  We present a method for classically simulating quantum circuits based on the
tensor contraction model of Markov and Shi (quant-ph/0511069). Using this
method we are able to classically simulate the approximate quantum Fourier
transform in polynomial time. Moreover, our approach allows us to formulate a
condition for the composability of simulable quantum circuits. We use this
condition to show that any circuit composed of a constant number of approximate
quantum Fourier transform circuits and log-depth circuits with limited
interaction range can also be efficiently simulated.
