We propose a new three-level XOR-AND-XOR form for autosymmetric functions, called XORAX expression. In general, a Boolean function f over n variables is k-autosymmetric if it can be projected onto a smaller function fk, which depends on n-k variables only. We show that XORAX expressions can ease the reversible synthesis of autosymmetric functions, producing compact reversible networks, without inserting additional new input lines. Autosymmetry occurs especially for functions that exhibit a regular structure, as for instance arithmetic functions. For this reason, compact reversible networks for autosymmetric functions might be interesting for quantum computing. Experimental results validate the proposed approach.

XOR-AND-XOR Logic Forms for Autosymmetric Functions and Applications to Quantum Computing / A. Bernasconi, A. Berti, V. Ciriani, G. Del Corso, I. Fulginiti. - In: IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS. - ISSN 0278-0070. - (2022), pp. 1-12. [Epub ahead of print] [10.1109/TCAD.2022.3213214]

XOR-AND-XOR Logic Forms for Autosymmetric Functions and Applications to Quantum Computing

V. Ciriani
;
2022

Abstract

We propose a new three-level XOR-AND-XOR form for autosymmetric functions, called XORAX expression. In general, a Boolean function f over n variables is k-autosymmetric if it can be projected onto a smaller function fk, which depends on n-k variables only. We show that XORAX expressions can ease the reversible synthesis of autosymmetric functions, producing compact reversible networks, without inserting additional new input lines. Autosymmetry occurs especially for functions that exhibit a regular structure, as for instance arithmetic functions. For this reason, compact reversible networks for autosymmetric functions might be interesting for quantum computing. Experimental results validate the proposed approach.
Autosymmetric function; Complexity theory; Costs; Logic functions; Logic gates; Quantum circuit; quantum circuits; Quantum computing; reversible logic; Standards;
Settore INF/01 - Informatica
Settore MAT/08 - Analisi Numerica
10-ott-2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/946530
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