Quantum contextuality
Recently, quantum contextuality has been explored as a potential tool for quantum computing. In 2013, Robert Raussendorf showed that in general, any Mermin-like, inequality-free proof for quantum contextuality (such as the Kochen-Specker theorem) can be turned into a measurement-based quantum computation. More formally, "under quite natural assumptions for multi-qubit systems, MBQCs (measurement based quantum computations) which compute a non-linear Boolean function with sufficiently high success probability are contextual." Then in 2014, Mark Howard, et. al. showed that applying contextuality to magic state distillation (MSD) provides a means for arriving at universal, fault-tolerant quantum computing. MSD is a process by which a single qubit's polarization is increased along one of several "magic" directions and its state is considered "magic" once its polarization reaches a certain level. In particular, the group proved that states are non-contextual if and only if they cannot be used as inputs for magic state distillation. This provides a selection criteria for proper input states needed in MSD, and by extension aids in the efficient creation of magic states that, when coupled with fault-tolerant operators, allows for universal quantum computing. In both cases, contextuality has a potential advantage over other quantum computational techniques since contextuality itself can be thought of as a theory of information that is built directly into quantum mechanics. Comparatively, more traditional quantum phenomena such as entanglement and interference use delicate physical states which are incredibly susceptible to noise and very difficult to manipulate experimentally.
Philosophy of artificial intelligence
After concluding that human reasoning is non-computable, Penrose went on to controversially speculate that some kind of hypothetical non-computable processes involving the collapse of quantum mechanical states give humans a special advantage over existing computers. Existing quantum computers are only capable of reducing the complexity of Turing computable tasks and are still restricted to tasks within the scope of Turing machines. . By Penrose and Lucas's arguments, existing quantum computers are not sufficient , so Penrose seeks for some other process involving new physics, for instance quantum gravity which might manifest new physics at the scale of the Planck mass via spontaneous quantum collapse of the wave function. These states, he suggested, occur both within neurons and also spanning more than one neuron. However, other scientists point out that there is no plausible organic mechanism in the brain for harnessing any sort of quantum computation, and furthermore that the timescale of quantum decoherence seems too fast to influence neuron firing.