Topological defects in a quantum annealer: Kibble-Zurek mechanism and beyond

The number of topological defects created in a system driven through a quantum phase transition exhibits a power-law scaling with the driving time. This universal scaling law is the key prediction of the Kibble-Zurek mechanism (KZM), and testing it using a hardware-based quantum simulator is a coveted goal of quantum information science. Here we provide such a test using quantum annealing. In addition, we probe physics beyond the KZM by identifying signatures of universality in the distribution and cumulants of the number of kinks and their decay, and again find agreement with the quantum simulator results. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system. To check whether an alternative, classical interpretation of these results is possible, we used the spin-vector Monte Carlo model, a candidate classical description of the D-Wave device. We also introduce a new benchmark, the spin-vector Langevin (SVL) model, in which Monte Carlo steps are replaced by time-continuous stochastic Langevin dynamics.

Refs.:

Yuki Bando, Yuki Susa, Hiroki Oshiyama, Naokazu Shibata, Masayuki Ohzeki, Fernando Javier Gómez-Ruiz, Daniel A. Lidar, Sei Suzuki, Adolfo del Campo, and Hidetoshi Nishimori, Phys. Rev. Research 2, 033369 – Published 8 September 2020

David Subires, Fernando J. Gómez-Ruiz, Antonia Ruiz-García, Daniel Alonso, Adolfo del Campo,  Benchmarking Quantum Annealing Dynamics: the Spin-Vector Langevin Model, arXiv:2109.09750