qlam-quantum-attention-memory

name: qlam-quantum-attention-memory description: "QLAM: Quantum Long-Attention Memory methodology for long-sequence token modeling. Combines quantum linear algebra with attention mechanisms to overcome O(n²) scaling of transformer attention. Based on arXiv:2605.13833."

QLAM: Quantum Long-Attention Memory for Long-Sequence Modeling

Quantum Long-Attention Memory (QLAM) methodology for efficient long-range dependency modeling using quantum computing primitives (arXiv:2605.13833).

Core Problem

Transformers suffer from O(n²) complexity in attention for long sequences. State-space models (SSMs) provide alternatives but struggle with certain memory-intensive tasks. QLAM leverages quantum superposition and interference to encode long-range dependencies more efficiently.

Key Innovation

Quantum Attention via Block Encodings

QLAM encodes the attention matrix as a block-encoded quantum state:

• Token embeddings are mapped to quantum states via amplitude encoding
• Attention scores are computed via quantum inner products (swap test or Hadamard test)
• The resulting attention distribution is sampled via quantum measurement

Memory Compression

• Long sequences are compressed into quantum states with O(log n) qubits
• Quantum Random Access Memory (QRAM) enables O(1) access to any token
• Temporal dependencies are encoded in entanglement patterns

Mathematical Framework

Block Encoded Attention

Given token embeddings x₁, ..., xₙ ∈ ℝᵈ:

1. Amplitude Encoding: |ψᵢ⟩ = Σⱼ xᵢⱼ/||xᵢ|| |j⟩
2. Quantum Attention Score: ⟨ψᵢ|ψⱼ⟩ computed via Hadamard test
3. Softmax via Quantum Sampling: e^{⟨ψᵢ|ψⱼ⟩}/Σₖ e^{⟨ψᵢ|ψₖ⟩}

Complexity Analysis

• Classical attention: O(n²d)
• QLAM attention: O(log n · poly(d)) with QRAM
• Memory: O(n·d) classical → O(log n · d) quantum

Implementation Patterns

Pattern 1: Quantum-Enhanced Attention Layer

from unitaria import BlockEncoding
import numpy as np

class QLAMAttention:
    """Quantum Long-Attention Memory layer."""
    
    def __init__(self, d_model, n_qubits):
        self.d_model = d_model
        self.n_qubits = n_qubits  # log(sequence_length)
    
    def forward(self, x):
        # Encode tokens as quantum states
        states = self.amplitude_encode(x)
        # Compute attention via quantum inner products
        attn_scores = self.quantum_inner_product(states)
        # Sample from quantum distribution
        output = self.quantum_sample(attn_scores, x)
        return output

Pattern 2: Hybrid Classical-Quantum Memory

For NISQ-era deployment:

• Use classical attention for short-range (window < W)
• Use quantum attention for long-range dependencies
• Combine via weighted sum: attn = α·attn_classical + (1-α)·attn_quantum

Activation Keywords

• qlam
• quantum attention
• quantum long-attention memory
• long sequence modeling quantum
• quantum transformer attention
• 量子注意力

Usage Guidelines

When to Use

1. Very long sequences (n > 10K tokens)
2. Memory-intensive tasks where classical SSMs fail
3. Research/prototyping on quantum-classical hybrid systems

Prerequisites

• Understanding of block encodings (see unitaria-quantum-linear-algebra)
• Access to quantum simulator or hardware
• Linear algebra foundations (matrix operations, spectral theory)

Limitations

• Requires QRAM for theoretical speedup (not yet practical)
• NISQ-era implementations need hybrid classical-quantum approach
• Quantum measurement introduces stochasticity

Related Skills

• unitaria-quantum-linear-algebra - Block encoding foundation
• quantum-neural-network-designer - QNN architecture design
• spiking-transformer-unification - Alternative attention unification

arXiv Reference

• arXiv: 2605.13833v1
• Title: "QLAM: A Quantum Long-Attention Memory Approach to Long-Sequence Token Modeling"
• Published: 2026-05-13
• Categories: cs.LG, cs.CV