Fault-Tolerant, but Paradoxical Path-Finding in Physical and Conceptual Systems

We report our initial investigations into reliability and path-finding based models and propose future areas of interest. Inspired by broken sidewalks during on-campus construction projects, we develop two models for navigating this "unreliable network." These are based on a concept of "accumulating risk" backward from the destination, and both operate on directed acyclic graphs with a probability of failure associated with each edge. The first serves to introduce and has faults addressed by the second, more conservative model. Next, we show a paradox when these models are used to construct polynomials on conceptual networks, such as design processes and software development life cycles. When the risk of a network increases uniformly, the most reliable path changes from wider and longer to shorter and narrower. If we let professional inexperience--such as with entry level cooks and software developers--represent probability of edge failure, does this change in path imply that the novice should follow instructions with fewer "back-up" plans, yet those with alternative routes should be followed by the expert?Comment: 8 page

Quantum Associative Memory

This paper combines quantum computation with classical neural network theory to produce a quantum computational learning algorithm. Quantum computation uses microscopic quantum level effects to perform computational tasks and has produced results that in some cases are exponentially faster than their classical counterparts. The unique characteristics of quantum theory may also be used to create a quantum associative memory with a capacity exponential in the number of neurons. This paper combines two quantum computational algorithms to produce such a quantum associative memory. The result is an exponential increase in the capacity of the memory when compared to traditional associative memories such as the Hopfield network. The paper covers necessary high-level quantum mechanical and quantum computational ideas and introduces a quantum associative memory. Theoretical analysis proves the utility of the memory, and it is noted that a small version should be physically realizable in the near future

Enhanced communication with the assistance of indefinite causal order

In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter we relax the assumption that quantum channels are combined classically, showing that a quantum communication network where quantum channels are combined in a superposition of different orders can achieve tasks that are impossible in conventional quantum Shannon theory. In particular, we show that two identical copies of a completely depolarizing channel become able to transmit information when they are combined in a quantum superposition of two alternative orders. This finding runs counter to the intuition that if two communication channels are identical, using them in different orders should not make any difference. The failure of such intuition stems from the fact that a single noisy channel can be a random mixture of elementary, non-commuting processes, whose order (or lack thereof) can affect the ability to transmit information