Transpilation for 64+ qubits fails for MPS, even though execution is supported

[Cryoris]

Informations

• Qiskit Aer version: 0.15.1 (same issue for 0.14.2)
• Python version: 3.11
• Operating system: macOS

What is the current behavior?

The AerSimulator(method="matrix_product_state") backend is able to execute circuits with a large number of qubits, but calling transpile only works for circuits with <64 qubits. This seems to be due to the backend reporting a Target with only 63 qubits (maybe related to #2116?). This was reported by @stefan-woerner and @ElePT.

Steps to reproduce the problem

from qiskit_aer import AerSimulator
from qiskit import qpy, QuantumCircuit, transpile

backend = AerSimulator(method="matrix_product_state")

circuit = QuantumCircuit(64)
circuit.measure_all()

result = backend.run(circuit).result()  # works

tqc = transpile(circuit, backend)  # fails

What is the expected behavior?

transpile should work

Suggested solutions

I'm not sure if it's viable to report a Target of enormous size... If not maybe some variadic properties or a simulation-specific Target is the right solution?