Digitized counterdiabatic quantum critical dynamics (2502.15100v1)

Abstract: We experimentally demonstrate that a digitized counterdiabatic quantum protocol reduces the number of topological defects created during a fast quench across a quantum phase transition. To show this, we perform quantum simulations of one- and two-dimensional transverse-field Ising models driven from the paramagnetic to the ferromagnetic phase. We utilize superconducting cloud-based quantum processors with up to 156 qubits. Our data reveal that the digitized counterdiabatic protocol reduces defect formation by up to 48% in the fast-quench regime -- an improvement hard to achieve through digitized quantum annealing under current noise levels. The experimental results closely match theoretical and numerical predictions at short evolution times, before deviating at longer times due to hardware noise. In one dimension, we derive an analytic solution for the defect number distribution in the fast-quench limit. For two-dimensional geometries, where analytical solutions are unknown and numerical simulations are challenging, we use advanced matrix-product-state methods. Our findings indicate a practical way to control the topological defect formation during fast quenches and highlight the utility of counterdiabatic protocols for quantum optimization and quantum simulation in material design on current quantum processors.

Digitized Counterdiabatic Quantum Critical Dynamics: An Overview

The paper entitled "Digitized Counterdiabatic Quantum Critical Dynamics" conducted by Anne-Maria Visuri et al., explores the implementation of counterdiabatic (CD) control protocols in quantum phase transitions using cloud-based superconducting quantum processors. This research investigates the role of CD driving in the dynamics near critical points, aiming to demonstrate experimentally the reduction in topological defects during fast quenches in quantum systems.

Core Findings and Numerical Results

The authors provide empirical evidence that a digitized CD protocol reduces the density of topological defects formed during rapid quenches across quantum phase transitions. This is achieved through quantum simulations in both one-dimensional (1D) and two-dimensional (2D) transverse-field Ising models (TFIM) using IBM's cloud-based superconducting circuits with up to 156 qubits. The paper reports a defect reduction of up to 48%, highlighting the potential of CD protocols beyond current noise-limited digitized quantum annealing.

In the 1D case, an analytic solution for the defect distribution is derived for the fast-quench limit. The results show a reduction of the defect number from the initial state even for very short quench times when CD is applied, marking a significant departure from Kibble-Zurek Mechanism (KZM) scaling in this regime. For 2D systems, where classical simulations face computational challenges, advanced matrix-product-state methods are leveraged to support experimental findings.

Implications in Quantum Computing

This paper emphasizes the practical implications of CD protocols in enhancing quantum system control. By reducing the density of topological defects, the authors demonstrate the utility of CD in quantum optimization tasks and simulations of material properties, which are critical for the design of stable quantum algorithms on contemporary quantum hardware.

Counterdiabatic driving is posited as a promising tool to facilitate faster quantum computations by maintaining adiabatic conditions over shorter timescales, which are otherwise limited by hardware coherence times. This capacity to fast-forward adiabatic evolution has profound implications, particularly for adiabatic quantum computing, where the typical time scales presently exceed those permissible by coherence times.

Theoretical and Practical Advances

The work by Visuri et al. contributes to bridging theoretical advancements in KZM with practical quantum computing applications. It connects previously theoretical-only insights on Kibble-Zurek dynamics and quantum speed limits, producing tangible improvement in experiments on available quantum devices.

The paper introduces several critical advancements:

• It provides a detailed account of defect reduction in quench dynamics, paving the way for further exploration into quantum critical dynamics controlled by CD protocols.
• It showcases a viable experimental setup using current quantum processors, thereby offering a blueprint for real-world quantum simulations in similar scenarios.
• It interrogates the universality aspect of QKZM in fast quenches, particularly concerning the defect plateauing phenomenon and its mitigation through CD.

Future Directions

The findings invite further investigation into higher-order CD approximations for even greater suppression of defects. Additionally, extending these experiments to diverse phase transition types, including first-order transitions relevant to certain quantum optimization problems, could provide broader insights. Moreover, it might be advantageous to explore the scalability and application of digitized CD protocols in larger, more complex systems as quantum hardware continues to evolve.

In conclusion, this paper presents a significant experimental and computational investigation into minimizing excitations near quantum critical points using CD protocols. It not only furthers the understanding of nonequilibrium dynamics in fast quantum quenches but also suggests a practical framework for exploiting these insights in quantum technology applications.