Stripping Quantum Decision Diagrams of their Identity

TL;DR

This paper improves quantum decision diagrams by removing identity structures, leading to more compact representations and up to 70x faster computations, advancing quantum circuit simulation efficiency.

Contribution

It introduces a novel method to strip identity matrices from quantum decision diagrams, significantly reducing complexity and enhancing computational speed.

Findings

Up to 70x speedup in quantum circuit simulation.

Reduced number of nodes in decision diagrams.

More natural and efficient representation for quantum computing.

Abstract

Classical representations of quantum states and operations as vectors and matrices are plagued by an exponential growth in memory and runtime requirements for increasing system sizes. Based on their use in classical computing, an alternative data structure known as Decision Diagrams (DDs) has been proposed, which, in many cases, provides both a more compact representation and more efficient computation. In the classical realm, decades of research have been conducted on DDs and numerous variations tailored for specific applications exist. However, DDs for quantum computing are just in their infancy and there is still room for tailoring them to this new technology. In particular, existing representations of DDs require extending all operations in a quantum circuit to the full system size through extension by nodes representing identity matrices. In this work, we make an important step forward for quantum DDs by stripping these identity structures from quantum operations. This significantly reduces the number of nodes required to represent them as well as eases the pressure on key building blocks of their implementation. As a result, we obtain a structure that is more natural for quantum computing and significantly speeds up with computations-with a runtime improvement of up to 70x compared to the state-of-the-art.