The European Physical Journal D

, Volume 63, Issue 1, pp 41–46 | Cite as

Controlling qubit arrays with anisotropic XXZ Heisenberg interaction by acting on a single qubit

  • R. Heule
  • C. Bruder
  • D. Burgarth
  • V. M. StojanovićEmail author
Topical issue: Hybrid Quantum Systems – New Perspectives on Quantum State Control Regular Article


We investigate anisotropic XXZ Heisenberg spin-1 / 2 chains with control fields acting on one of the end spins, with the aim of exploring local quantum control in arrays of interacting qubits. In this work, which uses a recent Lie-algebraic result on the local controllability of spin chains with “always-on” interactions, we determine piecewise-constant control pulses corresponding to optimal fidelities for quantum gates such as spin-flip (NOT), controlled-NOT (CNOT), and square-root-of-SWAP (). We find the minimal times for realizing different gates depending on the anisotropy parameter Δ of the model, showing that the shortest among these gate times are achieved for particular values of Δ larger than unity. To study the influence of possible imperfections in anticipated experimental realizations of qubit arrays, we analyze the robustness of the obtained results for the gate fidelities to random variations in the control-field amplitudes and finite rise time of the pulses. Finally, we discuss the implications of our study for superconducting charge-qubit arrays.


Rise Time Spin Chain Quantum Gate Control Pulse Single Qubit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • R. Heule
    • 1
  • C. Bruder
    • 1
  • D. Burgarth
    • 2
    • 3
  • V. M. Stojanović
    • 1
    Email author
  1. 1.Department of Physics, University of BaselBaselSwitzerland
  2. 2.Institute for Mathematical SciencesImperial College LondonUK
  3. 3.QOLS, The Blackett LaboratoryPrince Consort RoadUK

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