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

TL;DR

This paper explores how to control qubit arrays with anisotropic XXZ Heisenberg interactions by manipulating a single qubit, optimizing quantum gate fidelities, and analyzing robustness for potential superconducting qubit implementations.

Contribution

It applies a Lie-algebraic approach to determine optimal control pulses for quantum gates in anisotropic spin chains with single-qubit control.

Findings

Optimal gate times depend on anisotropy parameter $$.

Shortest gate times occur at specific $$ values greater than one.

Control robustness is analyzed against experimental imperfections.

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