Quantum NLP

Quantum NLP Overview

Quantum natural language processing (QNLP) uses quantum circuits to process natural language:

1. Compositional distributional semantics (DisCoCat): maps grammar to quantum circuits
2. Quantum word embeddings: encode word meanings as quantum states
3. Quantum sentence processing: compose word meanings using quantum operations

The key insight: grammar structures in language resemble circuit structures in quantum computing.

DisCoCat Framework

The DisCoCat (Distributional Compositional Categorical) framework:

1. Words are morphisms in a category:
2. Grammar is a string diagram (tensor network)
3. Meaning is a linear map (quantum channel)

For example, "Alice loves Bob":

• "Alice":
• "loves":
• "Bob":
• Sentence: compose these maps using grammar structure

Quantum Word Embeddings

Quantum word embeddings represent word meanings as quantum states:

where are concept basis states. For example:

Quantum embeddings can capture:

• Polysemy: multiple meanings via superposition
• Context dependence: meaning changes with measurement basis
• Compositionality: word combinations via tensor products

Quantum Circuit Models

QNLP models use parameterized quantum circuits:

1. Encoding layer: map classical word features to quantum states
2. Interaction layer: quantum gates model word relationships
3. Measurement layer: extract classical information

The circuit depth and entanglement structure encode the linguistic complexity of the sentence.

Training QNLP Models

Training QNLP models:

1. Classical pre-processing: parse sentences, extract features
2. Quantum encoding: map to parameterized circuits
3. Measurement: compute predictions
4. Classical optimization: update parameters

Challenges: barrens plateaus, noise, limited qubit count.

Applications

QNLP applications:

1. Sentiment analysis: quantum-enhanced text classification
2. Machine translation: quantum-aligned word embeddings
3. Question answering: quantum information retrieval
4. Text generation: quantum language models
5. Information extraction: quantum relation detection

Python: QNLP Simulation

import numpy as np

def quantum_word_embedding(word_idx, n_concepts=4):
    # Simplified quantum word embedding.
    # Random embedding (in practice, learned)
    np.random.seed(hash(word_idx) % 2**32)
    embedding = np.random.randn(n_concepts) + 1j * np.random.randn(n_concepts)
    embedding = embedding / np.linalg.norm(embedding)
    return embedding

def compose_sentence(words, embeddings):
    # Compose sentence meaning via tensor product.
    result = embeddings[words[0]]
    for w in words[1:]:
        result = np.kron(result, embeddings[w])
    return result / np.linalg.norm(result)

# Example: "Alice loves Bob"
n_concepts = 4
words = {"Alice": 0, "loves": 1, "Bob": 2}
embeddings = {w: quantum_word_embedding(idx, n_concepts) for w, idx in words.items()}

sentence = compose_sentence(["Alice", "loves", "Bob"], embeddings)
print(f"Sentence embedding dim: {len(sentence)}")
print(f"Norm: {np.linalg.norm(sentence):.4f}")

DisCoCat Categories

The DisCoCat framework uses:

• Vect: vector spaces and linear maps
• FHilb: finite-dimensional Hilbert spaces
• CPM: completely positive maps

The grammar is encoded as a compact closed category, enabling:

• Tensor products for parallel composition
• Braiding for sequential composition
• Duals for argument structure