docs(quantum-info): add qubit API map

[Robby955]

Motivation

Related to #1414, the tracking map for the qubit API in #850. An API map records the implemented status and source location of each requirement for an API, so the gap between a planned API and the current library stays visible in-tree.

Changes

Adds QuantumInfo/States/Pure/API-map.yaml, 25 requirements of which 11 are done. The done entries cover Qubit itself, the gates X, Y, Z, H, S and T with their relations, controllize and CNOT, states up to a global phase, POVM measurements, and the fidelity and trace distance, together with the finite dimensional constructions the qubit case instantiates: kets and bras, density matrices, unitary evolution and products. Those last are recorded as the ambient theory rather than as results about Qubit, since none of them mentions it.

Fourteen requirements are recorded as not done. Twelve have nothing behind them in the library yet: the Bloch vector and the Pauli decomposition of a state, the rotation gates and the decomposition of a general single-qubit unitary, the Born rule, the Bell and singlet-triplet bases, a closed form for the fidelity of two qubit states, the positive partial transpose criterion, registers of several qubits with universality of H, T and CNOT, and the link from kets on Qubit to the finite dimensional Hilbert space of a two element target. The other two are the Bloch sphere and the Bargmann invariant. Those are written and proved, in BlochSphere.lean and BargmannInvariant.lean, but QuantumInfo.lean imports neither, so nothing builds them and I did not want to record them as done; you may want to look at that separately from this map.

Two things I am unsure about. This is the first API map inside QuantumInfo rather than under Physlib, and the map is titled Qubits while it sits at QuantumInfo/States/Pure, whose largest module is the general Braket.lean. Tell me if you would rather it lived under Physlib/QuantumMechanics, or were split along the lines of #850 and #848.

Checks

python3 scripts/api_map_linter.py --repo . passes with no missing files and no missing names, resolving 74 declarations against the Lean sources, and no Lean source is touched.

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[jstoobysmith]

Could we move this to ./Physlib/QuantumMechanics/Qubit/API-map.yaml, as the long-term plan is to move the QuantumInfo stuff from ./QuantumInfo to ./Physlib eventually.

[jstoobysmith]

Maybe we should split this up a bit, as I think Density matrices should likely sit in another API map

[Robby955]

Moved to Physlib/QuantumMechanics/Qubit/API-map.yaml, and split the content: the map now keeps the qubit-scoped and pure-state entries only. The density matrix, evolution, measurement and distinguishability entries are gone from it and can get their own map under #848.

[jstoobysmith]

Approved - looks good. Will merge shortly