Rename multiplexer_dg with multiplexer_decomp_dg after UC.inverse()

[hhorii]

Summary

#8231 produced regression in transpilation from inverse isometry to multiplexer. Isometry.inverse() generates a multiplexer gate with basic Gate class. However, originally, multiplexer is based on UCGate that has parameters.

This PR provides a work around by naming multiplexer_decomp(_dg) instead of multiplexer(_dg) to generated multiplexer gates of Gate class.

Details and comments

This bug exists before #8231. UCGate.inverse().inverse() returns Gate instance that has not any parameters even though its name is multiplexer. Isometry.inverse() internally call UCGate.inverse().inverse() since #8231.

import numpy as np
from qiskit import QuantumCircuit
from qiskit.quantum_info.states import Statevector

qc = QuantumCircuit(1,1)
vector = [0.2, 0.1]
vector_circuit = QuantumCircuit(1)
vector_circuit.isometry(vector / np.linalg.norm(vector), [0], None)
vector_circuit = vector_circuit.inverse()
qc.append(vector_circuit, [0])

sv = Statevector(qc)
gate_list = [np.array([[sv[0], -sv[1]], [sv[1], sv[0]]])]
qc = QuantumCircuit(1,1)
qc.uc(gate_list, [], [0])

uc = qc.data[0][0]
uc_inverse = uc.inverse()
uc_inverse_inverse = uc_inverse.inverse()
print(uc.__class__, ", param_len=", len(uc.params), ", name=", uc.name)
print(uc_inverse.__class__, ", param_len=", len(uc_inverse.params), ", name=", uc_inverse.name)
print(uc_inverse_inverse.__class__, ", param_len=", len(uc_inverse_inverse.params), ", name=", uc_inverse_inverse.name)

Output:

<class 'qiskit.extensions.quantum_initializer.uc.UCGate'> , param_len= 1 , name= multiplexer
<class 'qiskit.circuit.gate.Gate'> , param_len= 0 , name= multiplexer_dg
<class 'qiskit.circuit.gate.Gate'> , param_len= 0 , name= multiplexer

If multiplexer must have parameter gatelist , UCGate.inverse() should not name multiplexer_dg to a returned Gate instance because it may produce multiplexer gate with its inverse().

This PR names multiplexer_decomp_dg to a returned Gate instance produced by UCGate.inverse().

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[coveralls]

Pull Request Test Coverage Report for Build 2815151750

• 0 of 0 changed or added relevant lines in 0 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+0.003%) to 84.037%

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Totals
Change from base Build 2800102724:	0.003%
Covered Lines:	56089
Relevant Lines:	66743

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💛 - Coveralls

[Cryoris]

I'm not sure I remember the outcome of the last meeting correctly, but did we decide that it would be nicer if UCGate.inverse() would return a UCGate again? Maybe we could implement that and and still re-use the synthesis doing something like

class UCGate(Gate):
    def inverse(self):
        definition = # compute inverse like right now
        
        # inverted gate list
        gate_list = list(reversed([np.conj(unitary.T) for unitary in self.params]))
        
        # ensure inverting twice gives again "multiplexer"
        name = "multiplexer_dg" if self.name == "multiplexer" else "multiplexer"
        
        inv = UCGate(gate_list, up_to_diagonal=self.up_to_diagonal)
        inv.name = name
        inv.definition = definition
        
        return inv