Bad Qubits — Learn Quantum by Doing

Multiple choice

What is the quantum natural gradient update rule, and what is the matrix F that preconditions the ordinary gradient?

theta -> theta + eta F^(-1) grad(C), where F is the identity matrix, recovering plain gradient ascent
theta -> theta - eta F^(-1) grad(C), where F is the quantum Fisher information matrix (the Fubini-Study metric) measuring how much the state moves per change in each parameter
theta -> theta - eta grad(C)/F, where F is a scalar learning rate inferred from the cost value
theta -> theta - eta F grad(C), where F is the Hamiltonian matrix evaluated at the current parameters