Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions
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Lloyd-2016-Adiabatic and Hamilt.pdf
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1.41 MB
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Author(s)
Terhal, Barbara M
Lloyd, Seth
Date Issued
February 2016
Journal
New Journal of Physics
Publisher
IOP Publishing
Citation
Lloyd, Seth, and Barbara M Terhal. “Adiabatic and Hamiltonian Computing on a 2D Lattice with Simple Two-Qubit Interactions.” New J. Phys. 18, no. 2 (February 12, 2016): 023042. © 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaf
Version
Final published version
Abstract
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a model for universal quantum computation with time-independent two-qubit ZZ and XX+YY interactions on an (almost) planar grid. The effective Hamiltonian is arrived at by a single use of first-order perturbation theory avoiding the use of perturbation gadgets. The dynamics and spectral properties of the effective Hamiltonian can be fully determined as it corresponds to a particular realization of a mapping between a quantum circuit and a Hamiltonian called the space–time circuit-to-Hamiltonian construction. Because of the simple interactions required, and because no higher-order perturbation gadgets are employed, our construction is potentially realizable using superconducting or other solid-state qubits.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1088/1367-2630/18/2/023042
