491 research outputs found
Techniques for the Synthesis of Reversible Toffoli Networks
This paper presents novel techniques for the synthesis of reversible networks
of Toffoli gates, as well as improvements to previous methods. Gate count and
technology oriented cost metrics are used. Our synthesis techniques are
independent of the cost metrics. Two new iterative synthesis procedure
employing Reed-Muller spectra are introduced and shown to complement earlier
synthesis approaches. The template simplification suggested in earlier work is
enhanced through introduction of a faster and more efficient template
application algorithm, updated (shorter) classification of the templates, and
presentation of the new templates of sizes 7 and 9. A novel ``resynthesis''
approach is introduced wherein a sequence of gates is chosen from a network,
and the reversible specification it realizes is resynthesized as an independent
problem in hopes of reducing the network cost. Empirical results are presented
to show that the methods are effective both in terms of the realization of all
3x3 reversible functions and larger reversible benchmark specifications.Comment: 20 pages, 5 figure
Synthesis and Optimization of Reversible Circuits - A Survey
Reversible logic circuits have been historically motivated by theoretical
research in low-power electronics as well as practical improvement of
bit-manipulation transforms in cryptography and computer graphics. Recently,
reversible circuits have attracted interest as components of quantum
algorithms, as well as in photonic and nano-computing technologies where some
switching devices offer no signal gain. Research in generating reversible logic
distinguishes between circuit synthesis, post-synthesis optimization, and
technology mapping. In this survey, we review algorithmic paradigms ---
search-based, cycle-based, transformation-based, and BDD-based --- as well as
specific algorithms for reversible synthesis, both exact and heuristic. We
conclude the survey by outlining key open challenges in synthesis of reversible
and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table
Design Automation and Design Space Exploration for Quantum Computers
A major hurdle to the deployment of quantum linear systems algorithms and
recent quantum simulation algorithms lies in the difficulty to find inexpensive
reversible circuits for arithmetic using existing hand coded methods. Motivated
by recent advances in reversible logic synthesis, we synthesize arithmetic
circuits using classical design automation flows and tools. The combination of
classical and reversible logic synthesis enables the automatic design of large
components in reversible logic starting from well-known hardware description
languages such as Verilog. As a prototype example for our approach we
automatically generate high quality networks for the reciprocal , which is
necessary for quantum linear systems algorithms.Comment: 6 pages, 1 figure, in 2017 Design, Automation & Test in Europe
Conference & Exhibition, DATE 2017, Lausanne, Switzerland, March 27-31, 201
Application of Permutation Group Theory in Reversible Logic Synthesis
The paper discusses various applications of permutation group theory in the
synthesis of reversible logic circuits consisting of Toffoli gates with
negative control lines. An asymptotically optimal synthesis algorithm for
circuits consisting of gates from the NCT library is described. An algorithm
for gate complexity reduction, based on equivalent replacements of gates
compositions, is introduced. A new approach for combining a group-theory-based
synthesis algorithm with a Reed-Muller-spectra-based synthesis algorithm is
described. Experimental results are presented to show that the proposed
synthesis techniques allow a reduction in input lines count, gate complexity or
quantum cost of reversible circuits for various benchmark functions.Comment: In English, 15 pages, 2 figures, 7 tables. Proceeding of the RC 2016
conferenc
Templates for positive and negative control Toffoli networks
Circuit realizations obtained from existing logic synthesis approaches may not be optimal and thus one commonly applies post-synthesis optimization techniques to get better realization of the circuits. This thesis proposes two new templates (templates 4 and 7) for positive and negative control Toffoli gates as well as proposing algorithms for post synthesis optimization of reversible positive and negative control Toffoli networks by utilizing the set of templates. When applying the templates to circuits generated by the improved shared cube synthesis approach [23] a reduction in quantum cost was achieved for 86 of the 110 circuits. On average a 21.34% reduction in quantum cost was achieved, and in some cases up to 53.58% reduction was obtained.Natural Sciences and Engineering Research Council of Canada (NSERC
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