Efficient Construction of Functional Representations for Quantum Algorithms

TL;DR

This paper introduces efficient methods for constructing functional representations of quantum algorithms using Decision Diagrams, significantly reducing computation time and enabling handling of algorithms with repetitive structures.

Contribution

The paper presents novel techniques for constructing quantum functional representations efficiently, exploiting small intermediate representations and repeating structures to achieve exponential speedups.

Findings

Constructed representations several times faster than existing methods.

Exploiting repeating structures yields exponential improvements.

Able to build certain quantum algorithms within seconds.

Abstract

Due to the significant progress made in the implementation of quantum hardware, efficient methods and tools to design corresponding algorithms become increasingly important. Many of these tools rely on functional representations of certain building blocks or even entire quantum algorithms which, however, inherently exhibit an exponential complexity. Although several alternative representations have been proposed to cope with this complexity, the construction of those representations remains a bottleneck. In this work, we propose solutions for efficiently constructing representations of quantum functionality based on the idea of conducting as many operations as possible on as small as possible intermediate representations -- using Decision Diagrams as a representative functional description. Experimental evaluations show that applying these solutions allows to construct the desired representations several factors faster than with state-of-the-art methods. Moreover, if repeating structures (which frequently occur in quantum algorithms) are explicitly exploited, exponential improvements are possible -- allowing to construct the functionality of certain algorithms within seconds, whereas the state of the art fails to construct it in an entire day.