Three-Josephson Junctions Flux Qubit Couplings

TL;DR

This paper develops a numerical method to derive effective Hamiltonians for coupled flux qubits, enabling the design of various interaction types, including ultra-strong couplings, with practical relevance for experimental quantum computing.

Contribution

It introduces a numerical tool to extract effective Hamiltonians for strongly coupled flux qubits, facilitating the engineering of diverse qubit interactions.

Findings

Effective Hamiltonians for coupled flux qubits with tunable interactions

Demonstration of ultra-strong coupling regimes

Applicability of the method to experimental systems

Abstract

We analyze the coupling of two flux qubits with a general many-body projector into the low-energy subspace. Specifically, we extract the effective Hamiltonians that controls the dynamics of two qubits when they are coupled via a capacitor and/or via a Josephson junction. While the capacitor induces a static charge coupling tunable by design, the Josephson junction produces a magnetic-like interaction easily tunable by replacing the junction with a SQUID. Those two elements allow to engineer qubits Hamiltonians with $XX$, $YY$ and $ZZ$ interactions, including ultra-strongly coupled ones. We present an exhaustive numerical study for two three-Josephson junctions flux qubit that can be directly used in experimental work. The method developed here, namely the numerical tool to extract qubit effective Hamiltonians at strong coupling, can be applied to replicate our analysis for general systems of many qubits and any type of coupling.