# Analytical modeling of parametrically-modulated transmon qubits

## TL;DR

This paper develops an analytical perturbation theory approach to accurately model parametrically-modulated transmon qubits, aiding the understanding and verification of complex quantum dynamics in superconducting quantum processors.

## Contribution

It introduces a systematic perturbation method to derive precise analytic expressions for transmon parameters, specifically applied to parametrically-modulated transmons for entangling gate analysis.

## Key findings

- Derived accurate analytic expressions for transmon parameters.
- Applied the model to study parametrically-activated entangling gates.
- Enhanced understanding of quantum dynamics in superconducting qubit networks.

## Abstract

Building a scalable quantum computer requires developing appropriate models to understand and verify its complex quantum dynamics. We focus on superconducting quantum processors based on transmons for which full numerical simulations are already challenging at the level of qubytes. It is thus highly desirable to develop accurate methods of modeling qubit networks that do not rely solely on numerical computations. Using systematic perturbation theory to large orders in the transmon regime, we derive precise analytic expressions of the transmon parameters. We apply our results to the case of parametrically-modulated transmons to study recently-implemented parametrically-activated entangling gates.