Observation of topological phenomena in a programmable lattice of 1,800 qubits (1803.02047v1)

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.

• The paper demonstrates a robust complex order parameter and KT phase transition in a 2D transverse field Ising model on a programmable superconducting lattice.
• It employs innovative reverse annealing and Monte Carlo techniques to align experimental observations with classical simulation results.
• The study validates quantum annealing processors for simulating complex magnetic systems, paving the way for advances in condensed matter physics.

Large-Scale Quantum Simulation of a Kosterlitz-Thouless Transition Using Superconducting Qubits

The paper presents a substantial case paper in the use of quantum annealing (QA) processors, leveraging a network of 1,800 superconducting qubits to observe topological phenomena predicted by the Kosterlitz-Thouless (KT) transition. In this work, a 2D transverse field Ising model (TFIM), notorious for its rich physical behaviors due to geometrical frustration, is the focal point. The experiments reported involve a processor from D-Wave Systems, employing an innovative approach to simulate low-energy properties of physically challenging magnetic systems.

Key Findings

The TFIM followed involves a Hamiltonian formulation that includes longitudinal fields $h_i$, coupling terms $J_{ij}$, and a transverse field $\Gamma$. The Hamiltonians are simulated on a square-octagonal lattice with full geometrical frustration, leading to a KT phase transition—a classic case of transitions that involve the binding and unbinding of vortex pairs under varying conditions of temperature and field.

1. Complex Order Parameter: The researchers identified the emergence of a robust complex order parameter in the neighborhood of critical temperature conditions, signifying a symmetry that bears characteristics similar to the 2D XY model, despite being derived from a discrete system.
2. Statistical Estimation and Monte Carlo Techniques: Utilizing a novel reverse annealing method, which inverts the standard quantum annealing pathway, substantial data representing the phase transitions were gathered. The experimental techniques allowed a strong degree of alignment with classical Quantum Monte Carlo simulations, validating the observed phenomena.
3. Observational Consistency with Theory: Despite being a theoretical anticipation primarily recorded in numerical simulations, the experimental KT transition becomes apparent here through manipulations feasible in quantum annealing physics.

Implications and Future Directions

Practically, the work suggests that QA processors can efficiently simulate systems traditionally posed as being computationally infeasible for classical analogues, particularly at larger scales. The deployment of the quantum processor as a programmable magnetic lattice indicates implications for material science, quantum information, and fundamental physics. It provides a template for following experimental pathways in the investigation of exotic materials.

Theoretically, the results support quantum annealing’s momentum as a mechanism not only for optimization problems but in estimating equilibrium statistics of complex systems. Given the specificity and scale of interaction terms, the handling of non-stoquastic couplings in future devices could push the limitations seen here, diving into realms classically problematic due to computational intractability.

Conclusion

Through rigorous control and observation of a quantum system using modern qubit technology, the authors manage to simulate, in detail, a KT transition in a programmable quantum medium. It opens up avenues both technologically, in terms of improving the annealing processors and control methodologies, and scientifically, further exploring untested territories of quantum state evolution and disorder. Circling back to the seminal goals of Richard Feynman, the paper underscores significant progress toward rendering complex quantum systems as tractable inquiries within the controlled framework offered by QA technology. This serves not merely as a discussion piece within quantum simulations but fortifies the standing of new computational paradigms in understanding and advancing condensed matter physics.