Protecting the $\sqrt{SWAP}$ operation from general and residual errors by continuous dynamical decoupling

TL;DR

This paper introduces a continuous dynamical decoupling method to protect a $\,\sqrt{SWAP}$ quantum operation from amplitude damping and dephasing errors, enhancing the robustness of quantum gates during decoherence.

Contribution

It proposes a novel continuous-dynamical-decoupling scheme that commutes with the Heisenberg Hamiltonian to mitigate specific quantum errors during two-qubit operations.

Findings

The scheme effectively reduces errors from amplitude damping and dephasing.

Protection performance varies with environmental spectral densities.

The method maintains entanglement and fidelity under decoherence.

Abstract

We study the occurrence of errors in a continuously decoupled two-qubit state during a $\sqrt{SWAP}$ quantum operation under decoherence. We consider a realization of this quantum gate based on the Heisenberg exchange interaction, which alone suffices for achieving universal quantum computation. Furthermore, we introduce a continuous-dynamical-decoupling scheme that commutes with the Heisenberg Hamiltonian to protect it from the amplitude damping and dephasing errors caused by the system-environment interaction. We consider two error-protection settings. One protects the qubits from both amplitude damping and dephasing errors. The other features the amplitude damping as a residual error and protects the qubits from dephasing errors only. In both settings, we investigate the interaction of qubits with common and independent environments separately. We study how errors affect the entanglement and fidelity for different environmental spectral densities.