Power of Anisotropic Exchange Interactions: Universality and Efficient Codes for Quantum Computing

Abstract

We study the quantum computational power of a generic class of anisotropic solid state Hamiltonians. A universal set of encoded logic operations are found which do away with difficult-to-implement single-qubit gates in a number of quantum computer proposals, e.g., quantum dots and donor atom spins with anisotropic exchange coupling, quantum Hall systems, and electrons floating on helium.We show how to make the corresponding Hamiltonians universal by encoding one qubit into two physical qubits, and by controlling nearest neighbor interactions.

5 pages, no figures. v4: Title and abstract changed. Added paragraph on state preparation and measurement. Parafermionic notation replaced with standard qubit notation. For treatment of qubits as parafermions see http://xxx.lanl.gov/abs/quant-ph/0109078

References in corpus (5)

• Cancellation of Spin-Orbit Effects in Quantum Gates Based on the Exchange Coupling in Quantum Dots
• Reducing Constraints on Quantum Computer Design by Encoded Selective Recoupling
• Anisotropic Spin Exchange in Pulsed Quantum Gates
• Constructing Qubits in Physical Systems
• Effect of an inhomogeneous external magnetic field on a quantum dot quantum computer

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