So far, only two approximations of the Quantum Natural Gradient optimizer are implemented: the exact version and the SPSA approximation. Another commonly used approximation is the block-diagonal approximation (proposed in the seminal paper) where the QFI is approximated via a block-diagonal matrix only taking in account correlations of variational parameters within each circuit block:
The block-diagonal approximation can be efficiently computed by measuring average values of the circuit layers generators. A further approximation that could be implemented is to only keep the diagonal terms.
So far, only two approximations of the Quantum Natural Gradient optimizer are implemented: the exact version and the SPSA approximation. Another commonly used approximation is the block-diagonal approximation (proposed in the seminal paper) where the QFI is approximated via a block-diagonal matrix only taking in account correlations of variational parameters within each circuit block:
The block-diagonal approximation can be efficiently computed by measuring average values of the circuit layers generators. A further approximation that could be implemented is to only keep the diagonal terms.