Optimize apply_matrix_to_slices when sparse

[daxfohl]

Improves the perf of apply_matrix_to_slices when the operator matrix has ones and zeroes. For example for ResetChannel on a large density matrix, this results in about a 3x speedup.

cirq.DensityMatrixSimulator(split_untangled_states=False).simulate(
    cirq.Circuit([cirq.reset(cirq.LineQubit(0))] * 100), qubit_order=cirq.LineQubit.range(11)
)

[viathor]

What is the performance impact of this change for dense matrices?

My hunch is that introducing branching to special-case multiplication by one and by zero is actually a bad idea for performance in the general case. Especially, if the branching is done in python rather than in C within numpy (though I doubt it would be helpful even in the latter case on the grounds that performance impact of branch misprediction is usually rather severe).

A better way to exploit matrix sparsity in python is to use a package such as scipy.sparse. However, in my view this is still not ideal since it makes cirq inconsistent in its approach to sparse operators. Instead, I think we should do for channels what we've done for unitary gates which is to special-case the handling of sparse operators in magic methods such as _apply_unitary_ and _apply_channel_. See here for an example.

[daxfohl]

Good callout. I'll look at the perf impact on various cases when I get a chance. It didn't have a noticeable effect on the unit tests in cirq/sim in either direction, but I'll look more explicitly.

[daxfohl]

Yes the perf impact does seem to be significant (about 20%) up to about 2^13 element input tensors, beyond which the numpy dominates.

I figured an if check would be negligible compared to the numpy operation at any size. Learn something new every day.