Quantum Multiple-Valued Decision Diagrams in Graphical Calculi

TL;DR

This paper establishes a formal connection between quantum multiple-valued decision diagrams (QMDDs) and the ZH-calculus, enabling translation and reduction techniques to be shared across these graphical formalisms for quantum processes.

Contribution

It introduces methods to convert between QMDDs and ZH-diagrams, facilitating cross-utilization of tools for quantum process analysis and synthesis.

Findings

QMDDs can be systematically translated into ZH-diagrams.

Reducing QMDDs corresponds to simplifications in ZH-calculus.

The approach enables tool interoperability in quantum computing analysis.

Abstract

Graphical calculi such as the ZH-calculus are powerful tools in the study and analysis of quantum processes, with links to other models of quantum computation such as quantum circuits, measurement-based computing, etc. A somewhat compact but systematic way to describe a quantum process is through the use of quantum multiple-valued decision diagrams (QMDDs), which have already been used for the synthesis of quantum circuits as well as for verification. We show in this paper how to turn a QMDD into an equivalent ZH-diagram, and vice-versa, and show how reducing a QMDD translates in the ZH-Calculus, hence allowing tools from one formalism to be used into the other.