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

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Author Heule R, Bruder C, Burgarth D, Stojanovic VM,
Project Quantum coherence, quantum statistics, and superconductivity in mesoscopic systems
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Original article (peer-reviewed)

Journal EUROPEAN PHYSICAL JOURNAL D
Volume (Issue) 63(1)
Page(s) 41 - 46
Title of proceedings EUROPEAN PHYSICAL JOURNAL D

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 Delta of the model, showing that the shortest among these gate times are achieved for particular values of Delta 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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