Local quantum control of Heisenberg spin chains

TL;DR

This paper explores the feasibility of controlling quantum states in Heisenberg spin chains using local operations, analyzing robustness to errors and effects of control smoothing.

Contribution

It introduces a method for local quantum control in Heisenberg spin chains and studies its robustness and sensitivity to control field variations.

Findings

Faster control switching improves robustness to errors.

Optimal gate fidelities are affected by spectral filtering of control fields.

System behavior resembles motional narrowing phenomena in NMR.

Abstract

Motivated by some recent results of quantum control theory, we discuss the feasibility of local operator control in arrays of interacting qubits modeled as isotropic Heisenberg spin chains. Acting on one of the end spins, we aim at finding piecewise-constant control pulses that lead to optimal fidelities for a chosen set of quantum gates. We analyze the robustness of the obtained results f or the gate fidelities to random errors in the control fields, finding that with faster switching between piecewise-constant controls the system is less susceptible to these errors. The observed behavior falls into a generic class of physical phenomena that are related to a competition between resonance- and relaxation-type behavior, exemplified by motional narrowing in NMR experiments. Finally, we discuss how the obtained optimal gate fidelities are altered when the corresponding rapidly-varying piecewise-constant control fields are smoothened through spectral filtering.