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Synthesis lectures on engineering, science, and technology

Decision Diagrams for Density Matrices

Thomas Grurl, Jürgen Fuß, Robert Wille

Published Nov 29, 2024• 0 citations
Publisher
DOI
10.1007/978-3-031-71036-0_4

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The data structure referred to as quantum multiple-valued decision diagrams (QMDD) is used to efficiently represent the unitary matrices describing reversible and quantum circuits. This paper investigates the conditions that cause skipped variables to appear in the QMDD of some binary and ternary quantum circuits. We have found that a unitary matrix that produces a skipped variable in a QMDD is likely to cause a specific anomaly when it is decomposed into a cascade of two-level unitary matrices by the Beck-Zeilinger-Bernstein-Bertani algorithm.
In this paper, we present a novel structure, QuantumMultiple- valued Decision Diagrams (QMDD), specifically designed to represent and manipulate the matrices encountered in the specification of reversible and quantum gates and circuits, both binary and multiple-valued. QMDD use many common decision diagram techniques, ideas introduced in QuIDDPro and novel techniques introduced here. Building the QMDD for the matrices for individual gates and the subsequent construction of the QMDD for the matrix describing a circuit are discussed. A prototype C implementation is described and experimental results are given that show the new structure is a promising and compact representation for reversible and quantum logic circuits.