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.
Quantum neural network
Rinkus proposes that distributed representation, specifically "sparse distributed representation" (SDR), provides a classical implementation of quantum computing. Specifically, the set of SDR codes stored in an SDR coding field will generally intersect with each other to varying degrees. In other work, Rinkus describes a fixed time learning (and inference) algorithm that preserves similarity in the input space into similarity (intersection size) in the SDR code space. Assuming that input similarity correlates with probability, this means that any single active SDR code is also a probability distribution over all stored inputs, with the probability of each input measured by the fraction of its SDR code that is active (i.e., the size of its intersection with the active SDR code). The learning/inference algorithm can also be viewed as a state update operator and because any single active SDR simultaneously represents both the probability of the single input, X, to which it was assigned during learning and the probabilities of all other stored inputs, the same physical process that updates the probability of X also updates all stored probabilities. By 'fixed time', it is meant that the number of computational steps comprising this process (the update algorithm) remains constant as the number of stored codes increases. This theory departs radically from the standard view of quantum computing and quantum physical theory more generally: rather than assuming that the states of the lowest level entities in the system, i.e., single binary neurons, exist in superposition, it assumes only that higher-level, i.e., composite entities, i.e., whole SDR codes (which are sets of binary neurons), exist in superposition.