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

TL;DR

This paper reports the large-scale quantum simulation of topological phenomena, specifically the Kosterlitz-Thouless transition, using a programmable lattice of 1,800 superconducting qubits, demonstrating emergent order and critical behavior.

Contribution

It introduces a novel approach to simulate topological phase transitions with a large quantum processor using annealing-based Monte Carlo sampling.

Findings

Observation of a complex order parameter with continuous symmetry

Detection of quasi-long-range order near the critical temperature

Consistency of results with classical simulations

Abstract

The celebrated work of Berezinskii, Kosterlitz and Thouless in the 1970s 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. 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. 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.