1,885 research outputs found
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
A Study of Optimal 4-bit Reversible Toffoli Circuits and Their Synthesis
Optimal synthesis of reversible functions is a non-trivial problem. One of
the major limiting factors in computing such circuits is the sheer number of
reversible functions. Even restricting synthesis to 4-bit reversible functions
results in a huge search space (16! {\approx} 2^{44} functions). The output of
such a search alone, counting only the space required to list Toffoli gates for
every function, would require over 100 terabytes of storage. In this paper, we
present two algorithms: one, that synthesizes an optimal circuit for any 4-bit
reversible specification, and another that synthesizes all optimal
implementations. We employ several techniques to make the problem tractable. We
report results from several experiments, including synthesis of all optimal
4-bit permutations, synthesis of random 4-bit permutations, optimal synthesis
of all 4-bit linear reversible circuits, synthesis of existing benchmark
functions; we compose a list of the hardest permutations to synthesize, and
show distribution of optimal circuits. We further illustrate that our proposed
approach may be extended to accommodate physical constraints via reporting
LNN-optimal reversible circuits. Our results have important implications in the
design and optimization of reversible and quantum circuits, testing circuit
synthesis heuristics, and performing experiments in the area of quantum
information processing.Comment: arXiv admin note: substantial text overlap with arXiv:1003.191
Depth-Optimized Reversible Circuit Synthesis
In this paper, simultaneous reduction of circuit depth and synthesis cost of
reversible circuits in quantum technologies with limited interaction is
addressed. We developed a cycle-based synthesis algorithm which uses negative
controls and limited distance between gate lines. To improve circuit depth, a
new parallel structure is introduced in which before synthesis a set of
disjoint cycles are extracted from the input specification and distributed into
some subsets. The cycles of each subset are synthesized independently on
different sets of ancillae. Accordingly, each disjoint set can be synthesized
by different synthesis methods. Our analysis shows that the best worst-case
synthesis cost of reversible circuits in the linear nearest neighbor
architecture is improved by the proposed approach. Our experimental results
reveal the effectiveness of the proposed approach to reduce cost and circuit
depth for several benchmarks.Comment: 13 pages, 6 figures, 5 tables; Quantum Information Processing (QINP)
journal, 201
A Library-Based Synthesis Methodology for Reversible Logic
In this paper, a library-based synthesis methodology for reversible circuits
is proposed where a reversible specification is considered as a permutation
comprising a set of cycles. To this end, a pre-synthesis optimization step is
introduced to construct a reversible specification from an irreversible
function. In addition, a cycle-based representation model is presented to be
used as an intermediate format in the proposed synthesis methodology. The
selected intermediate format serves as a focal point for all potential
representation models. In order to synthesize a given function, a library
containing seven building blocks is used where each building block is a cycle
of length less than 6. To synthesize large cycles, we also propose a
decomposition algorithm which produces all possible minimal and inequivalent
factorizations for a given cycle of length greater than 5. All decompositions
contain the maximum number of disjoint cycles. The generated decompositions are
used in conjunction with a novel cycle assignment algorithm which is proposed
based on the graph matching problem to select the best possible cycle pairs.
Then, each pair is synthesized by using the available components of the
library. The decomposition algorithm together with the cycle assignment method
are considered as a binding method which selects a building block from the
library for each cycle. Finally, a post-synthesis optimization step is
introduced to optimize the synthesis results in terms of different costs.Comment: 24 pages, 8 figures, Microelectronics Journal, Elsevie
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
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