Quantum Boolean Circuit Construction Methodology Using XOR-AND Reduction Technique
Omar Dajani, Prof. Harpreet Singh
Department of Electrical & Computer Engineering, Wayne State University
ABSTRACT
Quantum-dot cellular automata (QCA) has become one of most
rapidly expanding nanotechnology research field and has
received a lot of attention within engineering community due to its
extremely small feature size and ultralow power consumption
compared to COMS technology.
The process of QCA Boolean Logic construction is more
sophisticated than Boolean logic. The traditional Boolean logic
reduction methods produce simplified Boolean expressions.
However, converting these forms to QCA Boolean is not a simple
process due to the complexity of multilevel majority gates. Novel
methodology for generating QCA Boolean circuits from multioutput Boolean circuits is presented in this poster.
(QCA) Structure
• QCA Majority Gate: produces an output of one if the
majority of inputs are one.
Systematic QCA Logic Method
• Replace each node with equivalent majority XOR and
AND gates
• Generates simplified XOR-AND equivalent circuit.
Quantum-Dot Cellular Automata
(QCA) Structure
QCA Design Implementation
• QCA Inverter: generates an opposite logic of QCA
input Cell.
• Construct majority gate tree.
• A basic QCA cell consists of four quantum dots in a
square array coupled by tunnel barriers.
• XILINX and Cadence tools (Virtuoso, Encounter).
• QCADesigner tool set
• There are two energetically equivalent ground state
polarizations, which can be labeled logic "0" and" 1."
• QCA Clocking:
• Four phase clock scheme.
• Every clock is 90ο out of phase from its pervious
clock.
• Each clock has four states: switch, hold, release,
and relax.
• QCA Wire: is a line of cells. All cells have the same
polarization.
n1  M ( M ( M ( a ,0,1), M (b, c,0),0),
M ( M ( a,1,0), M (b, c,1),0),1)
n2  M ( M ( M (b, d ,1), M ( M (a, c,0), d ,0),0),
M ( M (b, d ,0), M ( M (a, c,1), d ,1)1),1)
CONCLUSIONS
• QCA Cells: small size and low power consumption compare to
COMS technology
• Systematic QCA logic construction is presented . Our method
takes Boolean function as its input, generates simplified XORAND equivalent circuit and output an equivalent QCA CKT.