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Multiple-basis representation of quantum states

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arXiv 2024年

作者： Pérez-Salinas, Adrián Emonts, Patrick Tura, Jordi Dunjko, Vedran 〈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

Classical simulation of quantum physics is a central approach to investigating physical phenomena. quantum computers enhance computational capabilities beyond those of classical resources, but it remains unclear to what extent existing limited quantum computers can contribute to this enhancement. In this work, we explore a new hybrid, efficient quantum-classical representation of quantum states, the multiple-basis representation. This representation consists of a linear combination of states that are sparse in some given and different bases, specified by quantum circuits. Such representation is particularly appealing when considering depth-limited quantum circuits within reach of current hardware. We analyze the expressivity of multiple-basis representation states depending on the classical simulability of their quantum circuits. In particular, we show that multiple-basis representation states include, but are not restricted to, both matrix-product states and stabilizer states. Furthermore, we find cases in which this representation can be used, namely approximation of ground states, simulation of deeper computations by specifying bases with shallow circuits, and a tomographical protocol to describe states as multiple-basis representations. We envision this work to open the path of simultaneous use of several hardware-friendly bases, a natural description of hybrid computational methods accessible for near-term hardware. © 2024, CC BY.

关键词： quantum computers

Error and Resource Estimates of Variational quantum algorithms for Solving Differential Equations Based on Runge-Kutta Methods

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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

Spectral Gap Optimization for Enhanced Adiabatic State Preparation

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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

Preparing low-variance states using a distributed quantum algorithm

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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

Analyzing variational quantum landscapes with information content

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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

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

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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

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

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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

Mitigating shot noise in local overlapping quantum tomography with semidefinite programming

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arXiv 2025年

作者： Wang, Zherui Jerry Dechant, David Patel, Yash J. Tura, Jordi 〈aQaL〉 Applied Quantum Algorithms Universiteit Leiden Netherlands Instituut-Lorentz Universiteit Leiden P.O. Box 9506 Leiden2300 RA Netherlands LIACS Universiteit Leiden Niels Bohrweg 1 Leiden2333 CA Netherlands QuTech Delft University of Technology P.O. Box 5046 Delft2600 GA Netherlands

Reduced density matrices (RDMs) are fundamental in quantum information processing, allowing the computation of local observables, such as energy and correlation functions, without the exponential complexity of fully characterizing quantum states. In the context of near-term quantum computing, RDMs provide sufficient information to effectively design variational quantum algorithms. However, their experimental estimation is challenging, as it involves preparing and measuring quantum states in multiple bases–a resource-intensive process susceptible to producing non-physical RDMs due to shot noise from limited measurements. To address this, we propose a method to mitigate shot noise by re-enforcing certain physicality constraints on RDMs. While verifying RDM compatibility with a global state is QMA-complete, we relax this condition by enforcing compatibility constraints up to a certain level using a polynomial-size semidefinite program to reconstruct overlapping RDMs from simulated experimental data. Our approach yields, on average, tighter bounds for the same number of measurements compared to tomography without compatibility constraints. We demonstrate the versatility and efficacy of our method by integrating it into an algorithmic cooling procedure to prepare low-energy states of local Hamiltonians. Simulations on frustrated Hamiltonians reveal notable improvements in accuracy and resource efficiency, highlighting the potential of our approach for practical applications in near-term quantum computing. Copyright © 2025, The Authors. All rights reserved.

关键词： Shot noise

An Adaptive Re-evaluation Method for Evolution Strategy under Additive Noise

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arXiv 2024年

作者： Dinu, Catalin-Viorel Patel, Yash J. Bonet-Monroig, Xavier Wang, Hao LIACS Leiden University Leiden Netherlands Applied Quantum Algorithms 〈aQaL〉 group and Instituut-Lorentz Leiden University Leiden Netherlands Honda Research Institute Europe GmbH Offenbach am Main Germany

The Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is one of the most advanced algorithms in numerical black-box optimization. For noisy objective functions, several approaches were proposed to mitigate the noise, e.g., re-evaluations of the same solution or adapting the population size. In this paper, we devise a novel method to adaptively choose the optimal re-evaluation number for function values corrupted by additive Gaussian white noise. We derive a theoretical lower bound of the expected improvement achieved in one iteration of CMA-ES, given an estimation of the noise level and the Lipschitz constant of the function’s gradient. Solving for the maximum of the lower bound, we obtain a simple expression of the optimal re-evaluation number. We experimentally compare our method to the state-of-the-art noise-handling methods for CMA-ES on a set of artificial test functions across various noise levels, optimization budgets, and dimensionality. Our method demonstrates significant advantages in terms of the probability of hitting near-optimal function values. Copyright © 2024, The Authors. All rights reserved.

关键词： Budget control