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The Holstein model, which describes purely local coupling of an itinerantexcitation (electron, hole, exciton) with zero-dimensional (dispersionless)phonons, represents the paradigm for short-range excitation-phononinteractions. It is demonstrated here how spectral properties of small Holsteinpolarons -- heavily phonon-dressed quasiparticles, formed in thestrong-coupling regime of the Holstein model -- can be extracted from an analogquantum simulator of this model. This simulator, which is meant to operate inthe dispersive regime of circuit quantum electrodynamics, has the form of anarray of capacitively coupled superconducting transmon qubits and microwaveresonators, the latter being subject to a weak external driving. The magnitudeof $XY$-type coupling between adjacent qubits in this system can be tunedthrough an external flux threading the SQUID loops between those qubits; thistranslates into an {\em in-situ} flux-tunable hopping amplitude of a fictitiousitinerant spinless-fermion excitation, allowing one to access all the relevantphysical regimes of the Holstein model. By employing the kernel-polynomialmethod, based on expanding dynamical response functions in Chebyshevpolynomials of the first kind and their recurrence relation, the relevantsingle-particle momentum-frequency resolved spectral function of this system iscomputed here for a broad range of parameter values. To complement theevaluation of the spectral function, it is also explained how -- by making useof the many-body version of the Ramsey interference protocol -- thisdynamical-response function can be measured in the envisioned analog simulator.

Extracting spectral properties of small Holstein polarons from a transmon-based analog quantum simulator