Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions

Seth Lloyd*, Barbara M. Terhal

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

18 Citations (Scopus)


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.

Original languageEnglish
Article number023042
Number of pages17
JournalNew Journal of Physics
Issue number2
Publication statusPublished - 2016
Externally publishedYes


  • Hamiltonian quantum computing
  • quantum computing
  • superconducting quantum computing


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