Generalized time-coarse graining as a systematic perturbation theory beyond RWA I: An introduction and computational framework

The rotating-wave approximation neglects the rapidly-oscillating (counter-rotating) terms in the Hamiltonian, assuming the effects average off over the relevant time-scales. However, these terms often yield non-negligible corrections to the dynamics, and one must go beyond that approximation. Specifically, they can become quite important in the study of parametric couplers and amplifiers, where accurate modeling of the system is critical for achieving high-fidelity operation.

Here, we implement a generalized time-coarse graining (TCG) approach developed in our group. Our method goes beyond first-order rotating-wave approximation and generalizes it to higher-order processes, at the cost of a more complicated, non-unitary evolution. The TCG calculations are very involved, with the number of terms proliferating with the order of truncation, quickly becoming unmanageable by hand. To address this problem, we developed QuantumGraining.jl – a Julia package for symbolic calculation of the TCG dynamics. The package automates the TCG process, and provides a symbolic representation of the Hamiltonian and effective dissipators up to the required order of truncation. The package integrates with other software packages to efficiently and conveniently solve the effective master equations.