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The celebrated work of Berezinskii, Kosterlitz and Thouless in the 1970srevealed exotic phases of matter governed by topological properties oflow-dimensional materials such as thin films of superfluids andsuperconductors. Key to this phenomenon is the appearance and interaction ofvortices and antivortices in an angular degree of freedom---typified by theclassical XY model---due to thermal fluctuations. In the 2D Ising model thisangular degree of freedom is absent in the classical case, but with theaddition of a transverse field it can emerge from the interplay betweenfrustration and quantum fluctuations. Consequently a Kosterlitz-Thouless (KT)phase transition has been predicted in the quantum system by theory andsimulation. Here we demonstrate a large-scale quantum simulation of thisphenomenon in a network of 1,800 in situ programmable superconducting fluxqubits arranged in a fully-frustrated square-octagonal lattice. Essential tothe critical behavior, we observe the emergence of a complex order parameterwith continuous rotational symmetry, and the onset of quasi-long-range order asthe system approaches a critical temperature. We use a simple but previouslyundemonstrated approach to statistical estimation with an annealing-basedquantum processor, performing Monte Carlo sampling in a chain of reversequantum annealing protocols. Observations are consistent with classicalsimulations across a range of Hamiltonian parameters. We anticipate that ourapproach of using a quantum processor as a programmable magnetic lattice willfind widespread use in the simulation and development of exotic materials.

Observation of topological phenomena in a programmable lattice of 1,800 qubits