[open-systems] Phased classical simulation

[mpharrigan]

This pull request is the second in a series for supporting open system (classical data & measurement), roadmap item #445.

This branch is based on #1584

Bloq.basis_state_phase

This new method can be overridden for phased-classical gates. In this PR, I show how CZ can support this new method. This leaves the basis states alone but applies a phase when 11 is encountered.

PhasedClassicalSimState(ClassicalSimState)

I refactored the classical simulator into a (mutable) class with initialization .from_cbloq(...), binst-by-binst stepping .step(), and finalization .finalize(). These can be combined with .simulate(), which is the new backend for the familiar entry points Bloq.call_classically(...) and friends.

Doing ordinary classical simulation will raise an error if it encounters a bloq with a non-trivial phase. The phased classical simulator will raise an error if it encounters a bloq without classical action; otherwise it will propagate phase. If a bloq does not specifically annotate a phase (but does indeed have classical action), the trivial +1 phase is assumed.

Non-changes (yet)

This PR does not directly support any "open systems" things. The ultimate goal is to support fuzz-testing measurement-based uncomputation. Since MBUC involves tracking phases, this PR is a necessary but not sufficient pre-requisite.

Related

• This PR unblocks Remove on_classical_vals for CSwapApprox? #1527
• Add leaf bloqs for relative phase Toffoli gates #1499 easier to test
• https://arxiv.org/abs/2105.13410 has a ton of cool circuit constructions that can be tested with this