  We consider quantum computing in the k-qubit model where the starting state
of a quantum computer consists of k qubits in a pure state and n-k qubits in a
maximally mixed state. We ask the following question: is there a general method
for simulating an arbitrary m-qubit pure state quantum computation by a quantum
computation in the k-qubit model? We show that, under certain constraints, this
is impossible, unless m=O(k+ log n).
