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

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.

arXiv commentExtended version of arXiv:1005.1666. To appear in PRA

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• Quadrupole transitions and quantum gates protected by continuous dynamic decoupling
• Quantum computation in silicon-vacancy centers based on nonadiabatic geometric gates protected by dynamical decoupling
• Continuous dynamical decoupling and decoherence-free subspaces for qubits with tunable interaction
• Time-dependent Rabi frequencies to protect quantum operations on an atomic qutrit by continuous dynamical decoupling