Density matrix returning complex conjugate

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Describe the bug

import cudaq 
import numpy as np

@cudaq.kernel
def kernel_a(): 
    
    q = cudaq.qvector(1)
    u3(1,2,3, q[0])

cudaq.set_target('density-matrix-cpu')
a0 = cudaq.get_state(kernel_a)
print(np.array(a0))

cudaq.set_target('qpp-cpu')

statevec = cudaq.get_state(kernel_a)

psi = np.array(statevec).reshape(-1,1)

psi_dagger = psi.conj().T

rho = np.outer(psi, psi_dagger)

The code above shows how one can manually compute the density matrix via the statevec simulator or directly via the density matrix simulator.

a0 and rho differ by a complex conjugate.

Physically they are the same states hence it does not matter but we should keep our convention consistent.

Steps to reproduce the bug

NA

Expected behavior

NA

Is this a regression? If it is, put the last known working version (or commit) here.

Not a regression

Environment

• CUDA-Q version:
• Python version:
• C++ compiler:
• Operating system:

Suggestions

No response

Start by running the supplied Python snippet with the density-matrix-cpu and qpp-cpu targets, comparing a0 with the manually computed rho. Trace the get_state paths for both targets and identify where the conjugation convention differs. Done means both paths return the same density-matrix convention, with a regression test covering the example.