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The vacuum of the lattice Schwinger model is prepared on up to 100 qubits of IBM’s Eagle-processor quantum computers. A new algorithm to prepare the ground state of a gapped translationally-invariant system on a quantum computer is presented, which we call Scalable Circuits ADAPT-VQE (SC ADAPT-VQE). This algorithm uses the exponential decay of correlations between distant regions of the ground state, together with ADAPT-VQE, to construct quantum circuits for state preparation that can be scaled to arbitrarily large systems. SC-ADAPT-VQE is applied to the Schwinger model, and shown to be systematically improvable, with an accuracy that converges exponentially with circuit depth. Both the structure of the circuits and the deviations of prepared wavefunctions are found to become independent of the number of spatial sites, L. This allows for a controlled extrapolation of the circuits, determined using small or modest-sized systems, to arbitrarily large L. The circuits for the Schwinger model are determined on lattices up to L=14 (28 qubits) with the qiskit classical simulator, and subsequently scaled up to prepare the L=50 (100 qubits) vacuum on IBM’s 127 superconducting-qubit quantum computers ibm_brisbane and ibm_cusco . After applying an improved error-mitigation technique, which we call Operator Decoherence Renormalization, the chiral condensate and charge-charge correlators obtained from the quantum computers are found to be in good agreement with classical Matrix Product State simulations.