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arXiv 2024年

作者： Dechant, David Markovich, Liubov Dunjko, Vedran Tura, Jordi 〈aQaL〉 Applied Quantum Algorithms Leiden Netherlands Instituut-Lorentz Universiteit Leiden P.O. Box 9506 Leiden2300 RA Netherlands LIACS Universiteit Leiden P.O. Box 9512 Leiden2300 RA Netherlands

A focus of recent research in quantum computing has been on developing quantum algorithms for differential equations solving using variational methods on near-term quantum devices. A promising approach involves variational algorithms, which combine classical Runge-Kutta methods with quantum computations. However, a rigorous error analysis, essential for assessing real-world feasibility, has so far been lacking. In this paper, we provide an extensive analysis of error sources and determine the resource requirements needed to achieve specific target errors. In particular, we derive analytical error and resource estimates for scenarios with and without shot noise, examining shot noise in quantum measurements and truncation errors in Runge-Kutta methods. Our analysis does not take into account representation errors and hardware noise, as these are specific to the instance and the used device. We evaluate the implications of our results by applying them to two scenarios: classically solving a 1D ordinary differential equation and solving an option pricing linear partial differential equation with the variational algorithm, showing that the most resource-efficient methods are of order 4 and 2, respectively. This work provides a framework for optimizing quantum resources when applying Runge-Kutta methods, enhancing their efficiency and accuracy in both solving differential equations and simulating quantum systems. Further, this work plays a crucial role in assessing the suitability of these variational algorithms for fault-tolerant quantum computing. The results may also be of interest to the numerical analysis community as they involve the accumulation of errors in the function description, a topic that has hardly been explored even in the context of classical differential equation solvers. Copyright © 2024, The Authors. All rights reserved.

关键词： Shot noise

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Spectral Gap Optimization for Enhanced Adiabatic State Preparation

arXiv

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arXiv 2024年

作者： Rai, Kshiti Sneh Chen, Jin-Fu Emonts, Patrick Tura, Jordi Instituut-Lorentz Universiteit Leiden P.O. Box 9506 Leiden2300 RA Netherlands 〈aQaL〉 Applied Quantum Algorithms Leiden Netherlands

The preparation of non-trivial states is crucial to the study of quantum many-body physics. Such states can be prepared with adiabatic quantum algorithms, which are restricted by the minimum spectral gap along the path. In this letter, we propose an efficient method to adiabatically prepare tensor networks states (TNSs). We maximize the spectral gap leveraging degrees of freedom in the parent Hamiltonian construction. We demonstrate this efficient adiabatic algorithm for preparing TNS, through examples of random TNS in one dimension, AKLT, and GHZ states. The Hamiltonian optimization applies to both injective and non-injective tensors, in the latter case by exploiting symmetries present in the tensors. Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

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Analyzing Prospects for quantum Advantage in Topological Data Analysis

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PRX quantum 2024年第1期5卷 010319-010319页

作者： Dominic W. Berry Yuan Su Casper Gyurik Robbie King Joao Basso Alexander Del Toro Barba Abhishek Rajput Nathan Wiebe Vedran Dunjko Ryan Babbush School of Mathematical and Physical Sciences Macquarie University Sydney NSW 2109 Australia Google Quantum AI Venice California 90291 USA applied Quantum algorithms (aQa) Leiden University Leiden 2300 RA Netherlands Department of Computing and Mathematical Sciences Caltech Pasadena California 91125 USA Department of Computer Science University of Toronto Ontario M5S 2E4 Canada Pacific Northwest National Laboratory Richland Washington 99354 USA

Lloyd et al. [Nat. Commun. 7, 10138 (2016)] were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that superquadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for superpolynomial advantage. We then introduce and analyze specific problem examples which have parameters in the regime where superpolynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve seemingly classically intractable instances.

关键词： quantum algorithms & computation

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Analyzing variational quantum landscapes with information content

arXiv

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arXiv 2023年

作者： Pérez-Salinas, Adrián Wang, Hao Bonet-Monroig, Xavier AQaL Applied Quantum Algorithms Universiteit Leiden Netherlands Instituut-Lorentz Universiteit Leiden Niels Bohrweg 2 Leiden2333 CA Netherlands LIACS Universiteit Leiden Niels Bohrweg 1 Leiden2333 CA Netherlands

The parameters of the quantum circuit in a variational quantum algorithm induce a landscape that contains the relevant information regarding its optimization hardness. In this work we investigate such landscapes through the lens of information content, a measure of the variability between points in parameter space. Our major contribution connects the information content to the average norm of the gradient, for which we provide robust analytical bounds on its estimators. This result holds for any (classical or quantum) variational landscape. We validate the analytical understating by numerically studying the scaling of the gradient in an instance of the barren plateau problem. In such instance we are able to estimate the scaling pre-factors in the gradient. Our work provides a new way to analyze variational quantum algorithms in a data-driven fashion well-suited for near-term quantum computers. Copyright © 2023, The Authors. All rights reserved.

关键词： Qubits

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Preparing low-variance states using a distributed quantum algorithm

arXiv

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arXiv 2025年

作者： Liu, Xiaoyu Schiffer, Benjamin F. Tura, Jordi 〈aQaL〉 Applied Quantum Algorithms Universiteit Leiden Netherlands Instituut-Lorentz Universiteit Leiden P.O. Box 9506 Leiden2300 RA Netherlands Max-Planck-Institut für Quantenoptik Hans-Kopfermann-Str. 1 GarchingD-85748 Germany

quantum computers are a highly promising tool for efficiently simulating quantum many-body systems. The preparation of their eigenstates is of particular interest and can be addressed, e.g., by quantum phase estimation algorithms. The routine then acts as an effective filtering operation, reducing the energy variance of the initial state. In this work, we present a distributed quantum algorithm inspired by iterative phase estimation to prepare low-variance states. Our method uses a single auxiliary qubit per quantum device, which controls its dynamics, and a postselection strategy for a joint quantum measurement on such auxiliary qubits. In the multi-device case, the result of this measurement heralds the successful runs of the protocol. This allows us to demonstrate that our distributed algorithm reduces the energy variance significantly faster compared to single-device implementations, thereby highlighting the potential of distributed algorithms for near-term and early fault-tolerant devices. © 2025, CC BY.

关键词： Qubits

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arXiv

引用

arXiv 2025年

作者： Shi, Chenyu Leoni, Gabriele Petrillo, Mauro Gallardo, Antonio Puertas Wang, Hao Applied Quantum Algorithms Leiden Leiden University Netherlands Leiden Institute of Advanced Computer Science Leiden University Netherlands Joint Research Centre Directorate F Health and Food Digital Health Unit European Commission Seidor Seidor Italy S.r.l. Milan Italy

Computing the similarity between two DNA sequences is of vital importance in bioscience. However, traditional computational methods can be resource-intensive due to the enormous sequence length encountered in practice. Recently, applied quantum algorithms have been anticipated to provide potential advantages over classical approaches. In this paper, we propose a permutation-invariant variational quantum kernel method specifically designed for DNA comparison. To represent the four nucleotide bases in DNA sequences with quantum states, we introduce a novel, theoretically motivated encoding scheme: the four distinct bases are encoded using the states of symmetric, informationally complete, positive operator-valued measures (SIC-POVMs). This encoding ensures mutual equality: each pair of symbols is equidistant on the Bloch sphere. Also, since permutation invariance is inherent to common DNA similarity measures such as Levenshtein distance, we realize it by using a specially designed parameterized quantum layer. We show that our novel encoding method and parameterized layers used in the quantum kernel model can effectively capture the symmetric characteristics of the pairwise DNA sequence comparison task. We validate our model through numerical experiments, which yield promising results on length-8 DNA sequences. Copyright © 2025, The Authors. All rights reserved.

关键词： Encoding (symbols)

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ON THE RELATION BETWEEN TRAINABILITY AND DEQUANTIZATION OF VARIATIONAL quantum LEARNING MODELS

arXiv

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arXiv 2024年

作者： Gil-Fuster, Elies Gyurik, Casper Pérez-Salinas, Adrián Dunjko, Vedran Dahlem Center for Complex Quantum Systems Freie Universität Berlin Berlin14195 Germany Fraunhofer Heinrich Hertz Institute Berlin10587 Germany 〈aQaL〉 Applied Quantum Algorithms Universiteit Leiden Netherlands Lorentz Instituut Universiteit Leiden Niels Bohrweg 2 Leiden2333 CA Netherlands LIACS Universiteit Leiden Niels Bohrweg 1 Leiden2333 CA Netherlands

quantum machine learning (QML) explores the potential advantages of quantum computers for machine learning tasks, with variational QML among the main current approaches. While quantum computers promise to solve problems that are classically intractable, it has been recently shown that a particular quantum algorithm which outperforms all pre-existing classical algorithms can be matched by a newly developed classical approach (often inspired by the quantum algorithm). We say such algorithms have been dequantized. For QML models to be effective, they must be trainable and non-dequantizable. The relationship between these properties is still not fully understood and recent works raised into question to what extent we could ever have QML models which are both trainable and non-dequantizable. This challenges the potential of QML altogether. In this work we answer open questions regarding when trainability and non-dequantization are compatible. We first formalize the key concepts and put them in the context of prior research. We introduce the role of "variationalness" of QML models using well-known quantum circuit architectures as leading examples. Our results provide recipes for variational QML models that are trainable and non-dequantizable. By ensuring that variational QML models are both trainable and non-dequantizable, we pave the way toward practical relevance. © 2024, CC BY.

关键词： quantum computers

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Phase shift rule with the optimal parameter selection

arXiv

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arXiv 2023年

作者： Markovich, L.A. Malikis, S. Polla, S. Brugués, J.T. Instituut-Lorentz Universiteit Leiden P.O. Box 9506 Leiden2300 RA Netherlands Applied Quantum Algorithms Leiden Netherlands

The phase shift rules enable the estimation of the derivative of a quantum state with respect to phase parameters, providing valuable insights into the behavior and dynamics of quantum systems. This capability is essential in quantum simulation tasks where understanding the behavior of complex quantum systems is of interest, such as simulating chemical reactions or condensed matter systems. However, parameter shift rules are typically designed for Hamiltonian systems with equidistant eigenvalues. For systems with closely spaced eigenvalues, effective rules have not been established. We provide insights about the optimal design of a parameter shift rule, tailored to various sorts of spectral information that may be available. The proposed method lets derivatives be calculated for any system, regardless of how close the eigenvalues are to each other. It also optimizes the number of phase shifts, which reduces the amount of gate resources needed. © 2023, CC BY.

关键词： Hamiltonians

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Randomness versus Nonlocality in Multiple-Input and Multiple-Output quantum Scenario

引用

Physical Review Letters 2025年第9期134卷 090201-090201页

作者： Chao Zhang Yi Li Xiao-Min Hu Yu Xiang Chuan-Feng Li Guang-Can Guo Jordi Tura Qihuang Gong Qiongyi He CAS Key Laboratory of Quantum Information University of Science and Technology of China Hefei 230026 China CAS Synergetic Innovation Center of Quantum Information and Quantum Physics University of Science and Technology of China Hefei 230026 China State Key Laboratory for Mesoscopic Physics School of Physics Frontiers Science Center for Nano-optoelectronics and Collaborative Innovation Center of Quantum Matter Peking University Beijing 100871 China Beijing Academy of Quantum Information Sciences Beijing 100193 China Collaborative Innovation Center of Extreme Optics Shanxi University Taiyuan Shanxi 030006 China ⟨aQa⟩ Applied Quantum Algorithms Leiden The Netherlands Instituut-Lorentz Universiteit Leiden P.O. Box 9506 2300 RA Leiden The Netherlands Peking University Yangtze Delta Institute of Optoelectronics Nantong Jiangsu 226010 China Hefei National Laboratory Hefei 230088 China

Device-independent randomness certification based on Bell nonlocality does not require any assumptions about the devices, thus provides adequate security. Great effort has been made to demonstrate that nonlocality is necessary for generating quantum randomness, but the minimal resource required has not been clarified. Here we prove and experimentally demonstrate that violating any two-input Bell inequality is both necessary and sufficient for certifying randomness, however, for the multiple-input cases, this sufficiency ceases to apply, leading to certain states exhibiting Bell nonlocality without the capability to certify randomness. We examine two typical classes of Bell inequalities with multiple input and multiple output, the facet inequalities and Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio inequalities, in the high-dimensional photonic system, and observe that the violation of the latter one can always certify randomness which is not true for the former. The private randomness with a generation rate of 1.867±0.018 bits per photon pair is obtained in the scenario of Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio inequalities with 3-input and 4-output. Our Letter unravels the internal connection between randomness and nonlocality, effectively enhancing the performance of tasks such as device-independent random number generation.

关键词： Random number generation

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Decoherence of electron spin qubit during transfer between two semiconductor quantum dots at low magnetic fields

arXiv

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arXiv 2024年

作者： Krzywda, Jan A. Cywiński, Lukasz 〈aQaL〉 Applied Quantum Algorithms Lorentz Institute Leiden Institute of Advanced Computer Science Leiden University P.O. Box 9506 Leiden2300 RA Netherlands Institute of Physics Polish Academy of Sciences al. Lotników 32/46 WarsawPL 02-668 Poland

Electron shuttling is one of the current avenues being pursued to scale semiconductor quantum dot-based spin qubits. Adiabatic spin qubit transfer along a chain of tunnel-coupled quantum dots is one of the possible schemes. In this scheme, we theoretically analyze the dephasing of a spin qubit that is adiabatically transferred between two tunnel-coupled quantum dots. We focus on the regime where the Zeeman splitting is lower than the tunnel coupling, such that interdot tunneling with spin flip is absent. We analyze the sources of errors in spin-coherent electron transfer for Si- and GaAs-based quantum dots. In addition to the obvious effect of fluctuations in spin splitting within each dot, leading to finite T2∗ for the stationary spin qubit, we consider the effects activated by detuning sweeps: failure of charge transfer due to charge noise and phonons, spin relaxation due to the enhancement of spin-orbit mixing at the tunnel-induced anticrossing of states localized in the two dots, and spin dephasing caused by low- and high-frequency noise coupling to the electron’s charge. We show that the latter effect is activated by differences in Zeeman splittings between the two dots. Importantly, all the error mechanisms are more dangerous at low tunnel couplings. Our results indicate that away from micromagnets, maximizing the fidelity of coherent transfer aligns with minimizing charge transfer error that was previously considered in J. A. Krzywda and L. Cywiński, Phys. Rev. B 104 075439 (2021). For silicon, we suggest having tunnel coupling fulfilling 2tc 60 µeV when one aims to coherently transfer a spin qubit across a ∼10 µm long array of ∼100 quantum dots with error less than 10−3 © 2024, CC BY.

关键词： Nanocrystals

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