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arXiv:2208.01050 · Frontiers in Quantum Science and Technology

Experimental validation of the Kibble-Zurek mechanism on a digital quantum computer

Santiago Higuera-Quintero, Ferney J. Rodríguez, Luis Quiroga, Fernando J. Gómez-Ruiz

Published Oct 25, 2022• 9 citations
arXivHTMLPDF

Abstract

The Kibble-Zurek mechanism (KZM) captures the essential physics of nonequilibrium quantum phase transitions with symmetry breaking. KZM predicts a universal scaling power law for the defect density which is fully determined by the system’s critical exponents at equilibrium and the quenching rate. We experimentally tested the KZM for the simplest quantum case, a single qubit under the Landau-Zener evolution, on an open access IBM quantum computer (IBM-Q). We find that for this simple one-qubit model, experimental data validates the central KZM assumption of the adiabatic-impulse approximation for a well isolated qubit. Furthermore, we report on extensive IBM-Q experiments on individual qubits embedded in different circuit environments and topologies, separately elucidating the role of crosstalk between qubits and the increasing decoherence effects associated with the quantum circuit depth on the KZM predictions. Our results strongly suggest that increasing circuit depth acts as a decoherence source, producing a rapid deviation of experimental data from theoretical unitary predictions.

DOI
10.3389/frqst.2022.1026025

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The Kibble-Zurek mechanism (KZM) captures the essential physics of nonequilibrium quantum phase transitions with symmetry breaking. KZM predicts a universal scaling power law for the defect density which is fully determined by the system’s critical exponents at equilibrium and the quenching rate. We experimentally tested the KZM for the simplest quantum case, a single qubit under the Landau-Zener evolution, on an open access IBM quantum computer (IBM-Q). We find that for this simple one-qubit model, experimental data validates the central KZM assumption of the adiabatic-impulse approximation for a well isolated qubit. Furthermore, we report on extensive IBM-Q experiments on individual qubits embedded in different circuit environments and topologies, separately elucidating the role of crosstalk between qubits and the increasing decoherence effects associated with the quantum circuit depth on the KZM predictions. Our results strongly suggest that increasing circuit depth acts as a decoherence source, producing a rapid deviation of experimental data from theoretical unitary predictions.
The Kibble-Zurek mechanism (KZM) predicts that when a system is driven through a continuous phase transition, the density of topological defects scales universally with the quench rate. Recent theoretical work [H.-B. Zeng \textit{et al.}, \textit{Phys. Rev. Lett.} \textbf{130}, 060402 (2023)] has challenged this picture, showing that under sufficiently fast quenches, both the defect density and freezing time become independent of the quench rate and instead scale universally with the quench range. Here, we experimentally test this prediction using a single trapped-ion qubit to simulate fast quantum quenches in the Landau-Zener and 1D Rice-Mele models. We identify a critical quench rate vc v_c vc​ that scales with the quench range δmax⁡ δ_{\max} δmax​, separating two distinct dynamical regimes. In the Rice-Mele model, for v<vc v < v_c v<vc​, the defect density follows the KZM scaling ∼v1/2 \sim v^{1/2} ∼v1/2; for v>vc v > v_c v>vc​, it exhibits a universal scaling ∼δmax⁡ \sim δ_{\max} ∼δmax​, independent of the quench rate. Our results provide direct experimental evidence of the predicted breakdown of KZM universality under fast quenches.
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena.
The Kibble-Zurek mechanism (KZM) captures the key physics of nonequilibrium dynamics in second order phase transitions, and accurately predicts the density of topological defects formed in such processes. However, the central prediction of KZM--i.e., the scaling of the density of defects with the quench rate--still needs further experimental confirmation, particularly for quantum transitions. Here, we perform a quantum simulation of the nonequilibrium dynamics of the Landau-Zener model based on a nine-stage optical interferometer with an overall visibility of 0.975±0.008. The results support the adiabatic-impulse approximation, which is the core of Kibble-Zurek theory. Moreover, the developed high-fidelity multistage optical interferometer can support more complex linear optical quantum simulations.
The crossing of a continuous phase transition gives rise to the formation of topological defects described by the Kibble-Zurek mechanism (KZM) in the limit of slow quenches. The KZM predicts a universal power-law scaling of the defect density as a function of the quench time. We focus on the deviations from KZM experimentally observed in rapid quenches and establish their universality. While KZM scaling holds below a critical quench rate, for faster quenches the defect density and the freeze-out time become independent of the quench rate and exhibit a universal power-law scaling with the final value of the control parameter. These predictions are verified in several paradigmatic scenarios in both the classical and quantum domains.
Abstract When a quantum phase transition is crossed within a finite time, critical slowing down disrupts adiabatic dynamics, resulting in the formation of topological defects. The average density of these defects scales with the quench rate, adhering to a universal power law as predicted by the Kibble–Zurek mechanism (KZM). In this study, we aim to investigate the counting statistics of kink density in the 1D transverse-field quantum Ising model. We demonstrate on multiple quantum processing units up to 100 qubits, that higher-order cumulants follow a universal power law scaling as a function of the quench time. We also show the breakdown of the KZM for short quenches for finite-size systems. Tensor network simulations corroborate our quantum simulation results for bigger systems not in the asymptotic limit.
Abstract The Kibble–Zurek mechanism (KZM) describes the dynamics across a phase transition leading to the formation of topological defects, such as vortices in superfluids and domain walls in spin systems. Here, we experimentally probe the distribution of kink pairs in a one-dimensional quantum Ising chain driven across the paramagnet-ferromagnet quantum phase transition, using a single trapped ion as a quantum simulator in momentum space. The number of kink pairs after the transition follows a Poisson binomial distribution, in which all cumulants scale with a universal power law as a function of the quench time in which the transition is crossed. We experimentally verified this scaling for the first cumulants and report deviations due to noise-induced dephasing of the trapped ion. Our results establish that the universal character of the critical dynamics can be extended beyond KZM, which accounts for the mean kink number, to characterize the full probability distribution of topological defects.