Theory of overparametrization in quantum neural networks

Larocca, Martín; Ju, Nathan; Coles, Patrick J.; Cerezo, M.

doi:10.1038/s43588-023-00467-6

Cited by 70 publications

(14 citation statements)

References 47 publications

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“…Furthermore, ORB circuit is found to necessitate the least number of parameters to achieve a similar performance when compared to the other circuits studied. Note that the observed quadratic scaling in the number of parameters matches closely the dimension of the DLAs consistently with [32]. Overall, in this example, ORB circuit emerges as an optimal construction, in terms of number layers and parameters required, allowing us to pack as many parameters per layer as is possible without increasing the expressibility of the ansatz.…”

Section: One-dimensional Transverse-field Ising Modelsupporting

confidence: 65%

“…to understand how expressive a circuit is. To this intent, several metrics have been proposed [9,31,32]. Here, we restrict our attention to the dimension of the circuit's Dynamical Lie Algebra (DLA), a measure originating from the field of algebraic quantum optimal control [33] that was revisited in the context of VQAs [9,32].…”

Section: Expressibility and The Dynamical Lie Algebramentioning

confidence: 99%

“…To this intent, several metrics have been proposed [9,31,32]. Here, we restrict our attention to the dimension of the circuit's Dynamical Lie Algebra (DLA), a measure originating from the field of algebraic quantum optimal control [33] that was revisited in the context of VQAs [9,32]. We now briefly review such concept, and refer the reader to [9] for a more detailed exposition.…”

Section: Expressibility and The Dynamical Lie Algebramentioning

confidence: 99%

See 2 more Smart Citations

Building spatial symmetries into parameterized quantum circuits for faster training

Sauvage,

Larocca,

Coles

et al. 2024

Quantum Sci. Technol.

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Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much research has been devoted to devising adequate gate-sets, typically respecting some symmetries of the problem, very little is known about how their parameters should be structured. In this work, we show that an ideal parameter structure naturallyemerges when carefully considering spatial symmetries (i.e., the symmetries that are permutations of parts of the system under study). Namely, we consider the automorphism group of the problem Hamiltonian, leading us to develop a circuit construction that is equivariant under this symmetry group. The benefits of our novel circuit structure, called ORB, are numerically probed in several ground-state problems. We find a consistent improvement (in terms of circuit depth, number of parameters required, and gradient magnitudes) compared to literature circuit constructions.

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Section: One-dimensional Transverse-field Ising Modelsupporting

confidence: 65%

Section: Expressibility and The Dynamical Lie Algebramentioning

confidence: 99%

Section: Expressibility and The Dynamical Lie Algebramentioning

confidence: 99%

See 1 more Smart Citation

Building spatial symmetries into parameterized quantum circuits for faster training

Sauvage,

Larocca,

Coles

et al. 2024

Quantum Sci. Technol.

Self Cite

View full text Add to dashboard Cite

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“…[ 99 ] Alternatively, the overparametrization of the variational circuit is also a current topic of interest and a potential method to reduce the effects of barren plateaus. [ 100 ]…”

Section: Resultsmentioning

confidence: 99%

“…[99] Alternatively, the overparametrization of the variational circuit is also a current topic of interest and a potential method to reduce the effects of barren plateaus. [100] Additionally, landscapes of variational quantum circuits may include multiple local minima. [101] However, we do not search for a ground state, but sufficiently good approximation of the quantile function, and this can change the loss landscape.…”

Section: Ornstein-uhlenbeck With Data-inferred Initial Conditionmentioning

confidence: 99%

Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time‐Series

Paine

Elfving²,

Kyriienko

2023

Adv Quantum Tech

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A quantum algorithm is proposed for sampling from a solution of stochastic differential equations (SDEs). Using differentiable quantum circuits (DQCs) with a feature map encoding of latent variables, the quantile function is represented for an underlying probability distribution and samples extracted as DQC expectation values. Using quantile mechanics the system is propagated in time, thereby allowing for time‐series generation. The method is tested by simulating the Ornstein‐Uhlenbeck process and sampling at times different from the initial point, as required in financial analysis and dataset augmentation. Additionally, continuous quantum generative adversarial networks (qGANs) are analyzed, and the authors show that they represent quantile functions with a modified (reordered) shape that impedes their efficient time‐propagation. The results shed light on the connection between quantum quantile mechanics (QQM) and qGANs for SDE‐based distributions, and point the importance of differential constraints for model training, analogously with the recent success of physics informed neural networks.

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How scanning probe microscopy can be supported by artificial intelligence and quantum computing?

Pregowska,

Roszkiewicz,

Osial

et al. 2024

Microscopy Res & Technique

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The impact of Artificial Intelligence (AI) is rapidly expanding, revolutionizing both science and society. It is applied to practically all areas of life, science, and technology, including materials science, which continuously requires novel tools for effective materials characterization. One of the widely used techniques is scanning probe microscopy (SPM). SPM has fundamentally changed materials engineering, biology, and chemistry by providing tools for atomic‐precision surface mapping. Despite its many advantages, it also has some drawbacks, such as long scanning times or the possibility of damaging soft‐surface materials. In this paper, we focus on the potential for supporting SPM‐based measurements, with an emphasis on the application of AI‐based algorithms, especially Machine Learning‐based algorithms, as well as quantum computing (QC). It has been found that AI can be helpful in automating experimental processes in routine operations, algorithmically searching for optimal sample regions, and elucidating structure–property relationships. Thus, it contributes to increasing the efficiency and accuracy of optical nanoscopy scanning probes. Moreover, the combination of AI‐based algorithms and QC may have enormous potential to enhance the practical application of SPM. The limitations of the AI‐QC‐based approach were also discussed. Finally, we outline a research path for improving AI‐QC‐powered SPM.Research Highlights Artificial intelligence and quantum computing as support for scanning probe microscopy. The analysis indicates a research gap in the field of scanning probe microscopy. The research aims to shed light into ai‐qc‐powered scanning probe microscopy.

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Theory of overparametrization in quantum neural networks

Cited by 70 publications

References 47 publications

Building spatial symmetries into parameterized quantum circuits for faster training

Building spatial symmetries into parameterized quantum circuits for faster training

Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time‐Series

How scanning probe microscopy can be supported by artificial intelligence and quantum computing?

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