Initializing the zero state and applying a circuit returns a different statevector than applying a circuit without initializing the zero state.

[JamesB-1qbit]

Informations

• Qiskit Aer version: 0.13.0
• Python version: 3.9.16
• Operating system: MacOS

What is the current behavior?

When using method="statevector" with AerSimulator, a circuit with an initialize of |00> (i.e. [1,0,0,0]) returns a different statevector than the same circuit without explicitly initializing the |00> state.

Steps to reproduce the problem

import qiskit
from qiskit_aer import AerSimulator

circuits = dict()

circuits["zero"] = qiskit.QuantumCircuit(2)
circuits["zero"].initialize([1., 0., 0., 0.])

circuits["X"] = qiskit.QuantumCircuit(2)
circuits["X"].x(0)

circuits["zero+X"] = circuits["zero"].compose(circuits["X"])

def transpile_run_and_return_statevector(circ):
    aersim = AerSimulator(method="statevector")
    transpiled_circ = qiskit.transpile(circ, aersim)
    transpiled_circ.save_statevector()
    sim_results = aersim.run(transpiled_circ).result()
    print(f"Circuit:\n{transpiled_circ}")
    print(f"Statevector:\n{sim_results.get_statevector(transpiled_circ)}")

for name, circ in circuits.items():
    print(f"For circuit {name}\n")
    transpile_run_and_return_statevector(circ)
    print("\n\n")

results in

For circuit zero

Circuit:
     ┌──────────────────────┐ statevector 
q_0: ┤0                     ├──────░──────
     │  Initialize(1,0,0,0) │      ░      
q_1: ┤1                     ├──────░──────
     └──────────────────────┘      ░      
Statevector:
Statevector([1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
            dims=(2, 2))



For circuit X

Circuit:
global phase: π/2
     ┌────────────────┐ statevector 
q_0: ┤ U3(π,-π/2,π/2) ├──────░──────
     └────────────────┘      ░      
q_1: ────────────────────────░──────
                             ░      
Statevector:
Statevector([3.74939946e-33+6.123234e-17j, 1.00000000e+00+0.000000e+00j,
             0.00000000e+00+0.000000e+00j, 0.00000000e+00+0.000000e+00j],
            dims=(2, 2))



For circuit zero+X

Circuit:
global phase: π/2
     ┌──────────────────────┐┌────────────────┐ statevector 
q_0: ┤0                     ├┤ U3(π,-π/2,π/2) ├──────░──────
     │  Initialize(1,0,0,0) │└────────────────┘      ░      
q_1: ┤1                     ├────────────────────────░──────
     └──────────────────────┘                        ░      
Statevector:
Statevector([6.123234e-17+0.j, 6.123234e-17-1.j, 0.000000e+00+0.j,
             0.000000e+00+0.j],
            dims=(2, 2))

What is the expected behavior?

Circuits "X" and "zero+X" should return the same statevector (i.e. [0, 1, 0, 0]) but "zero+X" returns [0,-1j,0,0].

Suggested solutions

I don't know the code well enough to determine where this bug is coming from. But it is new as of 0.13.0