Bad Qubits — Learn Quantum by Doing

Multiple choice

For a sufficiently random (approximately 2-design) ansatz on n qubits, how does the variance of each gradient component of the cost scale, and what does this imply for training?

Var[partial_k C] ~ n^2, so it grows polynomially; training becomes easier as qubits are added
Var[partial_k C] ~ 1/n, so it shrinks only polynomially; a constant number of shots always suffices
Var[partial_k C] ~ 1/2^n, so it shrinks exponentially in n; resolving the slope from shot noise would need on the order of 2^n shots
Var[partial_k C] ~ 2^n, so the gradient becomes exponentially large and the optimizer diverges