Computing with highly mixed states (extended abstract)
Andris Ambainis, Leonard J. Schulman, Umesh V. Vazirani · 2000
We consider quantum computing in the one-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). 1.