| Summary: | We consider mediated interactions in an array of floating transmons, where
each qubit capacitor consists of two superconducting pads galvanically isolated
from ground. Each such pair contributes two quantum degrees of freedom, one of
which is used as a qubit, while the other remains fixed. However, these
extraneous modes can generate coupling between the qubit modes that extends
beyond the nearest neighbor. We present a general formalism describing the
formation of this coupling and calculate it for a one-dimensional chain of
transmons. We show that the strength of coupling and its range (that is, the
exponential falloff) can be tuned independently via circuit design to realize a
continuum from nearest-neighbor-only interactions to interactions that extend
across the length of the chain. We present designs with capacitance and
microwave simulations showing that various interaction configurations can be
achieved in realistic circuits. Such coupling could be used in analog
simulation of different quantum regimes or to increase connectivity in digital
quantum systems. Thus mechanism must also be taken into account in other types
of qubits with extraneous modes.
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