Arithmetic Using Simulated Qubits - Brain Theory from a Circuits and Systems Perspective - page 118

Fig. 7.10 Symbol for
reversible N-bit adder

The above approach is easily extended to more bits by using more lines.
A symbol for N-bit addition (the addition of two binary numbers with N bits
each) appears in Fig. 7.10 . Input and output lines are reorganized for convenience.
The signals to port A go through unchanged to ensure logical reversibility; the
signals to ports A and B are added; the sum appears at port S. The lines into and out
of the port labeled Scratch are scratchpad lines that provide work space for
the various operations. The carry out (C N1 ) is also the most significant bit in the
case of unsigned addition. The above adder works from left to right, as indicated by
the bar on the right. Usage from right to left reverses the operations.

N Weights, Z Images

In what follows there will be N numbers or weights for each of Z images, labeled
from a to z. The weights are identified as a N1 ... a 1 a 0 , b N1 ... b 1 b 0 , and so on as

appropriate to z N1 ... z 1 z 0 .

Computing Priority

Initially the A-inputs of an adder are connected to scratchpad toggles which are
initially zero as in Fig. 7.11 . The weighting factors are copied one at a time to the
A-inputs of the adder. The first to be copied are a N1 ... a 1 a 0 . Copying involves

toggling respective scratchpad qubits to 1 on the left if the applied a i is one,
0

i N 1.