Fig. 3: Gradient measurement efficiency.
From: Trade-off between gradient measurement efficiency and expressivity in deep quantum neural networks
a–c Commutators between two gradient operators Γj(θ) and Γk(θ) in the SLPA and symmetric and non-symmetric ansatzes for n = 4 qubits and L = 48 parameters. The black and yellow regions represent [Γj(θ), Γk(θ)] = 0 and [Γj(θ), Γk(θ)] ≠ 0 for random θ, respectively. d Changes in gradient measurement efficiency when the number of parameters L is varied for n = 4. Their values are computed by minimizing the number of simultaneously measurable sets of Γj(θ)'s for random θ. The blue circles, orange squares, and green triangles are the results of SLPA and symmetric and non-symmetric ansatzes, approaching four and one in the limit of L → ∞, respectively. The dashed gray lines represent the DLA dimension of each model, \(\,\text{dim}\,({\mathfrak{g}})\).
