Quantum LLMs Using Quantum Computing to Analyze and Process Semantic Information

TL;DR

The paper investigates whether quantum mechanics can provide a valid and useful framework for understanding LLM semantic spaces by extending embeddings to the complex domain and mapping them to quantum circuits. It defines a complex cosine similarity $S_C$ and demonstrates a quantum-circuit-based method to estimate it, including a density-matrix interpretation of semantic features. The authors validate the approach with a real-quantum hardware experiment on embeddings from Google's EmbeddingGemma-300m (128-dim after MRl) and illustrate the method with a dog-vs-cat example, showing close agreement with classical calculations though subject to hardware noise. The work highlights a quantum-inspired perspective on semantic representation, outlines potential quantum advantages and error-mitigation paths, and points to future hybrid quantum-classical NLP pipelines and broader quantum NLP research.

Abstract

We present a quantum computing approach to analyzing Large Language Model (LLM) embeddings, leveraging complex-valued representations and modeling semantic relationships using quantum mechanical principles. By establishing a direct mapping between LLM semantic spaces and quantum circuits, we demonstrate the feasibility of estimating semantic similarity using quantum hardware. One of the key results is the experimental calculation of cosine similarity between Google Sentence Transformer embeddings using a real quantum computer, providing a tangible demonstration of a quantum approach to semantic analysis. This work reveals a connection between LLMs and quantum mechanics, suggesting that these principles can offer new perspectives on semantic representation and processing, and paving the way for future development of quantum algorithms for natural language processing.

Figures (6)

• Figure 1: Real-valued amplitude distribution in the double-slit experiment. This serves as an analogy for the representation of semantic information in traditional, real-valued LLM embeddings.
• Figure 2: Intensity distribution on the detection screen in the double-slit experiment, showing the alternating regions of high and low intensity resulting from wave interference.
• Figure 3: A single-qubit quantum circuit demonstrating superposition. The Hadamard gate creates an equal superposition of the $\lvert0\rangle$ and $\lvert1\rangle$ states, analogous to the superposition of waves in the double-slit experiment.
• Figure 4: Quantum circuit demonstrating phase manipulation. The S-gate introduces a $\pi/2$ phase shift to the $\lvert1\rangle$ state, enabling the estimation of both cosine and sine components of complex similarity.
• Figure 5: Quantum circuit for calculating the complex cosine similarity between simplified "dog" and "cat" embeddings. Qubits 0 and 2 estimate the real components, while qubits 1 and 3, incorporating S-gates, estimate the imaginary components.