How to Efficiently Handle Complex Values? Implementing Decision Diagrams for Quantum Computing

TL;DR

This paper introduces an efficient method for implementing decision diagrams in quantum computing, addressing complex number handling and demonstrating significant runtime improvements through experimental evaluation.

Contribution

It presents a novel approach to handle complex numbers in quantum decision diagrams, enhancing their efficiency and practicality for quantum computing applications.

Findings

Order of magnitude runtime improvements

Effective handling of complex numbers in quantum decision diagrams

Publicly available quantum DD package

Abstract

Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum functionality. In the classical domain, decision diagrams have been successfully employed as a powerful alternative to straightforward means such as truth tables. This motivated extensive research on whether decision diagrams provide similar potential in the quantum domain -- resulting in new types of decision diagrams capable of substantially reducing the complexity of representing quantum states and functionality. From an implementation perspective, many concepts and techniques from the classical domain can be re-used in order to implement decision diagrams packages for the quantum realm. However, new problems -- namely how to efficiently handle complex numbers -- arise. In this work, we propose a solution to overcome these problems. Experimental evaluations confirm that this yields improvements of orders of magnitude in the runtime needed to create and to utilize these decision diagrams. The resulting implementation is publicly available as a quantum DD package at http://iic.jku.at/eda/research/quantum_dd.