Observation of disorder-free localization using a (2+1)D lattice gauge theory on a quantum processor

Disorder-induced phenomena in quantum many-body systems pose a challenge for analytical and numerical approaches at relevant time and system scales. To reduce the cost of disorder sampling, we investigated quantum circuits initialized in states that form tunable superpositions over all disorder configurations, which in lattice gauge theories can be interpreted as superpositions over gauge sectors. On the experimentally accessible timescales, we observed localization in the absence of disorder in one and two dimensions: Perturbations failed to diffuse despite fully disorder-free evolution and initial states. However, entropy measurements revealed that superposition-prepared states fundamentally differ from those obtained by direct disorder sampling. Leveraging superposition, we propose an algorithm with a polynomial speedup in sampling disorder configurations, a long-standing challenge in many-body localization studies.