Arbitrary gate set conversion transpiler

[lqtmirage]

Overview

• Add a CircuitTranspiler to convert the gate set of the given circuit to the arbitrary gate set specified by the user.
• Fix redundant rotation angle in several gate kind decomposers.

Transpile path description

• Conversion to an arbitrary gate set is achieved by a combination of several components below.

1. Decompose non target "complex" gates into Clifford gates and 1 qubit rotation gates.
2. Convert between 2 qubit Clifford gates.
3. Convert between 1 qubit Clifford gates.
4. Convert non target 1 qubit Clifford gates into 1 qubit rotation gates.
5. Convert between 1 qubit rotation gates.

Note

• "complex" gates include Pauli, PauliRotation, UnitaryMatrix, TOFFOLI, U1, U2 ,and U3 gates.
• During the course of the transformation, minimal optimization passes are applied, such as converting rotational gates to named gates, fusing rotation gates and removing Identity gates.
• Some conversion paths use a best-effort approach and may not achieve the desired conversion. It is verified after the conversion that the circuit has been converted to the desired gate set.

[github-actions]

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