Controlling qubit arrays with anisotropic XXZ Heisenberg interaction by acting on a single qubit |
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Authors: | R Heule C Bruder D Burgarth V M Stojanović |
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Institution: | 1.Department of Physics, University of Basel,Basel,Switzerland;2.Institute for Mathematical Sciences,Imperial College London,UK;3.QOLS, The Blackett Laboratory,Prince Consort Road,UK |
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Abstract: | 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. |
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Keywords: | |
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