Qiskit / qiskit-fermions / 23818320805

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[Python] initial `circuit` and `transpiler` modules (#53)

* [wip] FermionCircuit as a Facade pattern to QuantumCircuit

* [wip] minimal fermion creation gate logic

The decomposition-style definition of this gate is not what the final
form is going to look like. Specifically because it currently assumes a
Jordan-Wigner like transformation and a 1-to-1 index mapping of
fermionic to qubit indices which is fairly restrictive.

However, this shows a simple proof of concept for what the circuit
library could look like.

* [wip] basic prototype of fermion-to-qubit evolution synthesis

* [wip] code restructuring

* fix: do not remove imaginary phase during evolution synthesis

This was done due to a faulty example test case...

* fix: lint

* [wip] refactor to handle all FermionGate types in one pass

Rather than having individual fermion-to-qubit gate `TransformationPass`
implementations, we should handle _all_ `FermionGate` objects in a
single pass. This is important because we need to translate all gates in
order that they appear and insert them into a new `DAGCircuit` with a
qubit-based register (rather than a fermion-based one) whose size may be
different. Thus, we cannot really have an intermediate object which has
a fermion- and qubit-based register at the same time (which is not what
is really happening anyways and feels clunky, too).

In this form, we can have our transpilation happen in the following
stages:

1. fermion-level optimization (translates FermionGate to FermionGate)
   (not yet implemented at this point)
2. fermion-to-qubit layouting (prepares the F2QLayout dataclass; creates
   the qubit-based register that will later be used to build the
   DAGCircuit on top of; associates each fermion with a qubit (and vice
   versa))
3. fermion-to-qubit gate translation (similar to Qiskit's
   HighLevelSynthesis, iterates over all `DAGOpNode`s in the
   fermion-based circuit, calls out to a registered routine for
   translating every single gate to... (continued)

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