# An initialization strategy for addressing barren plateaus in parametrized quantum circuits

@article{Grant2019AnIS, title={An initialization strategy for addressing barren plateaus in parametrized quantum circuits}, author={Edward Grant and Leonard Wossnig and Mateusz Ostaszewski and Marcello Benedetti}, journal={arXiv: Quantum Physics}, year={2019} }

Parametrized quantum circuits initialized with random initial parameter values are characterized by barren plateaus where the gradient becomes exponentially small in the number of qubits. In this technical note we theoretically motivate and empirically validate an initialization strategy which can resolve the barren plateau problem for practical applications. The technique involves randomly selecting some of the initial parameter values, then choosing the remaining values so that the circuit is… Expand

#### 97 Citations

Absence of Barren Plateaus in Quantum Convolutional Neural Networks

- Computer Science, Physics
- ArXiv
- 2020

This work rigorously analyze the gradient scaling for the parameters in the QCNN architecture and finds that the variance of the gradient vanishes no faster than polynomially, implying that QCNNs do not exhibit barren plateaus. Expand

Quantum compilation and circuit optimisation via energy dissipation

- Mathematics, Physics
- 2018

We describe a method for automatically recompiling a quantum circuit A into a target circuit B, with the goal that both circuits have the same action on a specific input i.e. A|in> = B|in>. This is… Expand

Effect of barren plateaus on gradient-free optimization

- Computer Science, Physics
- ArXiv
- 2020

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. Expand

Entanglement Devised Barren Plateau Mitigation

- Physics
- 2020

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… Expand

Quantum Generative Training Using R\'enyi Divergences

- Physics
- 2021

Quantum neural networks (QNNs) are a framework for creating quantum algorithms that promises to combine the speedups of quantum computation with the widespread successes of machine learning. A major… Expand

Layerwise learning for quantum neural networks

- Physics, Computer Science
- Quantum Mach. Intell.
- 2021

This work investigates a layerwise learning strategy for parametrized quantum circuits and shows that when considering sampling noise, this strategy can help avoid the problem of barren plateaus of the error surface due to the low depth of circuits, low number of parameters trained in one step, and larger magnitude of gradients compared to training the full circuit. Expand

Barren Plateaus Preclude Learning Scramblers.

- Medicine, Physics
- Physical review letters
- 2021

A no-go theorem for learning an unknown scrambling process with QML is proved, showing that it is highly probable for any variational Ansatz to have a barren plateau landscape, i.e., cost gradients that vanish exponentially in the system size. Expand

On barren plateaus and cost function locality in variational quantum algorithms

- Physics, Computer Science
- ArXiv
- 2020

A lower bound on the variance of the gradient is derived, which depends mainly on the width of the circuit causal cone of each term in the Pauli decomposition of the cost function. Expand

An efficient quantum algorithm for the time evolution of parameterized circuits

- Physics
- 2021

We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected Variational Quantum Dynamics" (p-VQD)… Expand

The Born supremacy: quantum advantage and training of an Ising Born machine

- Computer Science, Physics
- ArXiv
- 2019

This work defines a subset of a class of quantum circuits known as Born machines based on Ising Hamiltonians and shows that the circuits encountered during gradient-based training cannot be efficiently sampled from classically up to multiplicative error in the worst case. Expand

#### References

SHOWING 1-10 OF 10 REFERENCES

Barren plateaus in quantum neural network training landscapes

- Computer Science, Physics
- Nature Communications
- 2018

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. Expand

Universal discriminative quantum neural networks

- Computer Science, Physics
- Quantum Mach. Intell.
- 2021

This work trains near-term quantum circuits to classify data represented by non-orthogonal quantum probability distributions using the Adam stochastic optimization algorithm, and provides an example of quantum machine learning for a task that has inherently no classical analogue. Expand

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

- Physics, Medicine
- Nature
- 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. Expand

Hierarchical quantum classifiers

- Computer Science, Physics
- 2018

It is shown how quantum algorithms based on two tensor network structures can be used to classify both classical and quantum data and may enable classification of two-dimensional images and entangled quantum data more efficiently than is possible with classical methods. Expand

A variational eigenvalue solver on a photonic quantum processor

- Physics, Medicine
- Nature 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. Expand

Quantum t-designs: t-wise Independence in the Quantum World

- Computer Science, Physics
- Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)
- 2007

It is shown that an approximate 4-design provides a derandomization of the statedistinction problem considered by Sen (quant-ph/0512085), which is relevant to solving certain instances of the hidden subgroup problem. Expand

Adam: A Method for Stochastic Optimization

- Computer Science, Mathematics
- ICLR
- 2015

This work introduces Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments, and provides a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Expand

Symbolic integration with respect to the Haar measure on the unitary group in Mathematica

- Mathematics, Computer Science
- ArXiv
- 2011

A number of special cases which can be used to optimize the calcu-lation speed for some classes of integrals of the IntU package for Mathematica computer algebra system are described. Expand

Circuit-centric quantum classifiers

- Physics
- 2020

A machine learning design is developed to train a quantum circuit specialized in solving a classification problem. In addition to discussing the training method and effect of noise, it is shown that… Expand

Unitary 2-designs, variational quantum eigensolvers, and barren plateaus

- https://qitheory. blogs.bristol.ac.uk/files/2019/02/barrenplateausblogpost-1xqcazi.pdf,
- 2019