Gaussian initializations help deep variational quantum circuits escape from the barren plateau

@article{Zhang2022GaussianIH,
  title={Gaussian initializations help deep variational quantum circuits escape from the barren plateau},
  author={Kaining Zhang and Min-Hsiu Hsieh and Liu Liu and Dacheng Tao},
  journal={ArXiv},
  year={2022},
  volume={abs/2203.09376}
}
Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general belief that deep quantum circuits will not be feasible for practical tasks. In this work, we propose an initialization strategy with theoretical guarantees for the vanishing… 

Figures from this paper

Bandwidth Enables Generalization in Quantum Kernel Models
TLDR
Evidence is provided that quantum machine learning methods can generalize well on challenging datasets, including those far outside of the theoretical assumptions.
Classical Splitting of Parametrized Quantum Circuits
Cenk Tüysüz, 2, ∗ Giuseppe Clemente, Arianna Crippa, 2 Tobias Hartung, 4 Stefan Kühn, and Karl Jansen Deutsches Elektronen-Synchrotron (DESY), Platanenallee 6, 15738 Zeuthen, Germany Institüt für
Characterization of variational quantum algorithms using free fermions
Gabriel Matos, Chris N. Self, Zlatko Papić, Konstantinos Meichanetzidis, and Henrik Dreyer School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom Quantinuum, Partnership
Recent Advances for Quantum Neural Networks in Generative Learning
TLDR
This paper interprets these QGLMs, covering quantum circuit Born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum autoencoders, as the quantum extension of classical generative learning models, and explores their intrinsic relation and their fundamental differences.

References

SHOWING 1-10 OF 93 REFERENCES
Variational quantum algorithm for molecular geometry optimization
Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this
Cost function dependent barren plateaus in shallow parametrized quantum circuits
TLDR
This work rigorously proves two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs, that establish a connection between locality and trainability.
Hartree-Fock on a superconducting qubit quantum computer
TLDR
Several quantum simulations of chemistry with up to one dozen qubits are performed, including modeling the isomerization mechanism of diazene, and error-mitigation strategies based on N-representability that dramatically improve the effective fidelity of the experiments are demonstrated.
Qubit-ADAPT-VQE: An Adaptive Algorithm for Constructing Hardware-Efficient Ansätze on a Quantum Processor
TLDR
A hardware-efficient variant of ADAPT-VQE that drastically reduces circuit depths using an operator pool that is guaranteed to contain the operators necessary to construct exact ans\"atze and shows that the minimal pool size that achieves this scales linearly with the number of qubits.
An adaptive variational algorithm for exact molecular simulations on a quantum computer
TLDR
A new variational hybrid quantum-classical algorithm which allows the system being simulated to determine its own optimal state, and highlights the potential of the adaptive algorithm for exact simulations with present-day and near-term quantum hardware.
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator
Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to
Supervised learning with quantum-enhanced feature spaces
TLDR
Two classification algorithms that use the quantum state space to produce feature maps are demonstrated on a superconducting processor, enabling the solution of problems when the feature space is large and the kernel functions are computationally expensive to estimate.
Circuit-centric quantum classifiers
TLDR
A machine learning design is developed to train a quantum circuit specialized in solving a classification problem and it is shown that the circuits perform reasonably well on classical benchmarks.
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.
Toward Trainability of Deep Quantum Neural Networks
TLDR
This work provides the first viable solution to the vanishing gradient problem for deep QNNs with theoretical guarantees, and proves that for circuits with controlled-layer architectures, the expectation of the gradient norm can be lower bounded by a value that is independent of the qubit number and the circuit depth.
...
...