Observation of topological phenomena induced by frustration and quantum fluctuations in a programmable lattice of 1,800 qubits

The celebrated work of Berezinskii, Kosterlitz and Thouless in the 1970s [1] revealed exotic phases of matter governed by topological properties of low-dimensional materials such as thin films of superfluids and superconductors. Key to this phenomenon is the appearance and interaction of vortices and antivortices in an angular degree of freedom---typified by the classical XY model---due to thermal fluctuations. In the 2D Ising model this angular degree of freedom is absent in the classical case, but with the addition of a transverse field it can emerge from the interplay between frustration and quantum fluctuations. Consequently a Kosterlitz-Thouless (KT) phase transition has been predicted in the quantum system by theory and simulation [2]. Here we demonstrate a large-scale quantum simulation of this phenomenon in a network of 1,800 in situ programmable superconducting flux qubits arranged in a fully-frustrated square-octagonal lattice [3]. Essential to the critical behavior, we observe the emergence of a complex order parameter with continuous rotational symmetry, and the onset of quasi-long-range order as the system approaches a critical temperature. We use a simple but previously undemonstrated approach to statistical estimation with an annealing-based quantum processor, performing Monte Carlo sampling in a chain of reverse quantum annealing protocols. Observations are consistent with classical simulations across a range of Hamiltonian parameters. We anticipate that our approach of using a quantum processor as a programmable magnetic lattice will find widespread use in the simulation and development of exotic materials.

[1] J. Phys. C 6, 1181–1203 (1973).
[2] Phys. Rev. B 68, 104409 (2003).
[3] Nature 560, p 456–460 (2018)