Geometric Approach to Digital Quantum Information

  • Authors:

  • Chad Rigetti;Rémy Mosseri;Michel Devoret

  • Affiliations:

  • Department of Applied Physics, Yale University, New Haven, USA 06520-8284;Groupe de Physique des Solides, Université Paris VI, Paris, France 75015;Department of Applied Physics, Yale University, New Haven, USA 06520-8284

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2004

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Abstract

We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space HN. 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 HN allows us to define its digital quantum information content, and we show that this information content grows as N2. 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.PACS: 03.67.Lx; 03.67.pp; 03.67.-a; 03.67.Mn.