Modeling superconducting-qubit processors and simulators beyond 100 qubits

As superconducting quantum processors scale beyond 100 qubits, new theoretical tools are required to model their complex, many-body dynamics. In this talk, we introduce a scalable, non-perturbative renormalization method using continuous unitary transformations to systematically derive effective Hamiltonians. This method efficiently eliminates weakly coupled degrees of freedom, capturing the essential physics of large systems while maintaining polynomial memory scaling with system size, a key advantage shared with methods like tensor networks. We apply this method to a two-dimensional array of transmons with tunable couplers. In particular, we analyze the emergence of long-range couplings, quantifying how ZZ and effective qubit-qubit interactions scale across the array. This work provides an efficient and scalable tool for modeling these critical interactions in many-mode quantum systems, directly aiding the design of future superconducting processors and simulators.