Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond

Abstract

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. Specifically, we report on extensive experimental tests of topological defect formation via the one-dimensional transverse-field Ising model on two different D-Wave quantum annealing devices. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors, with certain quantitative deviations from the theory likely caused by factors such as random control errors and transient effects. 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. We support this result by extensive numerical computations. 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 find that the degree of agreement with the experimental data from the D-Wave annealing devices is better for the KZM, a quantum theory, than for the classical spin-vector Monte Carlo model, thus favoring a quantum description of the device. Our work provides an experimental test of quantum critical dynamics in an open quantum system, and paves the way to new directions in quantum simulation experiments.

Universal statistics of vortices in a newborn holographic superconductor: beyond the Kibble-Zurek mechanism

“…The verification of this prediction has been the subject of a longtime quest [7]. The validity of the KZM is not only supported by theoretical models and numerical simulations, but has been established in a variety of experimental platforms ranging from colloids [8] to quantum simulators [9,10].…”

“…Spatial correlations between topological defects have been discussed in the framework of the Halperin-Liu-Mazenko theory [23,24]. Fluctuations of the number of topological defects have recently been explored in spin chains [10,25,26] and one-dimensional φ 4 theory [27]. These studies have unveiled signatures of universality in the full counting statistics of topological defects that lie beyond the scope of the KZM.…”

Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets

“…Meanwhile, analog quantum simulations are an attractive proving ground for near-term quantum devices: the application can be chosen to suit the strengths of the platform, allowing the demonstration of a variety of engineered many-body quantum phenomena in noisy hardware. Examples include the Kibble-Zurek mechanism 4 , 5 , dynamical phase transitions 6 , 7 , many-body localization 8 , Coulomb blockade 9 , and magnetic phase transitions in quantum systems 10 , 11 . Having established the possibility of simulating complex quantum phenomena on a manufactured quantum device, as Feynman famously proposed 12 , one comes to the next question: can the quantum device confer a computational advantage?…”

Griffiths-McCoy singularity on the diluted Chimera graph: Monte Carlo simulations and experiments on quantum hardware

“…Figure 27 shows the relations in Eqs. (24) and (25). From this figure we read that the critical point s * = 0.386 corresponds to the parameter β = 2.49 and = 1.37 in the quantum Monte Carlo method, which is not far from 1.6 with the temperature β = 2.49 (T = 1/β 0.4) according to Fig.…”

“…The accuracy of this procedure nevertheless needs careful scrutiny as discussed below and in Refs. [20][21][22][23][24]. 2 is the total number of sites to be denoted as N), s * min is the minimum value of annealing schedule, s * max is the maximum value of the annealing schedule, N is the number of transverse field values, t 1 is the anneal time in the anneal-pause-quench protocol, t 2 − t 1 is the pause time, t f − t 2 is the quench time.…”