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Does provable absence of barren plateaus imply classical simulability? Or, why we need to rethink variational quantum computing
A large amount of effort has recently been put into understanding the barren plateau phenomenon.
Deep quantum neural networks form Gaussian processes
It is well known that artificial neural networks initialized from independent and identically distributed priors converge to Gaussian processes in the limit of large number of neurons per hidden layer.
On the universality of $S_n$-equivariant $k$-body gates
Our results show that if the QNN is generated by one- and two-body $S_n$-equivariant gates, the QNN is semi-universal but not universal.
Effects of noise on the overparametrization of quantum neural networks
In particular, it has been proposed that a QNN can be defined as overparametrized if it has enough parameters to explore all available directions in state space.
Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential.
Theory for Equivariant Quantum Neural Networks
Most currently used quantum neural network architectures have little-to-no inductive biases, leading to trainability and generalization issues.
Representation Theory for Geometric Quantum Machine Learning
Recent advances in classical machine learning have shown that creating models with inductive biases encoding the symmetries of a problem can greatly improve performance.
Group-Invariant Quantum Machine Learning
We present theoretical results underpinning the design of $\mathfrak{G}$-invariant models, and exemplify their application through several paradigmatic QML classification tasks including cases when $\mathfrak{G}$ is a continuous Lie group and also when it is a discrete symmetry group.
Theory of overparametrization in quantum neural networks
The prospect of achieving quantum advantage with Quantum Neural Networks (QNNs) is exciting.
