by different quantum computer architectures. We apply the expressibility quantifier and the average entanglement as diagnostics for the characteristics of the generated states and classify the circuits depending on the topology of the quantum computer where they can be implemented. As a function of the number of layers and qubits, circuits following a Ring topology will have the highest entanglement and expressibility values, followed by Linear/All-to-all almost together and the Star topology. In addition to the characterization of the differences between the entanglement and expressibility of these circuits, we also place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement. Circuits generating average and standard deviation for entanglement closer to values obtained with the truly uniformly random ensemble of unitaries present a steeper evolution when compared to others.

关键词： variational quantum algorithms parameterized quantum circuits expressibility average entanglement

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