Unexpected output from extended stabilizer simulator

[AthenaCaesura]

Environment

• Qiskit version: 1.3.2
• Python version: 3.11.11
• Operating system: MacOS

What is happening?

When I add in a CNOT to a simple circuit with T gates and hadamards, I seem to be getting an incorrect output. Issue persists even when accuracy is increased.

How can we reproduce the issue?

import qiskit

from qiskit_aer import AerSimulator

sim = AerSimulator(method="extended_stabilizer")

qc = qiskit.QuantumCircuit(2)

qc.h(0)
qc.t(0)
qc.h(0)
qc.cx(0, 1)

qc.measure_all()

opts = {
    'extended_stabilizer_approximation_error': 0.01,
    'extended_stabilizer_mixing_time': 1000,
}

results = sim.run(qc, shots=100, **opts).result()

print(results.get_counts())

What should happen?

Outputs 00 and 11 with 50% probability regardless of how I increase precision. I would expect to get 11 approximately 15% of the time and 00 approximately 85% of the time.

Any suggestions?

Unsure how this might be occurring as I get the correct ratio when I get rid of the CNOT. Perhaps I'm misusing the CNOT. Perhaps there is some other accuracy measure that I need to adjust that I just didn't see?