Numerical analysis of effective models for flux-tunable transmon systems

TL;DR

This paper compares effective models and original lumped-element models of flux-tunable transmons through numerical simulations, revealing how approximations impact gate operations under control pulses.

Contribution

It introduces a non-adiabatic effective Hamiltonian for flux-tunable transmons and assesses the deviations caused by common approximations in modeling gate transitions.

Findings

Effective models predict similar outcomes to circuit models for certain control pulses.

Common approximations can significantly alter the predicted system response.

The study provides insights into the accuracy of simplified models for quantum gate simulations.

Abstract

Simulations and analytical calculations that aim to describe flux-tunable transmons are usually based on effective models of the corresponding lumped-element model. However, when a control pulse is applied, in most cases it is not known how much the predictions made with the effective models deviate from the predictions made with the original lumped-element model. In this work we compare the numerical solutions of the time-dependent Schr\"odinger equation for both the effective and the lumped-element models, for microwave and unimodal control pulses (external fluxes). These control pulses are used to model single-qubit (X) and two-qubit gate (Iswap and Cz) transitions. First, we derive a non-adiabatic effective Hamiltonian for a single flux-tunable transmon and compare the pulse response of this model to the one of the corresponding circuit Hamiltonian. Here we find that both models predict similar outcomes for similar control pulses. Then, we study how different approximations affect single-qubit (X) and two-qubit gate (Iswap and Cz) transitions in two different two-qubit systems. For this purpose we consider three different systems in total: a single flux-tunable transmon and two two-qubit systems. In summary, we find that a series of commonly applied approximations (individually and/or in combination) can change the response of a system substantially, when a control pulse is applied.