Geometric Approach to Digital Quantum Information

Geometric Approach to Digital Quantum Information We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space H N . When considered as the vertices of a geometrical figure, the resulting states form the equivalent of a Platonic solid. The discretization technique inherently describes a class of π/2 rotations that connect neighboring states in the set, i.e., that leave the geometrical figures invariant. These rotations are shown to generate the Clifford group, a general group of discrete transformations on N qubits. Discretizing H N allows us to define its digital quantum information content, and we show that this information content grows as N 2. While we believe the discrete sets are interesting because they allow extra-classical behavior—such as quantum entanglement and quantum parallelism—to be explored while circumventing the continuity of Hilbert space, we also show how they may be a useful tool for problems in traditional quantum computation. We describe in detail the discrete sets for one and two qubits. Quantum Information Processing Springer Journals

Geometric Approach to Digital Quantum Information

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Kluwer Academic Publishers-Plenum Publishers
Copyright © 2004 by Springer Science+Business Media, Inc.
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
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