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Gradients and frequency profiles of quantum re-uploading models

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arXiv 2023年

作者： Barthe, Alice Pérez-Salinas, Adrián 〈aQaL〉 Applied Quantum Algorithms Universiteit Leiden Netherlands Quantum Technology Initiative CERN Geneva Switzerland Instituut-Lorentz Universiteit Leiden Netherlands

quantum re-uploading models have been extensively investigated as a form of machine learning within the context of variational quantum algorithms. Their trainability and expressivity are not yet fully understood and are critical to their performance. In this work, we address trainability through the lens of the magnitude of the gradients of the cost function. We prove bounds for the differences between gradients of the better-studied data-less parameterized quantum circuits and reuploading models. We coin the concept of absorption witness to quantify such difference. For the expressivity, we prove that quantum reuploading models output functions with vanishing high-frequency components and upper-bounded derivatives with respect to data. As a consequence, such functions present limited sensitivity to fine details and offer protection against overfitting. We performed numerical experiments extending the theoretical results to more relaxed and realistic conditions. Overall, future designs of quantum re-uploading models will benefit from the strengthened knowledge delivered by the uncovering of absorption witnesses and vanishing high frequencies. © 2023, CC BY.

关键词： Cost functions

Monitored quantum transport: full counting statistics of a quantum Hall interferometer

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arXiv 2025年

作者： Beenakker, C.W.J. Chen, Jin-Fu Instituut-Lorentz Universiteit Leiden P.O. Box 9506 Leiden2300 RA Netherlands 〈aQaL〉 Applied Quantum Algorithms Leiden Netherlands

We generalize the Levitov-Lesovik formula for the probability distribution function of the electron charge transferred through a phase coherent conductor, to include projective measurements that monitor the chiral propagation in quantum Hall edge modes. When applied to an electronic Mach-Zehnder interferometer, the monitoring reduces the visibility of the Aharonov-Bohm conductance oscillations while preserving the binomial form of the counting statistics, thereby removing a fundamental shortcoming of the dephasing-probe model of decoherence. Copyright © 2025, The Authors. All rights reserved.

关键词： Distribution functions

Thermodynamically Consistent Lindbladians for quantum Stochastic Thermodynamics

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arXiv 2025年

作者： Chen, Jin-Fu Instituut-Lorentz Universiteit Leiden P.O. Box 9506 Leiden2300 RA Netherlands 〈aQaL〉 Applied Quantum Algorithms Leiden Netherlands

We develop a Lindblad framework for quantum stochastic thermodynamics to study the nonequilibrium thermodynamics of open quantum systems. Our approach adopts the local quantum detailed balance condition, ensuring thermodynamic consistency and leading to a joint fluctuation theorem of quantum work and heat. Instead of solving the full evolution of the density matrix, we employ an effective parametrization to derive the full counting statistics of work and heat and determine the optimal protocols. As an application, we refine the quantum Brownian motion master equation to ensure the quantum detailed balance condition, derive the optimal protocols at different temperatures, and study the work statistics. Our framework provides fundamental insights and practical strategies for optimizing thermodynamic processes in open quantum systems. Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

QuAS: quantum Application Score for benchmarking the utility of quantum computers

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arXiv 2024年

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

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. © 2024, CC BY.

关键词： Benchmarking

QDarts: A quantum Dot Array Transition Simulator for finding charge transitions in the presence of finite tunnel couplings, non-constant charging energies and sensor dots

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arXiv 2024年

作者： Krzywda, Jan A. Liu, Weikun van Nieuwenburg, Evert Krause, Oswin 〈aQaL〉 Applied Quantum Algorithms Universiteit Leiden Netherlands Dept. of Computer Science University of Copenhagen Copenhagen Denmark Instituut-Lorentz and LIACS Universiteit Leiden Netherlands

We present QDarts, an efficient simulator for realistic charge stability diagrams of quantum dot array (QDA) devices in equilibrium states. It allows for pinpointing the location of concrete charge states and their transitions in a high-dimensional voltage space (via arbitrary two-dimensional cuts through it), and includes effects of finite tunnel coupling, non-constant charging energy and a simulation of noisy sensor dots. These features enable close matching of various experimental results in the literature, and the package hence provides a flexible tool for testing QDA experiments, as well as opening the avenue for developing new methods of device tuning. © 2024, CC BY.

关键词： Nanocrystals

Nonlinear functions of quantum states

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arXiv 2024年

作者： Yao, Hongshun Liu, Yingjian Lin, Tengxiang Wang, Xin Guangdong511453 China Applied Quantum Algorithms Leiden Netherlands Instituut-Lorentz Universiteit Leiden P.O. Box 9506 Leiden2300 RA Netherlands

Efficient estimation of nonlinear functions of quantum states is crucial for various key tasks in quantum computing, such as entanglement spectroscopy, fidelity estimation, and feature analysis of quantum data. Conventional methods using state tomography and estimating numerous terms of the series expansion are computationally expensive, while alternative approaches based on a purified query oracle impose practical constraints. In this paper, we introduce the quantum state function (QSF) framework by extending the SWAP test via linear combination of unitaries and parameterized quantum circuits. Our framework enables the implementation of arbitrary degree-n polynomial functions of quantum states with precision Ε using O(n/Ε2) copies. We further apply QSF for developing quantum algorithms for fundamental tasks, including entropy, fidelity, and eigenvalue estimations. Secifically, for estimating von Neumann entropy, quantum relative entropy, and quantum state fidelity, where κ represents the minimal nonzero eigenvalue, we achieve a sample complexity of Õ(1/(Ε2κ)). Our work establishes a concise and unified paradigm for estimating and realizing nonlinear functions of quantum states, paving the way for the practical processing and analysis of quantum data. © 2024, CC BY.

关键词： Eigenvalues and eigenfunctions

Bloch Sphere Binary Trees: A method for the visualization of sets of multi-qubit systems pure states

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arXiv 2023年

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

Understanding the evolution of a multi-qubit quantum system, or elucidating what portion of the Hilbert space is occupied by a quantum dataset becomes increasingly hard with the number of qubits. In this context, the visualisation of sets of multi-qubit pure quantum states on a single image can be helpful. However, the current approaches to visualization of this type only allow the representation of a set of single qubits (not allowing multi-qubit systems) or a just a single multi-qubit system (not suitable if we care about sets of states), sometimes with additional restrictions, on symmetry or entanglement for example. [1–3]. In this work we present a mapping that can uniquely represent a set of arbitrary multi-qubit pure states on what we call a Binary Tree of Bloch Spheres. The backbone of this technique is the combination of the Schmidt decomposition and the Bloch sphere representation. We illustrate how this can be used in the context of understanding the time evolution of quantum states, e.g. providing immediate insights into the periodicity of the system and even entanglement properties. We also provide a recursive algorithm which translates from the computational basis state representation to the binary tree of Bloch spheres representation. The algorithm was implemented together with a visualization library in Python released as open source. Copyright © 2023, The Authors. All rights reserved.

关键词： Visualization

Evolving Hard Maximum Cut Instances for quantum Approximate Optimization algorithms

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arXiv 2025年

作者： Pan, Shuaiqun Neumann, Frank Patel, Yash J. Bäck, Thomas Neumann, Aneta Wang, Hao LIACS Leiden University Leiden Netherlands Optimisation and Logistics School of Computer and Mathematical Sciences The University of Adelaide Adelaide Australia applied Quantum algorithms & LIACS Leiden University Leiden Netherlands

Variational quantum algorithms, such as the Recursive quantum Approximate Optimization Algorithm (RQAOA), have become increasingly popular, offering promising avenues for employing Noisy Intermediate-Scale quantum devices to address challenging combinatorial optimization tasks like the maximum cut problem. In this study, we utilize an evolutionary algorithm equipped with a unique fitness function. This approach targets hard maximum cut instances within the latent space of a Graph Autoencoder, identifying those that pose significant challenges or are particularly tractable for RQAOA, in contrast to the classic Goemans and Williamson algorithm. Our findings not only delineate the distinct capabilities and limitations of each algorithm but also expand our understanding of RQAOA’s operational limits. Furthermore, the diverse set of graphs we have generated serves as a crucial benchmarking asset, emphasizing the need for more advanced algorithms to tackle combinatorial optimization challenges. Additionally, our results pave the way for new avenues in graph generation research, offering exciting opportunities for future explorations. © 2025, CC BY.

关键词： Combinatorial optimization

Equating quantum imaginary time evolution, Riemannian gradient flows, and stochastic implementations

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arXiv 2025年

作者： McMahon, Nathan A. Pervez, Mahum Arenz, Christian 〈aQaL〉 Applied Quantum Algorithms Leiden University Netherlands LIACS Leiden University Netherlands School of Electrical Computer and Energy Engineering Arizona State University TempeAZ85281 United States

We identify quantum imaginary time evolution as a Riemannian gradient flow on the unitary group. We develop an upper bound for the error between the two evolutions that can be controlled through the step size of the Riemannian gradient descent which minimizes the energy of the system. We discuss implementations through adaptive quantum algorithms and present a stochastic Riemannian gradient descent algorithm in which each step is efficiently implementable on a quantum computer. We prove that for a sufficiently small step size, the stochastic evolution concentrates around the imaginary time evolution, thereby providing performance guarantees for cooling the system through stochastic Riemannian gradient descent. © 2025, CC BY.

关键词： Qubits