Optimized Dynamical Decoupling for Time Dependent Hamiltonians

TL;DR

This paper extends the validity of optimized dynamical decoupling techniques to analytically time-dependent Hamiltonians, enabling broader application in quantum control and decoherence suppression.

Contribution

It provides an analytical foundation for applying UDD to time-dependent Hamiltonians and hierarchical DD schemes with multi-axis pulses.

Findings

UDD remains effective for analytically time-dependent Hamiltonians

Extension enables application in time-dependent reference frames

Supports suppression of various decoherence mechanisms

Abstract

The validity of optimized dynamical decoupling (DD) is extended to analytically time dependent Hamiltonians. As long as an expansion in time is possible the time dependence of the initial Hamiltonian does not affect the efficiency of optimized dynamical decoupling (UDD, Uhrig DD). This extension provides the analytic basis for (i) applying UDD to effective Hamiltonians in time dependent reference frames, for instance in the interaction picture of fast modes and for (ii) its application in hierarchical DD schemes with $\pi$ pulses about two perpendicular axes in spin space. to suppress general decoherence, i.e., longitudinal relaxation and dephasing.