Expressive Power of Decision Diagrams and Quantum Computation Models

Robert Wille, Stefan Hillmich, Lukas Burgholzer

Renaud Vilmart

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.

María Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini +1 more

Matthias Homeister, Stephan Waack

Quantum branching programs (quantum binary decision diagrams, respectively) are a convenient tool for examining quantum computations using only a logarithmic amount of space. Recently several types of restricted quantum branching programs have been considered, e. g. read--once quantum branching programs. This paper considers quantum ordered binary decision diagrams (QOBDDs) and answers the question: How does the computational power of QOBDDs increase, if we allow repeated tests. Additionally it is described how to synthesize QOBDDs according to Boolean operations.

Philipp Niemann, Robert Wille

Alwin Zulehner, Stefan Hillmich, Robert Wille

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.