  This paper discusses how to implement certain classes of quantum computer
algorithms using classical discrete switching networks that are amenable to
implementation in main stream CMOS transistor IC technology. The methods differ
from other classical approaches in that asynchronous feedback is exploited in
classical transistor reversible logic circuits to implement the Hadamard
transform in one simultaneous step over all qubits as in a true quantum
computer. The Simon problem is used as an example. The method is used to
provide an order n execution speed method for the Gaussian elimination step in
the Simon problem. The approach is referred to as a Thermodynamic Turing
Machine in that it behaves like an artificial molecule where solutions to a
problem are found by evolving the classical circuits from one thermodynamic
equilibrium state to another.
