We will explore a fundamental aspect of the quantum world: How is it structured? How do quantum processes generate structure and organization? Can we define a quantitative notion of structure inherent to quantum processes? How do these answers differ from their classical counterparts? Over the last three decades the PI and his colleagues developed computational mechanics to answer these questions but for classical systems, including nonlinear dynamical systems and stochastic processes. The strategy of the proposed project, therefore, is rather straightforward to state: We propose to adapt computational mechanics to quantum processes and so develop a predictive theory of their structural complexity. Though the quantum domain will present its own unique challenges, computational mechanics' theoretical and experimental successes over the last several decades give one confidence that the goals can be achieved and that they will lead to a deeper understanding of the quantum nature of structural reality. The first step of our research program is to lay out the objects of study---these are quantum processes. We will then explore how a quantum computational mechanics can be developed to capture their intrinsic computation. We will probe the theory's physical implications---a new view of entanglement and new kinds of exclusion principle. A key part of this is to delineate the intrinsic semantics of information storage and flow in the quantum world. To test these predictions, on the one hand, we will pursue an experimental mathematical exploration of quantum dynamics and information generation, using the Google-Apple-NASA-Ames D-Wave quantum machine. On the other, we will apply quantum computational mechanics to molecular dynamics, single-molecule spectroscopy, and complex materials. We also hope to develop new quantum inference algorithms for complex systems, again on the D-wave simulator.
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