Beyond hard-core bosons in transmon arrays

TL;DR

This paper develops a theoretical framework to analyze the dynamics of highly-excited states in coupled transmon arrays, revealing collective phenomena beyond the traditional two-level approximation, with implications for quantum simulation.

Contribution

It introduces a high-order degenerate perturbation theory approach to study the attractive Bose-Hubbard model in transmon arrays beyond the hard-core boson limit.

Findings

Describes boson stacking and edge localization phenomena.

Provides a unified method for effective long-range interactions.

Applicable to various geometries beyond 1D chains.

Abstract

Arrays of transmons have proven to be a viable medium for quantum information science and quantum simulations. Despite their widespread popularity as qubit arrays, there remains yet untapped potential beyond the two-level approximation or, equivalently, the hard-core boson model. With the higher excited levels included, coupled transmons naturally realize the attractive Bose-Hubbard model. The dynamics of the model has been difficult to study due to unfavorable scaling of the dimensionality of the Hilbert space with the system size. In this work, we present a framework for describing the effective unitary dynamics of highly-excited states of coupled transmons based on high-order degenerate perturbation theory. This allows us to describe various collective phenomena -- such as bosons stacked onto a single site behaving as a single particle, edge-localization, and effective longer-range interactions -- in a unified, compact and accurate manner. While our examples deal with one-dimensional chains of transmons for the sake of clarity, the theory can be readily applied to more general geometries.