Transitionless Quantum Driving in Spin Echo

Spin echo can be used to refocus random dynamical phases caused by inhomogeneities in control fields and thereby retain the purity of a spatial distribution of quantum spins. This technique for accurate spin control is an essential ingredient in many applications, such as nuclear magnetic resonance, magnetic resonance imaging, and quantum information processing. Here, we show how all the elements of a spin echo sequence can be performed at high speed by means of transitionless quantum driving. This technique promises accurate control of rapid quantum spin evolution. We apply the scheme to universal nonadiabatic geometric single-and two-qubit gates in a nuclear magnetic resonance setting.

Automated summary

Spin echo technique can be used to refocus random dynamical phases and retain the purity of quantum spins. High-speed execution of all elements of a spin echo sequence can be achieved using transitionless quantum driving. This technique has applications in nuclear magnetic resonance and quantum information processing.