Barren Plateaus Preclude Learning Scramblers.

@article{Holmes2021BarrenPP,
  title={Barren Plateaus Preclude Learning Scramblers.},
  author={Z. Holmes and A. Arrasmith and B. Yan and Patrick J. Coles and A. Albrecht and A. Sornborger},
  journal={Physical review letters},
  year={2021},
  volume={126 19},
  pages={
          190501
        }
}
Scrambling processes, which rapidly spread entanglement through many-body quantum systems, are difficult to investigate using standard techniques, but are relevant to quantum chaos and thermalization. In this Letter, we ask if quantum machine learning (QML) could be used to investigate such processes. We prove a no-go theorem for learning an unknown scrambling process with QML, showing that it is highly probable for any variational Ansatz to have a barren plateau landscape, i.e., cost gradients… Expand

Figures from this paper

Entanglement Devised Barren Plateau Mitigation
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 scaleExpand
Absence of Barren Plateaus in Quantum Convolutional Neural Networks
TLDR
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
Equivalence of quantum barren plateaus to cost concentration and narrow gorges
TLDR
This work analytically proves the connection between three different landscape features that have been observed for PQCs: exponentially vanishing gradients, exponential cost concentration about the mean, and the exponential narrowness of minina. Expand
Effect of barren plateaus on gradient-free optimization
TLDR
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
Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?
Variational Quantum Algorithms (VQAs) are widely viewed as the best hope for near-term quantum advantage. However, recent studies have shown that noise can severely limit the trainability of VQAs,Expand
Variational Quantum Algorithms
TLDR
An overview of the field of Variational Quantum Algorithms is presented and strategies to overcome their challenges as well as the exciting prospects for using them as a means to obtain quantum advantage are discussed. Expand
Experimental Quantum Learning of a Spectral Decomposition
Currently available quantum hardware allows for small scale implementations of quantum machine learning algorithms. Such experiments aid the search for applications of quantum computers byExpand
Fast suppression of classification error in variational quantum circuits
Variational quantum circuits (VQCs) have shown great potential in near-term applications. However, the discriminative power of a VQC, in connection to its circuit architecture and depth, is notExpand
Recent advances for quantum classifiers
Machine learning has achieved dramatic success in a broad spectrum of applications. Its interplay with quantum physics may lead to unprecedented perspectives for both fundamental research andExpand
Variational Quantum Algorithm for Estimating the Quantum Fisher Information
TLDR
A variational quantum algorithm called Variational Quantum Fisher Information Estimation (VQFIE) is presented, which estimates lower and upper bounds on the QFI, based on bounding the fidelity, and outputs a range in which the actual QFI lies. Expand
...
1
2
3
...

References

SHOWING 1-10 OF 71 REFERENCES
Trainability of Dissipative Perceptron-Based Quantum Neural Networks
TLDR
This work analyzes the gradient scaling (and hence the trainability) for a recently proposed architecture that is called dissipative QNNs (DQNNs), where the input qubits of each layer are discarded at the layer's output and finds that DQNN's can exhibit barren plateaus. Expand
Barren plateaus in quantum neural network training landscapes
TLDR
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
Disentangling Scrambling and Decoherence via Quantum Teleportation
Out-of-time-order correlation (OTOC) functions provide a powerful theoretical tool for diagnosing chaos and the scrambling of information in strongly-interacting, quantum systems. However, theirExpand
Verified quantum information scrambling
TLDR
A quantum circuit in an ion-trap quantum computer provides a positive test for the scrambling features of a given unitary process, and is implemented as part of a seven-qubit circuit on an ion trap quantum computer to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement. Expand
Chaos in quantum channels
A bstractWe study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize theExpand
An initialization strategy for addressing barren plateaus in parametrized quantum circuits
TLDR
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. Expand
Effect of barren plateaus on gradient-free optimization
TLDR
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
Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model
Scrambling of quantum information is the process by which information initially stored in the local degrees of freedom of a quantum many-body system spreads over its many-body degrees of freedom,Expand
Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model
TLDR
It is demonstrated that fidelity out-of-time-order correlators (FOTOCs) can elucidate connections between scrambling, entanglement, ergodicity and quantum chaos (butterfly effect) and establish quantitative relationships between experimentally-measureable correlators, the Rényi entropy and Lyapunov exponents in the Dicke model. Expand
Quantum computation vs. firewalls
A bstractIn this paper we discuss quantum computational restrictions on the types of thought experiments recently used by Almheiri, Marolf, Polchinski, and Sully to argue against the smoothness ofExpand
...
1
2
3
4
5
...