Instructions as Transformation Matrices

• $\vert\mbox{probability vector}\vert=2^{n}$ $v=\underbrace{0,0,\ldots,1,0,\ldots,0}_{2^{n}\ \mbox{elements}}$
• At any time t in one state $i \Rightarrow v_{i}^{t}=1$ and $v_{\not \,i}^{t}=0$
• Each instruction $=2^n\times2^n$ matrix

  (matrix is an enormous sparse lookup table)

• v^t+1=v^tN
• Every $N_{ij} = 0 \mbox{ or } 1$, N is stochastic