Computing with highly mixed states

Device initialization is a difficult challenge in some proposed realizations of quantum computers, and as such, must be treated as a computational resource. The degree of initialization can be quantified by k, the number of clean qubits in the initial state of the register. In this article, we show that unless m ∈O(k + log n), oblivious (gate-by-gate) simulation of an ideal m-qubit quantum circuit by an n-qubit circuit with k clean qubits is impossible. Effectively, this indicates that there is no avoiding physical initialization of a quantity of qubits proportional to that required by the best ideal quantum circuit.