Trainability ยท Algorithms

Overparametrization: capacity saturation

Theorem statement

The effective quantum dimension (capacity) of a QNN is the achievable QFIM rank $D_1(M):=R(M)=\sup_\theta\operatorname{rank}F(\theta)$, with saturated value $R:=\sup_M R(M)$. When the network is overparametrized at parameter count $M$ (achievable rank saturated for every training state), the capacity attains this maximum, $D_1(M)=R$.

Sources

  1. Theory of overparametrization in quantum neural networks

    Martin Larocca, Nathan Ju, Diego Garcia-Martin, Patrick J. Coles, M. Cerezo, 2021

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