  We present a new implementation of quantum computation that treats quantum
computers as a special type of Bayesian Network called a QuDot Net. QuDot Nets
allow for the efficient representation of some qubit systems. Single qubit
quantum gates can be implemented as edge transformations on QuDot Nets. The X,
H, R(k), M and SWAP gates are discussed in detail and results show linear
scaling as the number of qubits are increased. We show that measurement and
semi-quantum control gates can be efficiently implemented using QuDot Nets and
present results from a QuDot Net implementation of the terminal Quantum Fourier
Transform. We show how QuDot Nets can implement coherent control gates using
multi-digraphs by labelling parallel edges. Lastly, we discuss implications to
quantum foundations if a classical implementation of quantum computation is
realized.
