Hello!

I am trying to experiment with amplitude damping in a QNN setting. Below is my 4-qubit circuit i am using:

```
wires = 4
layers = 2
dev = qml.device("default.mixed", wires=wires)
def quantum_node_1(rotations):
for i in range(layers):
#
for i in range(wires):
#
qml.RX(rotations[0][i], wires=i)
qml.RY(rotations[1][i], wires=i)
qml.broadcast(qml.CZ, wires=range(wires), pattern="chain")
qml.AmplitudeDamping(sigmoid(rotations[1][1]), wires=0)
qml.AmplitudeDamping(sigmoid(rotations[1][1]), wires=1)
qml.AmplitudeDamping(sigmoid(rotations[1][1]), wires=2)
qml.AmplitudeDamping(sigmoid(rotations[1][1]), wires=3)
H = np.zeros((2 ** wires, 2 ** wires))
H[0, 0] = 1
wirelist = [i for i in range(wires)]
return qml.expval(qml.Hermitian(H, wirelist))
QNODE_1 = qml.QNode(quantum_node_1, dev)
rotations = [[np.random.uniform(low=-np.pi, high=np.pi) for i in range(wires)],
[np.random.uniform(low=-np.pi, high=np.pi) for i in range(wires)]]
rotations = np.array(rotations, requires_grad=True)
```

The cost function i am trying to optimize is `1-(QNODE_1(rotations))**2`

. To be fair with the optimizer to have somewhat same starting point to navigate through the optimization landscape, both RX and RY are initialized with same random values both in case of noise and no-noise.

My question is how to decide the appropriate value of `gamma`

here since changing its value significantly affect optimization performance. For instance `qml.AmplitudeDamping(sigmoid(rotations[0][1]), wires=0) for all wires`

yields better performance than the ones used in code above. What would be the appropriate and logical way of defining this value???

Secondly, is there an upper bound on the number of qubits for qubits.mixed device as I cant go beyond 10 qubits?

the output of `qml.about()`

.

Name: PennyLane

Version: 0.32.0

Summary: PennyLane is a Python quantum machine learning library by Xanadu Inc.

Home-page: GitHub - PennyLaneAI/pennylane: PennyLane is a cross-platform Python library for differentiable programming of quantum computers. Train a quantum computer the same way as a neural network.

Author:

Author-email:

License: Apache License 2.0

Location: /Users/mk9430/anaconda3/lib/python3.11/site-packages

Requires: appdirs, autograd, autoray, cachetools, networkx, numpy, pennylane-lightning, requests, rustworkx, scipy, semantic-version, toml, typing-extensions

Required-by: PennyLane-Lightning, PennyLane-qiskit

Platform info: macOS-13.6.2-arm64-arm-64bit

Python version: 3.11.4

Numpy version: 1.23.5

Scipy version: 1.10.1

Installed devices:

- default.gaussian (PennyLane-0.32.0)
- default.mixed (PennyLane-0.32.0)
- default.qubit (PennyLane-0.32.0)
- default.qubit.autograd (PennyLane-0.32.0)
- default.qubit.jax (PennyLane-0.32.0)
- default.qubit.tf (PennyLane-0.32.0)
- default.qubit.torch (PennyLane-0.32.0)
- default.qutrit (PennyLane-0.32.0)
- null.qubit (PennyLane-0.32.0)
- lightning.qubit (PennyLane-Lightning-0.32.0)
- qiskit.aer (PennyLane-qiskit-0.31.0)
- qiskit.basicaer (PennyLane-qiskit-0.31.0)
- qiskit.ibmq (PennyLane-qiskit-0.31.0)
- qiskit.ibmq.circuit_runner (PennyLane-qiskit-0.31.0)
- qiskit.ibmq.sampler (PennyLane-qiskit-0.31.0)
- qiskit.remote (PennyLane-qiskit-0.31.0)

Thanks.