# Connecting ansatz expressibility to gradient magnitudes and barren plateaus

@article{Holmes2021ConnectingAE, title={Connecting ansatz expressibility to gradient magnitudes and barren plateaus}, author={Zoe Holmes and Kunal Sharma and Mar{\'i}a Cerezo and Patrick J. Coles}, journal={ArXiv}, year={2021}, volume={abs/2101.02138} }

Zoë Holmes,1 Kunal Sharma,2, 3 M. Cerezo,3, 4 and Patrick J. Coles3 Information Sciences, Los Alamos National Laboratory, Los Alamos, NM, USA. Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA

## 49 Citations

Long-time simulations with high fidelity on quantum hardware

- Computer Science, PhysicsArXiv
- 2021

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.

Diagnosing barren plateaus with tools from quantum optimal control

- Physics
- 2021

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…

Theory of overparametrization in quantum neural networks

- Computer Science, PhysicsArXiv
- 2021

This paper presents a meta-analyses of the LaSalle–Cerezo–Larocca–Bouchut–Seiden–Stein cellular automaton, a model derived from the model developed by J. J. Giambiagi in 2007, which states that the model derived in this paper can be modified for flows on rugous topographies varying around an inclined plane.

Subtleties in the trainability of quantum machine learning models

- Computer Science, PhysicsArXiv
- 2021

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.

Entangled Datasets for Quantum Machine Learning

- Computer Science, PhysicsArXiv
- 2021

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.

Adaptive shot allocation for fast convergence in variational quantum algorithms

- Physics, Computer ScienceArXiv
- 2021

This paper presents a probabilistic simulation of the response of the Higgs boson to a proton-proton collision and shows clear patterns in the responses of the immune system to these collisions.

A semi-agnostic ansatz with variable structure for quantum machine learning

- Computer Science, PhysicsArXiv
- 2021

This paper presents a meta-analyses of the Fisica Teorica: Informacio i Fenomens Quantics, a large-scale probabilistic simulation of the response of the immune system to quantum entanglement.

Reflection-Based Adiabatic State Preparation

- Physics
- 2021

Jessica Lemieux,1, 2, 3, ∗ Artur Scherer,4 and Pooya Ronagh5, 6, 7, 8 Département de Physique, Université de Sherbrooke, Sherbrooke, QC, Canada Institut Quantique, Université de Sherbrooke,…

Generalization in quantum machine learning from few training data

- Computer Science, PhysicsArXiv
- 2021

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.

Automatic quantum circuit encoding of a given arbitrary quantum state

- Physics
- 2021

Tomonori Shirakawa, 2 Hiroshi Ueda, 1, 4 and Seiji Yunoki 2, 5, 6 Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS), Kobe, Hyogo 650-0047, Japan Quantum…

## References

SHOWING 1-10 OF 63 REFERENCES

Impact of Barren Plateaus on the Hessian and Higher Order Derivatives.

- Mathematics
- 2020

The Barren Plateau (BP) phenomenon is an issue for certain quantum neural networks and variational quantum algorithms, whereby the gradient vanishes exponentially in the system size $n$. The question…

Effect of barren plateaus on gradient-free optimization

- Computer Science, PhysicsQuantum
- 2021

It is shown that gradient-free optimizers do not solve the barren plateau problem, and the main result proves that cost function differences, which are the basis for making decisions in a gradient- free optimization, are exponentially suppressed in a barren plateau.

A variational eigenvalue solver on a photonic quantum processor

- Physics, MedicineNature communications
- 2014

The proposed approach drastically reduces the coherence time requirements and combines this method with a new approach to state preparation based on ansätze and classical optimization, enhancing the potential of quantum resources available today and in the near future.

The theory of variational hybrid quantum-classical algorithms

- 2016

Many quantumalgorithms have daunting resource requirements when compared towhat is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as ‘the…

Entanglement devised barren plateau mitigation

- PhysicsPhysical Review Research
- 2021

Hybrid quantum-classical variational algorithms are one of the most propitious implementations of quantum computing on near-term devices, offering classical machine learning support to quantum scale…

Quantum Assisted Simulator

- Physics, Computer Science
- 2020

A novel hybrid quantum-classical algorithm for simulating the dynamics of quantum systems that does not require any classical-quantum feedback loop and by construction bypasses the barren plateau problem.

Iterative quantum-assisted eigensolver

- PhysicsPhysical Review A
- 2021

The task of estimating ground state and ground state energy of Hamiltonians is an important problem in physics with numerous applications ranging from solid-state physics to combinatorial…

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets

- Physics, MedicineNature
- 2017

The experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms is demonstrated, determining the ground-state energy for molecules of increasing size, up to BeH2.

From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz

- Physics, MathematicsAlgorithms
- 2019

The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter.

An initialization strategy for addressing barren plateaus in parametrized quantum circuits

- Physics, Computer ScienceQuantum
- 2019

This technical note theoretically motivate and empirically validate an initialization strategy which can resolve the barren plateau problem for practical applications and shows empirically that variational quantum eigensolvers and quantum neural networks initialized using this strategy can be trained using a gradient based method.