Computing with highly mixed states

@article{Ambainis2006ComputingWH,
  title={Computing with highly mixed states},
  author={Andris Ambainis and Leonard J. Schulman and Umesh V. Vazirani},
  journal={J. ACM},
  year={2006},
  volume={53},
  pages={507-531}
}
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… 

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