Foundation for Quantum Computing II

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In this continuation of an earlier paper we develop further the theme of quantum logical specification and derive from it some apparently physically viable instantiations of potential quantum computing devices. Specifically, in the case of a one-parameter set of terms (or labels)—read as instants of time—we find, emerging quite naturally from the algebraic setup, the paradigm for a single qubit epitomized by the case of a two-state fermion interacting with an external single mode boson. This covers the cases: cavity QED, trapped ions, and, when the qubits are multiplexed appropriately, NMR based systems. (This case degenerates to one in which only bosons are relevant as in the case of pure bosonic harmonic oscillator models in the “dual rail” representation. Such models fly in the face of the logic itself, thus clearly revealing even at this level their well-known shortcomings as practical quantum computing devices. Here as elsewhere logical constraints apparently dominate physical ones.) In a final section we indicate briefly how this process exactly generalizes, in the case of a manifold of terms more general than the one-parameter case, to yield the notion of holonomic quantum computation. In the course of this investigation we find an interpretation of path integrals as limits of sequences of logical CUTS, thus establishing a link—though still tenuous—between ensembles of acts of quantum computation and Lagrangians.