87 research outputs found
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
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
Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning
Most work in quantum circuit optimization has been performed in isolation
from the results of quantum fault-tolerance. Here we present a polynomial-time
algorithm for optimizing quantum circuits that takes the actual implementation
of fault-tolerant logical gates into consideration. Our algorithm
re-synthesizes quantum circuits composed of Clifford group and T gates, the
latter being typically the most costly gate in fault-tolerant models, e.g.,
those based on the Steane or surface codes, with the purpose of minimizing both
T-count and T-depth. A major feature of the algorithm is the ability to
re-synthesize circuits with additional ancillae to reduce T-depth at
effectively no cost. The tested benchmarks show up to 65.7% reduction in
T-count and up to 87.6% reduction in T-depth without ancillae, or 99.7%
reduction in T-depth using ancillae.Comment: Version 2 contains substantial improvements and extensions to the
previous version. We describe a new, more robust algorithm and achieve
significantly improved experimental result
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