Encoded Universality for Generalized Anisotropic Exchange Hamiltonians

Details Encoded Universality for Generalized Anisotropic Exchange Hamiltonians Encoded Universality for Generalized Anisotropic Exchange Hamiltonians

2002-04-04

arxiv.org/abs/quant-ph/0204016v1

Phys. Rev. A 66, 022304 (2002)

Physics

Quantum Physics

11 pages, 4 figures

Scientific paper

10.1103/PhysRevA.66.022304

We derive an encoded universality representation for a generalized anisotropic exchange Hamiltonian that contains cross-product terms in addition to the usual two-particle exchange terms. The recently developed algebraic approach is used to show that the minimal universality-generating encodings of one logical qubit are based on three physical qubits. We show how to generate both single- and two-qubit operations on the logical qubits, using suitably timed conjugating operations derived from analysis of the commutator algebra. The timing of the operations is seen to be crucial in allowing simplification of the gate sequences for the generalized Hamiltonian to forms similar to that derived previously for the symmetric (XY) anisotropic exchange Hamiltonian. The total number of operations needed for a controlled-Z gate up to local transformations is five. A scalable architecture is proposed.

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