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Computer architecture and design methodologies

Empowering the Design of Reversible and Quantum Logic with Decision Diagrams

Robert Wille, Philipp Niemann, Alwin Zulehner, Rolf Drechsler

Published Jul 9, 2022• 0 citations
Publisher
DOI
10.1007/978-981-16-7487-7_11

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Ternary Galois field sum of products (TGFSOP) expressions are found to be good choice for ternary reversible, and especially quantum, logic design. In this paper, we propose 16 ternary Galois field expansions (TGFE) and introduce three ternary Galois field decision diagrams (TGFDD) using the proposed TGFEs, which are useful for reversible and quantum logic design. We also propose a heuristic for creating TGFDDs and a method for flattening the TGFDDs for determining TGFSOP expressions. We provide experimental results to show the effectiveness of the developed methods.
Reversible logic is a circuit which has the ability to reduce the power dissipation. This type of logic circuit is used for the process of running the system both forward and backward.One of the main advantages of using any reversible logic is to get back the original data and to reduce the garbage output. Logic synthesis based on the Kronecker Functional Decision Diagram (KFDD) are generated for different reversible cascade methods both complemented and uncomplemented edge by using different reversible gates such as the CNOT (Controlled NOT), NOT, Toffoli gates, Peres gates, etc., and implemented in a quantum processor. In order to reduce the qubits which in turn reduces the quantum cost, it is implemented using reversible logic synthesis in KFDD method.The proposed method shows the implementation of these reversible circuits in an IBM quantum computer to find the probabilities, as it gives less quantum cost and also consumes less time when compared to other decision diagram. Reversible logic finds a wide range of applications in quantum computing and also in areas which deals with the low power design.This paper presents the implementation of KFDD using quantum circuits in IBM Quantum (IBM-Q) processor using different reversible logics and the output is discussed.