Power of one non-clean qubit

Understand

The one-clean qubit model (or the DQC1 model) is a restricted model of quantum computing where only a single qubit of the initial state is pure and others are maximally mixed.

• Although the model is not universal, it can efficiently solve several problems whose classical efficient solutions are not known.
• Furthermore, it was recently shown that if the one-clean qubit model is classically efficiently simulated, the polynomial hierarchy collapses to the second level.
• A disadvantage of the one-clean qubit model is, however, that the clean qubit is too clean: for example, in realistic NMR experiments, polarizations are not enough high to have the perfectly pure qubit.