111 research outputs found
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
S-Restricted Compositions Revisited
An S-restricted composition of a positive integer n is an ordered partition
of n where each summand is drawn from a given subset S of positive integers.
There are various problems regarding such compositions which have received
attention in recent years. This paper is an attempt at finding a closed- form
formula for the number of S-restricted compositions of n. To do so, we reduce
the problem to finding solutions to corresponding so-called interpreters which
are linear homogeneous recurrence relations with constant coefficients. Then,
we reduce interpreters to Diophantine equations. Such equations are not in
general solvable. Thus, we restrict our attention to those S-restricted
composition problems whose interpreters have a small number of coefficients,
thereby leading to solvable Diophantine equations. The formalism developed is
then used to study the integer sequences related to some well-known cases of
the S-restricted composition problem
Algebraic Characterization of CNOT-Based Quantum Circuits with its Applications on Logic Synthesis
The exponential speed up of quantum algorithms and the fundamental limits of
current CMOS process for future design technology have directed attentions
toward quantum circuits. In this paper, the matrix specification of a broad
category of quantum circuits, i.e. CNOT-based circuits, are investigated. We
prove that the matrix elements of CNOT-based circuits can only be zeros or
ones. In addition, the columns or rows of such a matrix have exactly one
element with the value of 1. Furthermore, we show that these specifications can
be used to synthesize CNOT-based quantum circuits. In other words, a new scheme
is introduced to convert the matrix representation into its SOP equivalent
using a novel quantum-based Karnaugh map extension. We then apply a
search-based method to transform the obtained SOP into a CNOT-based circuit.
Experimental results prove the correctness of the proposed concept.Comment: 8 pages, 13 figures, 10Th EUROMICRO Conference on Digital System
Design, Architectures, Methods and Tools, Germany, 200
- …