• Corpus ID: 237635210

Theory of overparametrization in quantum neural networks

  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},
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… 

Figures from this paper

Subtleties in the trainability of quantum machine learning models
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.
Generalization in quantum machine learning from few training data
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
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
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
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
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
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.
Algebraic Bethe Circuits
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
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
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.


Entangled Datasets for Quantum Machine Learning
This paper presents a parallel version of the Celada–Seiden cellular automaton, a probabilistic model that simulates the dynamic response of the immune system to infectious disease.
Diagnosing barren plateaus with tools from quantum optimal control
Martín Larocca,1, 2 Piotr Czarnik,2 Kunal Sharma,3, 2 Gopikrishnan Muraleedharan,2 Patrick J. Coles,2 and M. Cerezo2, 4 Departamento de Física “J. J. Giambiagi” and IFIBA, FCEyN, Universidad de
Long-time simulations with high fidelity on quantum hardware
This paper presents a probabilistic simulation of the response of the immune system to x-ray diffraction and shows clear patterns in the response to the proton-proton collision.
Avoiding local minima in Variational Quantum Algorithms with Neural Networks
Javier Rivera-Dean, ∗ Patrick Huembeli, Antonio Aćın, 3 and Joseph Bowles ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona),
Progress toward favorable landscapes in quantum combinatorial optimization
Juneseo Lee, 2 Alicia B. Magann, Herschel A. Rabitz, and Christian Arenz 4 Department of Mathematics, Princeton University, Princeton, New Jersey 08544, USA Department of Chemistry, Princeton
Critical Points in Hamiltonian Agnostic Variational Quantum Algorithms
This work shows that a certain randomized class of variational quantum algorithms can be mapped to Wishart random fields on the hypertorus, and analytically finds the expected distribution of critical points in such random processes.
Barren plateaus in quantum neural network training landscapes
It is shown that for a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits.
The quantum technologies roadmap: a European community view
Within the last two decades, quantum technologies (QT) have made tremendous progress, moving from Nobel Prize award-winning experiments on quantum physics (1997: Chu, Cohen-Tanoudji, Phillips; 2001:
Trainability of Dissipative Perceptron-Based Quantum Neural Networks
This work represents the first rigorous analysis of the scalability of a perceptron-based QNN and provides quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths.
Evaluating analytic gradients on quantum hardware
This paper shows how gradients of expectation values of quantum measurements can be estimated using the same, or almost the same the architecture that executes the original circuit, and proposes recipes for the computation of gradients for continuous-variable circuits.