How Quantum RNNs Work (Step-by-Step)

We’ll visualize every step of how a Quantum Recurrent Neural Network works with simple Python code.

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📌 What is a Quantum RNN?

A QRNN is similar to a classical RNN: it processes sequences step by step, keeping a hidden state. But here, the hidden state is a quantum system represented by qubits.

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📊 Step 1: Define the Problem

We’ll use a toy example — predicting the next character in "hello".

python
text = "hello"
chars = sorted(list(set(text)))
char_to_int = {ch: i for i, ch in enumerate(chars)}
int_to_char = {i: ch for i, ch in enumerate(chars)}

print(char_to_int)  # {'e': 0, 'h': 1, 'l': 2, 'o': 3}

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🧠 Step 2: Encoding Data into Qubits

We need to represent characters as quantum states. For simplicity, we’ll use basis encoding: each character maps to a computational basis state.

• 'e' → |00⟩
• 'h' → |01⟩
• 'l' → |10⟩
• 'o' → |11⟩

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🔁 Step 3: Quantum RNN Cell (Concept)

In a QRNN, the hidden state is a set of qubits. Each step:

• Encode input into qubits.
• Apply parameterized gates (like Rx, Ry, Rz).
• Entangle input and hidden state.
• Measure to get predictions.

python
from qiskit import QuantumCircuit

def qrnn_cell(params, input_qubit, hidden_qubit):
    qc = QuantumCircuit(2)
    qc.ry(params[0], input_qubit)
    qc.ry(params[1], hidden_qubit)
    qc.cx(input_qubit, hidden_qubit)
    return qc

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📉 Step 4: Training (High-Level)

Like classical RNNs, QRNNs are trained by:

• Defining a loss (e.g., cross-entropy).
• Running the quantum circuit.
• Using classical optimizers (like gradient descent) to update gate parameters.

Training is slower (many circuit runs), but the Hilbert space grows exponentially with hidden qubits.

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🧩 Step 5: Prediction

After training, we feed "h" and predict the next characters. The output probabilities come from measurement statistics of the qubits.

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📈 Step 6: Why QRNNs?

• Exponential state space: n qubits → 2^n states.
• Potentially more expressive with fewer parameters.
• Hybrid training possible: classical optimizer + quantum forward pass.

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✅ Conclusion

QRNNs are an exciting frontier:

• They extend RNN concepts into the quantum domain.
• Encoding and training are the main challenges.
• With enough qubits, they might model sequences more efficiently than classical RNNs.

This workflow mirrors classical ML: define model → encode data → train → predict → evaluate.

Quantum makes the hidden state exponentially richer.