✨ Add Hadamard Lifting

[LiRem101]

Description

This PR introduces the optimization pass Hadamard lifting.

The optimization pass lifts Hadamard gates in front of Pauli gates in order to improve the results bu measurement-lifting. The implemented liftings are:
z followed by h to h followed by x.
x followed by h to h followed by z.
y followed by h to h followed by y.

The transformation are also applied on controlled gates, provided both participating gates have the same target qubit and the same control qubits.
An exception is the z gate: The transformation exchanges the target and control qubits of a controlled z gate, if it is followed by a controlled Hadamard gate it can be swapped with afterwards.

Additionally, a transformation routine is implemented which swaps the target and control qubits of a CNOT operation (by adding four Hadamard gates before/after the target/control qubits). This is applied if a Hadamard gate is applied to the CNOT target, and afterwards the qubit is measured. The whole transformation routine is:

After the transformation routine, measurement-lifting can be used to lift the measurement in front of the control and to remove a costly two-qubit gate.

The paper in which the routine is published is currently under review.

Microsoft Copilot has been occasionally used to draft first versions of code, but was not integrated into an IDE.

Fixes #1386

Checklist

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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