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

Abstract

The work of Berezinskii, Kosterlitz and Thouless in the 1970s revealed exotic phases of matter governed by the topological properties of low-dimensional materials such as thin films of superfluids and superconductors. A hallmark of this phenomenon is the appearance and interaction of vortices and antivortices in an angular degree of freedom-typified by the classical XY model-owing to thermal fluctuations. In the two-dimensional 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 phase transition has been predicted in the quantum system-the two-dimensional transverse-field Ising model-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 niobium flux qubits whose pairwise couplings are arranged in a fully frustrated square-octagonal lattice. Essential to the critical behaviour, 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 describe and use a simple approach to statistical estimation with an annealing-based quantum processor that performs 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.

Theory of open quantum dynamics with hybrid noise

“…With the proper rotation of the basis, we have solved the master equations and theoretically confirmed the main experimental findings of [33]. The results of the paper may be useful for understanding a dissipative evolution of various systems, from chromophores in quantum biology [30][31][32] to qubits in real-world quantum processors [14,15,44].…”

“…We are interested in dissipative evolution of a quantum annealer [8,14,15,33,37] treated as a system of N qubits coupled to a heat bath. The qubits are described by the Hamiltonian:…”

“…At the end of the evolution, the system will occupy a low-energy state of the final Hamiltonian, which may represent a solution to an optimization or a sampling problem. Another important direction of research is related to the simulation of large quantum systems with various quantum hardware [10] including quantum dots [11], ion traps [12,13], and lattices of coupled superconducting qubits [14,15].…”

VanQver: the variational and adiabatically navigated quantum eigensolver

“…Reverse annealing is a method for annealing backwards from a particular state by increasing quantum fluctuations and then reducing them in order to reach a new state. It has been implemented on D-Wave system's quantum annealer [43,44]. In [34], a uniform transverse field is considered as an additional Hamiltonian with a 'sombrero-like' time-dependent amplitude (similar to H nav in VanQver, but with different functionality), while the initial Hamiltonian is diagonal in the computational basis and updated iteratively with heuristic guesses.…”

Quantum machine learning with D‐wave quantum computer

“…The developments of QML by the D‐Wave system are still at the beginning stage to be used for problems spanning chemistry, materials, and biology . The limit‐connection quantum hardware can hardly solve large‐scale problems although it can achieve the comparable performance to classical ML in small cases.…”