Expressibility and trainability of parametrized analog quantum systems for machine learning applications

Tangpanitanon, Jirawat; Thanasilp, Supanut; Dangniam, Ninnat; Lemonde, Marc-Antoine; Angelakis, Dimitris G.

doi:10.1103/physrevresearch.2.043364

Cited by 28 publications

(15 citation statements)

References 56 publications

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“…It has also been noticed that highly expressive ansatzes are more difficult to train [22,32,39], which is the same with classical machine learning. Various strategies [35,17,30,19] have been proposed to improve VQA trainability.…”

Section: Related Workmentioning

confidence: 77%

Towards Efficient Ansatz Architecture for Variational Quantum Algorithms

Wang

et al. 2021

Preprint

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Variational quantum algorithms are the quantum analogy of the successful neural network in classical machine learning. The ansatz architecture design, which is similar to classical neural network architecture design, is critical to the performance of a variational quantum algorithm. In this paper, we explore how to design efficient ansatz and investigate several common design options in today's quantum software frameworks. In particular, we study the number of effective parameters in different ansatz architectures and theoretically prove that an ansatz with parameterized RX and RZ gates and alternating two-qubit gate entanglement layers would be more efficient (i.e., more effective parameters per two-qubit gate). Such ansatzes are expected to have stronger expressive power and obtain better solutions. Numerical experimental results show that our efficient ansatz architecture outperforms other ansatzes with smaller ansatz size and better optimization results.

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Section: Related Workmentioning

confidence: 77%

Towards Efficient Ansatz Architecture for Variational Quantum Algorithms

Wang

et al. 2021

Preprint

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“…Different tasks can be solved by exploiting the trade-off between linear and nonlinear memory at the phase transition, and actually the onset of thermalization proves to be particularly advantageous for QRC, a feature reminiscent of classical RC at the edge of stability. Quantum machine learning and computing can be favored by different dynamical phases [30][31][32][33][34]. The reported study of QRC offers an original perspective on thermal and localized phases in terms of their ability to process information and can be further explored in the context of quantum correlations, information scrambling, OTOC (out-of-timeorder correlators) [55] and transient real-time evolution of Loschmidt echoes [26,56].…”

Section: Discussionmentioning

confidence: 99%

“…For instance, systems presenting MBL can provide quantum memories at finite temperature [27] and avoid overheating in Floquet systems [28,29]. In quantum machine learning, MBL can improve the trainability of parameterized quantum Ising chains [30]. Contrariwise, localization can be computationally detrimental in quantum annealing [31,32] or quantum random walk algorithms [33,34].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Phase Transitions in Quantum Reservoir Computing

Martínez-Peña

Giorgi²,

Nokkala³

et al. 2021

Phys. Rev. Lett.

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Closed quantum systems exhibit different dynamical regimes, like Many-Body Localization or thermalization, which determine the mechanisms of spread and processing of information. Here we address the impact of these dynamical phases in quantum reservoir computing, an unconventional computing paradigm recently extended into the quantum regime that exploits dynamical systems to solve nonlinear and temporal tasks. We establish that the thermal phase is naturally adapted to the requirements of quantum reservoir computing and report an increased performance at the thermalization transition. Uncovering the underlying physical mechanisms behind optimal information processing capabilities of spin networks is essential for future experimental implementations and provides a new perspective on dynamical phases.

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“…In this work we study the trainability and the existence of barren plateaus in QML models. Our work represents a general treatment that goes beyond previous analysis of gradient scaling and trainability in specific QML models [49][50][51][52][53][54][55][56]. Our main results are two-fold.…”

Section: Introductionmentioning

confidence: 86%

Subtleties in the trainability of quantum machine learning models

Thanasilp¹,

Wang²,

Nghiem³

et al. 2021

Preprint

Self Cite

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A new paradigm for data science has emerged, with quantum data, quantum models, and quantum computational devices. This field, called Quantum Machine Learning (QML), aims to achieve a speedup over traditional machine learning for data analysis. However, its success usually hinges on efficiently training the parameters in quantum neural networks, and the field of QML is still lacking theoretical scaling results for their trainability. Some trainability results have been proven for a closely related field called Variational Quantum Algorithms (VQAs). While both fields involve training a parametrized quantum circuit, there are crucial differences that make the results for one setting not readily applicable to the other. In this work we bridge the two frameworks and show that gradient scaling results for VQAs can also be applied to study the gradient scaling of QML models. Our results indicate that features deemed detrimental for VQA trainability can also lead to issues such as barren plateaus in QML. Consequently, our work has implications for several QML proposals in the literature. In addition, we provide theoretical and numerical evidence that QML models exhibit further trainability issues not present in VQAs, arising from the use of a training dataset. We refer to these as dataset-induced barren plateaus. These results are most relevant when dealing with classical data, as here the choice of embedding scheme (i.e., the map between classical data and quantum states) can greatly affect the gradient scaling.

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Expressibility and trainability of parametrized analog quantum systems for machine learning applications

Cited by 28 publications

References 56 publications

Towards Efficient Ansatz Architecture for Variational Quantum Algorithms

Towards Efficient Ansatz Architecture for Variational Quantum Algorithms

Dynamical Phase Transitions in Quantum Reservoir Computing

Subtleties in the trainability of quantum machine learning models

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