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Superconducting circuits constitute a promising platform for futureimplementation of quantum processors and simulators. Arrays of capacitivelycoupled transmon qubits naturally implement the Bose-Hubbard model withattractive on-site interaction. The spectrum of such many-body systems ischaracterised by low-energy localised states defining the lattice analog ofbright solitons. Here, we demonstrate that these bright solitons can be pinnedin the system, and we find that a soliton moves while maintaining its shape.Its velocity obeys a scaling law in terms of the combined interaction andnumber of constituent bosons. In contrast, the source-to-drain transport ofphotons through the array occurs through extended states that have higherenergy compared to the bright soliton. For weak coupling between thesource/drain and the array, the populations of the source and drain oscillatein time, with the chain remaining nearly unpopulated at all times. Such aphenomenon is found to be parity dependent. Implications of our results for theactual experimental realisations are discussed.

Soliton versus single photon quantum dynamics in arrays of superconducting qubits