Eur. Phys. J. D 63, 41-46 (2011)
https://doi.org/10.1140/epjd/e2010-10623-y

Regular Article

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

¹ Department of PhysicsUniversity of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
² Institute for Mathematical Sciences, Imperial College London, SW7 2PG, UK
³ QOLS, The Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2BW, UK

^a e-mail: vladimir.stojanovic@unibas.ch

Received: 27 October 2010
Published online: 14 January 2011

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.