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I want to implement a Quantum Recurrent Neural Network and use it for time series forecasting. As a starting point, I chose to implement it using the architecture given in this paper: https://arxiv.org/pdf/2302.03244.pdf. I already got some basic implementation, but I don't know how to continue implementing the forward part. I'm not 100% sure if the implementation I already did is correct in any way, but I do hope so. If you do see any errors or have any suggestions, in which way I should continue with my implementation, I'd be thankful for every help.

Thank you all in advance.

Here is the code I already implemented:

import torch
import torch.nn as nn
import numpy as np
import pennylane as qml

class QRNN(nn.module):

    def __init__(
        self,
        input_size,
        hidden_size,
        n_qubits = 5,
        n_qlayers = 1,
        batch_first=True,
        backend = "default.qubit"
    ):
        
        super(QRNN, self).__init__()
        self.n_inputs = input_size
        self.hidden_size = hidden_size
        self.concat_size = self.n_inputs + self.hidden_size
        self.n_qubits = n_qubits
        self.n_qlayers = n_qlayers
        self.backend = backend

        self.wires = [f"wire_{i}" for i in range(self.n_qubits)]
        self.dev = qml.device(self.backend, wires = self.wires)

        def _layer_qrnn_block(W):
            def layer(W):

                qml.RX(W[0,0], wires = 0)
                qml.RZ(W[0,1], wires = 0)
                qml.RX(W[0,2], wires = 0)

                qml.RX(W[1,0], wires = 1)
                qml.RZ(W[1,1], wires = 1)
                qml.RX(W[1,2], wires = 1)

                qml.RX(W[2,0], wires = 2)
                qml.RZ(W[2,1], wires = 2)
                qml.RX(W[2,2], wires = 2)

                qml.RX(W[3,0], wires = 3)
                qml.RZ(W[3,1], wires = 3)
                qml.RX(W[3,2], wires = 3)

                qml.RX(W[4,0], wires = 4)
                qml.RZ(W[4,1], wires = 4)
                qml.RX(W[4,2], wires = 4)

                qml.RX(W[5,0], wires = 5)
                qml.RZ(W[5,1], wires = 5)
                qml.RX(W[5,2], wires = 5)

                qml.CNOT(wires = [0,1])
                qml.RZ(W[1,0], wires = 1)
                qml.CNOT(wires = [0,1])

                qml.CNOT(wires = [1,2])
                qml.RZ(W[2,0], wires = 2)
                qml.CNOT(wires = [1,2])

                qml.CNOT(wires = [2,3])
                qml.RZ(W[3,0], wires = 3)
                qml.CNOT(wires = [2,3])

                qml.CNOT(wires = [3,4])
                qml.RZ(W[4,0], wires = 4)
                qml.CNOT(wires = [3,4])

                qml.CNOT(wires = [4,5])
                qml.RZ(W[5,0], wires = 5)
                qml.CNOT(wires = [4,5])

                qml.CNOT(wires = [5,0])
                qml.RZ(W[0,0], wires = 0)
                qml.CNOT(wires = [5,0])

        def _circuit_qrnn_block(inputs, weights):
            qml.AngleEmbedding(inputs, self.wires)

            for W in weights:
                _layer_qrnn_block(W)

            return [qml.expval(qml.PauliZ(wires = w)) for w in self.wires]
        
        self.qlayer_circuit = qml.QNode(_circuit_qrnn_block, self.dev, interface = "torch")

        weights_shapes = {"weights": (n_qlayers, n_qubits)}
        print(f"weight_shapes = (n_qlayers, n_qubits) = ({n_qlayers}, {n_qubits})")

        self.clayer_in = torch.nn.Linear(self.concat_size, n_qubits)
        self.VQC = {
            'circuit': qml.qnn.TorchLayer(self.qlayer_circuit, weights_shapes)
        }
        self.clayer_out = torch.nn.Linear(self.n_qubits, self.hidden_size)

    def forward(self, x):
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1 Answer 1

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Your implementation of a Quantum Recurrent Neural Network (QRNN) using PyTorch and PennyLane is a good start but needs some adjustments and completion. Let's go through the code to identify areas for improvement and complete the forward method:

  1. Class Inheritance:

    • The class QRNN should inherit from nn.Module, not nn.module. Python is case-sensitive, so this needs to be corrected.
  2. Quantum Circuit Definition:

    • The definition of the quantum circuit inside _layer_qrnn_block seems hardcoded for a specific number of qubits. This could be made more flexible to work with any number of qubits by iterating over them.
    • The use of the CNOT gates to create entanglement is a good approach, but the hardcoded indices might lead to issues if the number of qubits (n_qubits) is changed. A more dynamic approach would be beneficial.
  3. Weight Shape

    • The weights_shapes definition is somewhat unclear. It is currently defined as {"weights": (n_qlayers, n_qubits)}. However, this might not correctly represent the weight matrix needed for your quantum layers. Each layer typically needs a weight matrix of shape (n_qubits, 3) for the RX and RZ rotations.
  4. Quantum Layer:

    • The quantum layer (self.VQC['circuit']) is defined correctly as a qml.qnn.TorchLayer. This allows it to be integrated into the PyTorch model seamlessly.
  5. Forward Method:

    • The forward method is incomplete. It should take an input x and a hidden state h (initially set to zeros or some initial value), concatenate them, and then pass through the classical layer, quantum layer, and another classical layer to produce the output and the new hidden state.

Here's a completion and correction of your forward method:

def forward(self, x, h=None): # Initialize hidden state if not provided if h is None: h = torch.zeros(self.hidden_size)

# Concatenate input and hidden state
combined = torch.cat((x, h), dim=1)

# Pass through the classical layer
combined = self.clayer_in(combined)

# Apply the quantum circuit layer
q_out = self.VQC['circuit'](combined)

# Output layer
out = self.clayer_out(q_out)

# Update the hidden state
new_h = out

return out, new_h

In this forward method, we assume that the input x and the hidden state h are compatible with the dimensions expected by self.clayer_in. The method processes the input and hidden state through the QRNN layer and returns the output and the updated hidden state.

Remember, the QRNN model's efficacy depends on the specific task and data it's being applied to, so you may need to adjust the architecture and parameters according to your specific use case.

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