RotorMap and Quantum Fingerprints of DNA Sequences via Rotary Position Embeddings

TL;DR

This paper introduces a novel quantum encoding for DNA sequences based on Rotary Position Embeddings, enabling faster classical DNA mapping and potential quantum advantages in DNA authentication.

Contribution

It presents a new quantum encoding method for DNA sequences, a classical GPU-accelerated algorithm called RotorMap, and experimental validation on quantum computers.

Findings

RotorMap achieves 50-700x speedup over Minimap2.

Quantum encoding correlates Levenshtein distance with quantum state fidelity.

Experiments conducted on 56- and 98-qubit quantum computers.

Abstract

For strings of letters from a small alphabet, such as DNA sequences, we present a quantum encoding that empirically provides a strong correlation between the Levenshtein edit distance and the fidelity between quantum states defined by the encodings. It is based on the principles of Rotary Position Embeddings (RoPE), employed in modern large language models. Classically, this encoding yields RotorMap - a GPU-accelerated DNA mapping algorithm that achieves speedups of 50-700x over single-thread Minimap2 in proof-of-concept tests on human and maize genomes. For use on quantum devices, we introduce the Angular encoding, which is built from RoPE and directly outputs state preparation circuits. To verify its properties and utility on NISQ devices, we report results of experiments conducted on quantum computers from Quantinuum: the 56-qubit H2-1, H2-2 and the latest 98-qubit Helios-1. As a potential application, we consider a quantum DNA authentication problem and conjecture that a quantum advantage in one-way communication complexity could be achieved over any comparable classical solution.