Hello! I’ve put together a QLSTM model per the following paper: https://arxiv.org/pdf/2310.17032.pdf. If possible, could you provide feedback on the circuit configuration for the purpose of time series forecasting?

The model is converging and returning good MSE scores but the final post-processed results seem to be stuck within a limited range.

```
# Define the angle translation function
def get_angles(x):
# Split the data into chunks
chunk1 = x[0] * 0.1 / 2
chunk2 = x[1] * 0.1 / 2
chunk3 = x[2] * 0.1 / 2
chunk4 = x[3] * 0.1 / 2
chunk5 = x[4] * 0.1 / 2
angle1 = np.sin(chunk1)
angle2 = np.sin(chunk2)
angle3 = np.sin(chunk3)
angle4 = np.sin(chunk4)
angle5 = np.sin(chunk5)
return angle1, angle2, angle3, angle4, angle5
# Define the device
dev = qml.device('default.qubit', wires=4)
# Define the state preparation function.
def state_preparation(a):
qml.Hadamard(wires=0)
qml.RY(a[0], wires=0)
qml.RZ(a[0], wires=0)
qml.Hadamard(wires=1)
qml.RY(a[1], wires=1)
qml.RZ(a[1], wires=1)
qml.Hadamard(wires=2)
qml.RY(a[2], wires=2)
qml.RZ(a[2], wires=2)
qml.Hadamard(wires=3)
qml.RY(a[3], wires=3)
qml.RZ(a[3], wires=3)
# Define the variational layer
@qml.qnode(dev)
def layer(layer_weights):
qml.CNOT(wires=[0, 1])
qml.CNOT(wires=[1, 2])
qml.CNOT(wires=[2, 3])
qml.CNOT(wires=[3, 0])
qml.CNOT(wires=[0, 2])
qml.CNOT(wires=[1, 3])
qml.CNOT(wires=[2, 0])
qml.CNOT(wires=[3, 1])
for i in range(4):
qml.RX(layer_weights[i], i)
qml.RY(layer_weights[i], i)
qml.RZ(layer_weights[i], i)
return [qml.expval(qml.PauliY(0))]
# Define the variational quantum circuit with the state preparation routine
# and the layer structure.
@qml.qnode(dev)
def circuit(weights, x):
state_preparation(x)
for layer_weights in weights:
layer(layer_weights)
return qml.expval(qml.PauliZ(0))
# Define the full QLSTM model as the output of the quantum circuit
# plus the trainable bias
def QLSTM(weights, bias, x):
return circuit(weights, x) + bias
# Define the square loss (MSE) function
def square_loss(labels, predictions):
# Use a call to qml.math.stack to allow subtracting the arrays directly
return np.mean((labels - qml.math.stack(predictions)) ** 2)
# Define the cost function
def cost(weights, bias, X, Y):
predictions = [QLSTM(weights, bias, x) for x in X]
return square_loss(Y, predictions)
```

The model takes in a sequence features data i.e. 3, 4, 5, 6, 7 and is expected to return a prediction i.e, 8 after processing the expectation values.

Any guidance is greatly appreciated.