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4th IEEE International Conference on quantum Computing and Engineering, QCE 2023

作者： Barthe, Alice Grossi, Michele Tura, Jordi Dunjko, Vedran Cern Quantum Technology Initiative Geneva Switzerland Leiden University Applied Quantum Algorithms Leiden Netherlands

ISBN: (纸本)9798350343236

Solving Ordinary Differential Equations (ODE) is important for a broad range of domains, such as engineering, weather forecast, and finance. Most quantum algorithms proposed to solve them revolve around transforming ODEs into a system of linear equations, in order to benefit from the exponential advantage promised by the HHL algorithm. However, there are known limitations to this subroutine such as the linear scaling with condition number. In particular, for HHL-based ODE solvers, this dependency yields a complexity that generally grows exponentially with the integration time. In this paper, we present a scheme that does not rely on the HHL subroutine. We use the Koopman Von Neumann (KvN) formalism that maps arbitrary nonlinear dynamics to a Hilbert space where the dynamics are unitary. This effectively reduces the ODE problem to a Hamiltonian time evolution, which is a well-known problem in quantum computing. However, this comes at a cost as the KvN formalism is expressed in an infinite-dimensional Hilbert space, and involves nonphysical states with infinite energies. Previous works have tackled this by truncating the Hilbert space, and by approximating all the relevant states and operations on qubit-based systems. Instead of mapping to qubit-based computations, in this paper, we investigate the direct use of continuous-variable quantum computers for this problem. We provide an algorithm to compile a sequence of Gaussian and non-Gaussian continuous variables gates to solve an arbitrary one-dimensional polynomial ODE. We analyze the algorithm and propose that it is intrinsically better suited for solving so-called initial distribution problems, rather than initial condition problems. We propose the first steps towards a comprehensive complexity and specify which steps need to be developed for a complete analysis. © 2023 IEEE.

关键词： Ordinary differential equations

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Classification of Hybrid quantum-Classical Computing 1

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23rd International Conference on Computational Science, ICCS 2023

作者： Phillipson, Frank Neumann, Niels Wezeman, Robert Department Applied Cryptography and Quantum Algorithms TNO The Hague Netherlands School of Business and Economics Maastricht University Maastricht Netherlands

ISBN: (数字)9783031360305

ISBN: (纸本)9783031360299

As quantum computers mature, the applicability in practice becomes more important. quantum computers will often be used in a hybrid setting, where classical computers still play an important role in operating and using the quantum computer. However the term hybrid is diffuse and multi-interpretable. In this work we define two classes of hybrid quantum-classical computing: vertical and horizontal hybrid quantum-classical computing. The first is application-agnostic and concerns using and operating quantum computers. The second is application-specific and concerns running an algorithm. For both, we give a further subdivision in different types of hybrid quantum-classical computing and we introduce terms for them. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.

关键词： quantum theory

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qgym: A Gym for Training and Benchmarking RL-Based quantum Compilation 4

qgym: A Gym for Training and Benchmarking RL-Based Quantum C...

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4th IEEE International Conference on quantum Computing and Engineering, QCE 2023

作者： Van Der Linde, Stan De Kok, Willem Bontekoe, Tariq Feld, Sebastian Applied Cryptography & Quantum Algorithms The Hague Netherlands Bernoulli Institute University of Groningen Faculty of Science and Engineering Groningen Netherlands QuTech Delft University of Technology Quantum & Computer Engineering Delft Netherlands

ISBN: (纸本)9798350343236

Compiling a quantum circuit for specific quantum hardware is a challenging task. Moreover, current quantum computers have severe hardware limitations. To make the most use of the limited resources, the compilation process should be optimized. To improve currents methods, Reinforcement Learning (RL), a technique in which an agent interacts with an environment to learn complex policies to attain a specific goal, can be used. In this work, we present qgym, a software framework derived from the OpenAI gym, together with environments that are specifically tailored towards quantum compilation. The goal of qgym is to connect the research fields of Artificial Intelligence (AI) with quantum compilation by abstracting parts of the process that are irrelevant to either domain. It can be used to train and benchmark RL agents and algorithms in highly customizable environments. © 2023 IEEE.

关键词： Reinforcement learning

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Explainable Representation Learning of Small quantum States

arXiv

引用

arXiv 2023年

作者： Frohnert, Felix van Nieuwenburg, Evert Applied Quantum Algorithms Universiteit Leiden Netherlands

Unsupervised machine learning models build an internal representation of their training data without the need for explicit human guidance or feature engineering. This learned representation provides insights into which features of the data are relevant for the task at hand. In the context of quantum physics, training models to describe quantum states without human intervention offers a promising approach to gaining insight into how machines represent complex quantum states. The ability to interpret the learned representation may offer a new perspective on non-trivial features of quantum systems and their efficient representation. We train a generative model on two-qubit density matrices generated by a parameterized quantum circuit. In a series of computational experiments, we investigate the learned representation of the model and its internal understanding of the data. We observe that the model learns an interpretable representation which relates the quantum states to their underlying entanglement characteristics. In particular, our results demonstrate that the latent representation of the model is directly correlated with the entanglement measure concurrence. The insights from this study represent proof of concept towards interpretable machine learning of quantum states. Our approach offers insight into how machines learn to represent small-scale quantum systems autonomously. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning

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Continuous Variables quantum Algorithm for Solving Ordinary Differential Equations

Continuous Variables Quantum Algorithm for Solving Ordinary ...

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quantum Computing and Engineering (QCE), IEEE International Conference on

作者： Alice Barthe Michele Grossi Jordi Tura Vedran Dunjko Quantum Technology Initiative CERN Geneva Switzerland Applied Quantum Algorithms Leiden University Leiden The Netherlands

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Parameterized quantum circuits as universal generative models for continuous multivariate distributions

arXiv

引用

arXiv 2024年

作者： Barthe, Alice Grossi, Michele Vallecorsa, Sofia Tura, Jordi Dunjko, Vedran aQaL Applied Quantum Algorithms Universiteit Leiden Netherlands Quantum Technology Initiative CERN Geneva Switzerland Instituut-Lorentz Universiteit Leiden Netherlands

Parameterized quantum circuits have been extensively used as the basis for machine learning models in regression, classification, and generative tasks. For supervised learning, their expressivity has been thoroughly investigated and several universality properties have been proven. However, in the case of quantum generative modelling, much less is known, especially when the task is to model distributions over continuous variables. In this work, we elucidate expectation value sampling-based models. Such models output the expectation values of a set of fixed observables from a quantum circuit into which classical random data has been uploaded. We prove the universality of such variational quantum algorithms for the generation of multivariate distributions. We explore various architectures which allow universality and prove tight bounds connecting the minimal required qubit number, and the minimal required number of measurements needed. Our results may help guide the design of future quantum circuits in generative modelling tasks. Copyright © 2024, The Authors. All rights reserved.

关键词： Timing circuits

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CURRICULUM REINFORCEMENT LEARNING FOR quantum ARCHITECTURE SEARCH UNDER HARDWARE ERRORS 12

CURRICULUM REINFORCEMENT LEARNING FOR QUANTUM ARCHITECTURE S...

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12th International Conference on Learning Representations, ICLR 2024

作者： Patel, Yash J. Kundu, Akash Ostaszewski, Mateusz Bonet-Monroig, Xavier Dunjko, Vedran Danaci, Onur 〈aQaL〉 Applied Quantum Algorithms Leiden University Netherlands Institute of Theoretical and Applied Informatics Polish Academy of Sciences Poland Joint Doctoral School Silesian University of Technology Poland Warsaw University of Technology Institute of Computer Science Poland Lorentz Institute Leiden University Netherlands LIACS Leiden University Netherlands

The key challenge in the noisy intermediate-scale quantum era is finding useful circuits compatible with current device limitations. Variational quantum algorithms (VQAs) offer a potential solution by fixing the circuit architecture and optimizing individual gate parameters in an external loop. However, parameter optimization can become intractable, and the overall performance of the algorithm depends heavily on the initially chosen circuit architecture. Several quantum architecture search (QAS) algorithms have been developed to design useful circuit architectures automatically. In the case of parameter optimization alone, noise effects have been observed to dramatically influence the performance of the optimizer and final outcomes, which is a key line of study. However, the effects of noise on the architecture search, which could be just as critical, are poorly understood. This work addresses this gap by introducing a curriculum-based reinforcement learning QAS (CRLQAS) algorithm designed to tackle challenges in realistic VQA deployment. The algorithm incorporates (i) a 3D architecture encoding and restrictions on environment dynamics to explore the search space of possible circuits efficiently, (ii) an episode halting scheme to steer the agent to find shorter circuits, and (iii) a novel variant of simultaneous perturbation stochastic approximation as an optimizer for faster convergence. To facilitate studies, we developed an optimized simulator for our algorithm, significantly improving computational efficiency in simulating noisy quantum circuits by employing the Pauli-transfer matrix formalism in the Pauli-Liouville basis. Numerical experiments focusing on quantum chemistry tasks demonstrate that CRLQAS outperforms existing QAS algorithms across several metrics in both noiseless and noisy environments. © 2024 12th International Conference on Learning Representations, ICLR 2024. All rights reserved.

关键词： Reinforcement learning

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Translating Constraints into QUBOs for the Quadratic Knapsack Problem 1

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23rd International Conference on Computational Science, ICCS 2023

作者： Bontekoe, Tariq Phillipson, Frank Schoot, Ward van der TNO Department Applied Cryptography and Quantum Algorithms The Hague Netherlands School of Business and Economics Maastricht University Maastricht Netherlands

ISBN: (数字)9783031360305

ISBN: (纸本)9783031360299

One of the first fields where quantum computing will likely show its use is optimisation. Many optimisation problems naturally arise in a quadratic manner, such as the quadratic knapsack problem. The current state of quantum computers requires these problems to be formulated as a quadratic unconstrained binary optimisation problem, or QUBO. Constrained quadratic binary optimisation can be translated into QUBOs by translating the constraint. However, this translation can be made in several ways, which can have a large impact on the performance when solving the QUBO. We show six different formulations for the quadratic knapsack problem and compare their performance using simulated annealing. The best performance is obtained by a formulation that uses no auxiliary variables for modelling the inequality constraint. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.

关键词： Simulated annealing

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Weighted Approximate quantum Natural Gradient for Variational quantum Eigensolver

arXiv

引用

arXiv 2025年

作者： Shi, Chenyu Dunjko, Vedran Wang, Hao 〈aQaL〉 Applied Quantum Algorithms Universiteit Leiden Netherlands LIACS Universiteit Leiden Niels Bohrweg 1 Leiden2333 CA Netherlands

Variational quantum eigensolver (VQE) is one of the most prominent algorithms using near-term quantum devices, designed to find the ground state of a Hamiltonian. In VQE, a classical optimizer iteratively updates the parameters in the quantum circuit. Among various optimization methods, quantum natural gradient descent (QNG) stands out as a promising optimization approach for VQE. However, standard QNG only leverages the quantum Fisher information of the entire system and treats each subsystem equally in the optimization process, without accounting for the different weights and contributions of each subsystem corresponding to each observable. To address this limitation, we propose a Weighted Approximate quantum Natural Gradient (WA-QNG) method tailored for k-local Hamiltonians. In this paper, we theoretically analyze the potential advantages of WA-QNG compared to QNG from three distinct perspectives and reveal its connection with the Gauss-Newton method. We also show it outperforms standard quantum natural gradient descent in the numerical experiments for seeking the ground state of the Hamiltonian. Copyright © 2025, The Authors. All rights reserved.

关键词： quantum electronics

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QuAS: quantum Application Score for Benchmarking the Utility of quantum Computers

QuAS: Quantum Application Score for Benchmarking the Utility...

引用

quantum Computing and Engineering (QCE), IEEE International Conference on

作者： Koen J. Mesman Ward van der Schoot Matthias Möller Niels M. P. Neumann QAIMS Delft University of Technology Delft Netherlands Applied Cryptography and Quantum Algorithms TNO The Hague Netherlands Applied Mathematics Delft University of Technology Delft Netherlands

ISBN: (数字)9798331541378

ISBN: (纸本)9798331541385

Benchmarking quantum computers helps to quantify them and bringing the technology to the market. Various application-level metrics exist to benchmark a quantum device at an application level. This paper presents a revised holistic scoring method called the quantum Application Score (QuAS) incorporating strong points of previous metrics, such as QPack and the Q-score. We discuss how to integrate both and thereby obtain an application-level metric that better quantifies the practical utility of quantum computers. We evaluate the new metric on different hardware platforms such as D- Wave and IBM as well as quantum simulators of quantum Inspire and Rigetti.

关键词： Measurement Computers quantum computing Benchmark testing Hardware

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