Fig. 6: Circuit implementing the Aubry-André model in multiple dimensions.
Shown is the 3D version but the circuit can be generalized to arbitrary higher dimensions by continuing the structure. In d dimensions we need d auxiliary transmons (with a Josephson junction of energy EJT,j) each capacitively connected (via capacitance Cjμ, μ ∈ {x, y, …}) to d islands (marked blue) with the corresponding charges (\({\widehat{N}}_{x}\), \({\widehat{N}}_{y}\), …) and the phases (\({\widehat{\varphi }}_{x}\), \({\widehat{\varphi }}_{y}\), …) forming a d-dimensional charge and phase vector, \(\boldsymbol{\widehat{{{{\rm{N}}}}}}\) and \(\pmb{\widehat{\varphi }}\), respectively. Each island is subject to an offset charge Ng,μ = Cg,μVg,μ/2e and connected to ground via a Josephson junction of energy EJ,μ, both of which also form a vector \({\boldsymbol{{{{\rm{N}}}}}}_{{{{\rm{g}}}}}\) and \({\boldsymbol{{{{\rm{E}}}}}}_{{{{\rm{J}}}}}\).
