gated-qkan-fwp

name: gated-qkan-fwp description: "Quantum-inspired sequence learning using Gated QKAN-FWP (Quantum Fast Weight Programmers with variational quantum Kolmogorov-Arnold Networks). Use this skill for designing quantum-inspired sequence models, temporal encoding for quantum ML, fast weight programming patterns, and Kolmogorov-Arnold Network architectures for sequential data. Also triggered by: quantum sequence learning, QKAN, fast weight programmer, quantum-inspired RNN, temporal encoding quantum, 量子序列学习."

Gated QKAN-FWP: Quantum-Inspired Sequence Learning

Based on "Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning" (arXiv: 2605.06734).

When to Use

Designing quantum-inspired sequence models for time-series or NLP
Replacing traditional RNN/LSTM with quantum-inspired fast weight architectures
Implementing temporal encoding for quantum machine learning
Building Kolmogorov-Arnold Network variants for sequential data
Seeking scalable alternatives to full quantum circuits for sequence tasks

Core Concepts

Quantum Fast Weight Programmers (QFWP)

Fast Weight Programmers generate weight matrices dynamically from input. In the quantum-inspired variant:

# Classical FWP pattern
def fast_weight(input_seq, base_weights):
    """Generate dynamic weights from input sequence."""
    # Input-dependent weight generation
    for x in input_seq:
        delta_w = generate_delta(x)  # quantum-inspired transformation
        base_weights += delta_w
    return base_weights

Variational Quantum Kolmogorov-Arnold Networks (QKAN)

Kolmogorov-Arnold Networks parameterize functions as sums of 1D functions:

f(x) = Σ φ_q(Σ ψ_{q,p}(x_p))

QKAN replaces classical 1D functions with parameterized quantum circuits:

f(x) = Σ_q ⟨0| U_q(x)† O_q U_q(x) |0⟩

Quantum-Inspired Temporal Encoding

Key insight: quantum circuits naturally encode temporal information through gate sequencing. The temporal encoding pattern:

Time-aware initialization: Map temporal position to phase angles
Sequential gate application: Each timestep applies a rotation conditioned on previous state
Interference-based memory: Constructive/destructive interference captures long-range dependencies

Implementation Pattern

Step 1: Define the QKAN Layer

import numpy as np
from pennylane import numpy as pnp

def qkan_layer(x, params, n_qubits):
    """Single QKAN layer with variational quantum circuit."""
    # Initialize quantum state
    # Apply data encoding
    # Apply variational ansatz
    # Measure expectation value
    pass

def qkan_forward(x_seq, qkan_params, n_qubits):
    """Process sequence through QKAN."""
    outputs = []
    for x in x_seq:
        out = qkan_layer(x, qkan_params, n_qubits)
        outputs.append(out)
    return np.array(outputs)

Step 2: Fast Weight Generation

def gated_qkan_fwp(x_seq, base_weights, gate_params):
    """Gated QKAN-FWP for sequence learning.
    
    Args:
        x_seq: Input sequence (T, d_input)
        base_weights: Base weight matrix (d_model, d_model)
        gate_params: Parameters for quantum-inspired gates
    
    Returns:
        outputs: Processed sequence (T, d_model)
    """
    # Generate fast weights from input
    fast_weights = generate_fast_weights(x_seq, gate_params)
    
    # Apply gated mechanism (sigmoid gate controls information flow)
    gate = sigmoid(linear(x_seq, gate_params))
    
    # Combine base and fast weights
    effective_weights = base_weights + gate * fast_weights
    
    # Apply to sequence
    outputs = einsum('td,dm->tm', x_seq, effective_weights)
    return outputs

Step 3: Training Loop

def train_gated_qkan_fwp(data, labels, n_qubits, lr=0.001, epochs=100):
    """Train Gated QKAN-FWP model."""
    # Initialize parameters
    qkan_params = init_qkan_params(n_qubits)
    gate_params = init_gate_params()
    
    for epoch in range(epochs):
        # Forward pass
        outputs = gated_qkan_fwp(data, qkan_params, gate_params)
        loss = compute_loss(outputs, labels)
        
        # Compute gradients (parameter-shift rule or finite differences)
        qkan_grad = compute_gradients(loss, qkan_params)
        gate_grad = compute_gradients(loss, gate_params)
        
        # Update parameters
        qkan_params -= lr * qkan_grad
        gate_params -= lr * gate_grad
        
    return qkan_params, gate_params

Key Patterns

Pattern 1: Temporal Encoding via Quantum Gates

Map temporal sequence to quantum circuit:

t=0 → R_z(θ_0) R_x(ϕ_0)
t=1 → R_z(θ_1) R_x(ϕ_1)  
t=2 → R_z(θ_2) R_x(ϕ_2)

Where θ_t, ϕ_t are functions of input at time t.

Pattern 2: Fast Weight Decomposition

Decompose fast weight generation into:

Key extraction: k_t = W_k x_t
Value generation: v_t = W_v x_t
Fast weight: ΔW_t = k_t ⊗ v_t (outer product)

Pattern 3: Gated Information Flow

Use sigmoid gates to control how much fast weight contributes:

g_t = σ(W_g [x_t; h_{t-1}])
W_fast = g_t ⊙ ΔW_t

Design Guidelines

Qubit count: Start with 4-8 qubits for sequence modeling
Circuit depth: Keep shallow (2-4 layers) to avoid barren plateaus
Encoding: Use amplitude encoding for dense data, angle encoding for sparse
Measurement: Expectation value of Pauli-Z for classification tasks
Training: Use parameter-shift rule for gradient computation

When NOT to Use

Very long sequences (>1000 steps) — consider classical alternatives
Real-time inference on edge devices — quantum-inspired overhead
Tasks requiring exact reproducibility — quantum stochasticity