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

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 ($\sqrt{\text{SWAP}}$). 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.

6 pages, 4 figures

References in corpus (9)

• Superconducting Circuits and Quantum Information
• Robust optimal quantum gates for Josephson charge qubits
• Local controllability of quantum networks
• Enhancement of entanglement transfer in a spin chain by phase shift-control
• Quantum state transfer and time-dependent disorder in Quantum Chains
• Universal quantum interfaces
• Use of dynamical coupling for improved quantum state transfer
• Global controllability with a single local actuator
• Controllability and Observability of Multi-Spin Systems: Constraints by Symmetry and by Relaxation

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