The Basis of Design Tools for Quantum Computing: Arrays, Decision Diagrams, Tensor Networks, and ZX-Calculus

TL;DR

This paper reviews various data structures like arrays, decision diagrams, tensor networks, and ZX-calculus used in quantum computing tools, highlighting their roles in simulation, compilation, and verification of quantum circuits.

Contribution

It provides an overview of current data structures and techniques employed in quantum software tools, illustrating their applications in different quantum computing tasks.

Findings

Decision diagrams are inspired by design automation.

Tensor networks are effective for quantum simulation.

ZX-calculus aids in circuit verification.

Abstract

Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude of complex tasks from the classical simulation of quantum circuits, over their compilation to specific devices, to the verification of the circuits to be executed as well as the obtained results. All of these tasks are highly non-trivial and necessitate efficient data structures to tackle the inherent complexity. Starting from rather straight-forward arrays over decision diagrams (inspired by the design automation community) to tensor networks and the ZX-calculus, various complementary approaches have been proposed. This work provides a look "under the hood" of today's tools and showcases how these means are utilized in them, e.g., for simulation, compilation, and verification of quantum circuits.