Quantum fluctuations drive non-monotonic correlations in a qubit lattice

We present a study based on entropy principles and experiments carried out using a programmable array of superconducting qubits to illustrate how a minimal degree of uncertainty can promote the emergence of order within a system influenced by both thermal and quantum fluctuations. A series of experiments performed on a quantum annealer employing a triangular geometric configuration allows for precise manipulation of disorder, effective temperature, and quantum fluctuations. Our results reveal the development of layered anisotropic disordered states that exhibit qualities reminiscent of the elegant concept of order by disorder. We provide substantial experimental evidence highlighting the role of quantum fluctuations in reducing the system's total energy by increasing entropy and promoting defect clustering.