Quantum Phase Recognition via Quantum Kernel Methods

Wu, Yusen; Wu, Bujiao; Wang, Jingbo; Yuan, Xiao

doi:10.22331/q-2023-04-17-981

Cited by 14 publications

(10 citation statements)

References 88 publications

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“…However, the features currently used to describe the processes, collected from detector measurements, are fully classical. This loss of 'quantumness' could in fact represent an important limitation to the use of more sophisticated QML techniques for the analysis and classification of quantum states [32,[72][73][74]. We therefore believe that a different setup bypassing the extraction of classical features could be a promising road towards quantum advantage also in the context of HEP.…”

Section: Discussionmentioning

confidence: 99%

Unravelling physics beyond the standard model with classical and quantum anomaly detection

Schuhmacher,

Boggia,

Belis

et al. 2023

Mach. Learn.: Sci. Technol.

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Much hope for finding new physics phenomena at microscopic scale relies on the observations obtained from High Energy Physics experiments, like the ones performed at the Large Hadron Collider (LHC). However, current experiments do not indicate clear signs of new physics that could guide the development of additional Beyond Standard Model (BSM) theories. Identifying signatures of new physics out of the enormous amount of data produced at the LHC falls into the class of anomaly detection and constitutes one of the greatest computational challenges. In this article, we propose a novel strategy to perform anomaly detection in a supervised learning setting, based on the artificial creation of anomalies through a random process. For the resulting supervised learning problem, we successfully apply classical and quantum support vector classifiers (CSVC and QSVC respectively) to identify the artificial anomalies among the SM events. Even more promising, we find that employing an SVC trained to identify the artificial anomalies, it is possible to identify realistic BSM events with high accuracy. In parallel, we also explore the potential of quantum algorithms for improving the classification accuracy and provide plausible conditions for the best exploitation of this novel computational paradigm.

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Section: Discussionmentioning

confidence: 99%

Unravelling physics beyond the standard model with classical and quantum anomaly detection

Schuhmacher,

Boggia,

Belis

et al. 2023

Mach. Learn.: Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…Given such training dataset {x a , y a } ND a=1 , the task is to construct a function that approximates this input-output mapping with good generalization capability for an unseen input data. This problem is related to the general quantum phase recognition (QPR) problem [12,65,66] in condensed-matter physics [67], which is inherently classically hard but some quantum machine learning methods may solve efficiently [68][69][70].…”

Section: Machine Learning Task and Modelsmentioning

confidence: 99%

Quantum-classical hybrid neural networks in the neural tangent kernel regime

Nakaji,

Tezuka,

Yamamoto

2023

Quantum Sci. Technol.

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Recently, quantum neural networks or quantum–classical neural networks (qcNN) have been actively studied, as a possible alternative to the conventional classical neural network (cNN), but their practical and theoretically-guaranteed performance is still to be investigated. In contrast, cNNs and especially deep cNNs, have acquired several solid theoretical basis; one of those basis is the neural tangent kernel (NTK) theory, which can successfully explain the mechanism of various desirable properties of cNNs, particularly the global convergence in the training process. In this paper, we study a class of qcNN composed of a quantum data-encoder followed by a cNN. The quantum part is randomly initialized according to unitary 2-designs, which is an effective feature extraction process for quantum states, and the classical part is also randomly initialized according to Gaussian distributions; then, in the NTK regime where the number of nodes of the cNN becomes infinitely large, the output of the entire qcNN becomes a nonlinear function of the so-called projected quantum kernel. That is, the NTK theory is used to construct an effective quantum kernel, which is in general nontrivial to design. Moreover, NTK defined for the qcNN is identical to the covariance matrix of a Gaussian process, which allows us to analytically study the learning process. These properties are investigated in thorough numerical experiments; particularly, we demonstrate that the qcNN shows a clear advantage over fully classical NNs and qNNs for the problem of learning the quantum data-generating process.

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“…[ 7 ] However, noise and qubit limitations prevent serious implementations of the aforementioned quantum algorithms in the current Noisy Intermediate‐Scale Quantum (NISQ) devices. [ 8,9 ] As such, hybrid quantum‐classical algorithms [ 10–19 ] are proposed to fully exploit the power of NISQ devices.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Leapfrogging Initialization Strategy for Quantum Approximate Optimization Algorithm

Ni,

Cai,

Liu

et al. 2024

Adv Quantum Tech

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Recently, Zhou et al. have proposed an Interpolation‐based (INTERP) strategy to generate the initial parameters for Quantum Approximate Optimization Algorithm (QAOA). INTERP guesses the initial parameters at level by applying interpolation to the optimized parameters at level , achieving better performance than random initialization (RI). Nevertheless, INTERP consumes extensive costs for deep QAOA because it necessitates optimization at each level depth. To address it, a Multilevel Leapfrogging Interpolation (MLI) strategy is proposed. MLI produces initial parameters from level to () at level , omitting the optimization rounds from level to . MLI executes optimization at few levels rather than each level, and this operation is called Multilevel Leapfrogging optimization (M‐Leap). The performance of MLI is investigated on the Maxcut problem. The simulation results demonstrate MLI achieves the same quasi‐optima as INTERP while consuming 1/2 of costs required by INTERP. Besides, for MLI, where there is no RI except for level 1, the greedy‐MLI strategy is presented. The simulation results suggest greedy‐MLI has better stability than INTERP and MLI beyond obtaining the quasi‐optima. According to the efficiency of finding the quasi‐optima, the idea of M‐Leap might be extended to other training tasks, especially those requiring numerous optimizations.

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Quantum Phase Recognition via Quantum Kernel Methods

Cited by 14 publications

References 88 publications

Unravelling physics beyond the standard model with classical and quantum anomaly detection

Unravelling physics beyond the standard model with classical and quantum anomaly detection

Quantum-classical hybrid neural networks in the neural tangent kernel regime

Multilevel Leapfrogging Initialization Strategy for Quantum Approximate Optimization Algorithm

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