# Theory of overparametrization in quantum neural networks

@article{Larocca2021TheoryOO, title={Theory of overparametrization in quantum neural networks}, author={Martin Larocca and Nathan Ju and Diego Garc'ia-Mart'in and Patrick J. Coles and Mar{\'i}a Cerezo}, journal={ArXiv}, year={2021}, volume={abs/2109.11676} }

Martín Larocca,1, 2, ∗ Nathan Ju,1, ∗ Diego García-Martín,1, 3, 4 Patrick J. Coles,1 and M. Cerezo5, 1, 6 Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Departamento de Física “J. J. Giambiagi” and IFIBA, FCEyN, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina Barcelona Supercomputing Center, Barcelona 08034, Spain Instituto de Física Teórica, UAM-CSIC, Madrid 28049, Spain Information Sciences, Los Alamos National Laboratory, Los Alamos, NM…

## 14 Citations

Subtleties in the trainability of quantum machine learning models

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This paper presents a probabilistic procedure for estimating the uncertainty in the response of the proton-proton collision of superconducting particles with each other over a discrete-time period.

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This paper presents a probabilistic simulation of the response of the immune system to a proton-proton collision and shows clear patterns in the response to quantum entanglement.

Quantum tangent kernel

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Norihito Shirai,1, ∗ Kenji Kubo,1, 2, † Kosuke Mitarai,1, 3, 4, ‡ and Keisuke Fujii1, 3, 5 Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531,…

Quantum Chaos and Circuit Parameter Optimization

- Physics
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Joonho Kim, Yaron Oz, 3 and Dario Rosa School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA. Simons Center for Geometry and Physics, SUNY, Stony Brook, NY 11794, USA.…

Surviving The Barren Plateau in Variational Quantum Circuits with Bayesian Learning Initialization

- Computer Science, Physics
- 2022

The fast-and-slow algorithm is introduced, which uses Bayesian Learning to identify a promising region in parameter space and is used to initialize a fast local optimizer to find the global optimum point efficiently.

Quantum neural networks force fields generation

- Computer Science, PhysicsArXiv
- 2022

A direct connection between classical and quantum solutions for learning neural network potentials is established and a quantum neural network architecture is designed and applied successfully to different molecules of growing complexity, pointing towards potential quantum advantages in natural science applications via quantum machine learning.

Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps

- Computer Science
- 2022

It is proved that a wide class of variational quantum models—which are shallow, and exhibit no barren plateus—have only a superpolynomially small fraction of local minima within any constant energy from the global minimum, rendering these models untrainable if no good initial guess of the optimal parameters is known.

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- Computer Science, Physics
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This work distills the non-unitary R matrices that make up the ABA into unitaries using the QR decomposition, and derives a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.

Multi-angle quantum approximate optimization algorithm

- Computer ScienceScientific reports
- 2022

This work investigates a multi-angle ansatz for QAOA that reduces circuit depth and improves the approximation ratio by increasing the number of classical parameters, and finds that good parameters can be found in polynomial time for a test dataset the authors consider.

Expressivity of Variational Quantum Machine Learning on the Boolean Cube

- Computer Science
- 2022

It is shown that for any function on the Boolean cube, there exists a variational linear quantum model based on a phase embedding that can represent it, and it is proved that an ensemble of variationallinear quantum models that use the quantum random access code embedding can represent any function.

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