A Quantum Dot Plot Generation Algorithm for Pairwise Sequence Alignment

TL;DR

This paper introduces the Quantum Dot Plot (QDP) as an explicit oracle construction for quantum sequence alignment algorithms, analyzing its complexity and practical limitations on current quantum architectures.

Contribution

It provides a new explicit quantum oracle construction for sequence alignment and evaluates its complexity and practicality on existing quantum hardware.

Findings

QDP's data encoding is exponentially complex, limiting its use on general-purpose quantum computers.

QDP and QPSA circuit depths are estimated for IBM and AQT architectures.

QDP offers a practical way to analyze quantum sequence alignment algorithms despite encoding challenges.

Abstract

The Quantum Pairwise Sequence Alignment (QPSA) algorithm offers exponential speedups in data alignment tasks. However, it relies on an open problem of efficiently encoding the classical data being aligned into quantum superposition. Previous works suggest the use of specialized nonlinear Kerr media to implement a black-box oracle that achieves the superposition. We provide an alternative, explicit construction of this oracle called the Quantum Dot Plot (QDP), which is compatible with universal gate machines. We evaluate QDP's operational complexity via analysis of the quantum machine instructions generated by the Q# and Qiskit software frameworks for various sample circuits. Our analysis confirms that the data encoding scheme is exponentially difficult, precluding QDP's (and thus, QPSA's) employment on general-purpose quantum computers. Nevertheless, we find utility in estimating the circuit depth and run time of both QDP and QPSA for IBM's superconducting architecture and AQT's trapped ion architecture for direct comparison and overall practicality purposes.