Accurately computing electronic properties of materials using eigenenergies

A promising approach to study quantum materials is to synthesize them on an engineered platform. However, realizing the necessary parameter regimes with sufficient accuracy has been an outstanding challenge. Here, using superconducting qubits, we provide an experimental blueprint for a programmable and accurate quantum matter simulator. We illustrate the underlying method by resolving the single-particle band-structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors and arrive at an unprecedented accuracy of 0.01 radians in energy eigenvalues. Insight into this result is provided by highlighting robust properties of a Fourier transform. Furthermore, we synthesize magnetic flux and disordered potentials, two key tenets of a condensed-matter system. When sweeping flux, we observe avoided level crossings in the spectrum, a signature of the spatial pattern of disorder. Finally, we reconstruct electronic properties of the eigenstates where we observe persistent currents and a strong suppression of conductance with added disorder. Our work outlines an accurate method for quantum simulation and paves the way to study novel quantum materials with superconducting qubits.