Digitized counterdiabatic quantum critical dynamics

npj | quantum information Article Published in partnership with The University of New South Wales https://doi.org/10.1038/s41534-026-01208-z Digitized counterdiabatic quantum critical dynamics Check for updates 1234567890():,; 1234567890():,; Anne-Maria Visuri 1 , Alejandro Gomez Cadavid 1,2, Balaganchi A. Bhargava 1, Sebastián V. Romero 1,2, András Grabarits 3, Pranav Chandarana 1,2, Enrique Solano Adolfo del Campo 3,4 & Narendra N. Hegade 1 1 , 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 cloudbased 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 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. The critical dynamics close to phase transitions has universal features that connect phenomena at vastly different energy scales: the polarization of magnetic materials, the superfluid transition of liquid helium, and the inflationary dynamics of the early universe1. Close to a continuous symmetry-breaking phase transition, the spatial correlation length and relaxation time diverge. As a result, a system driven through the phase transition at a nonzero rate fails to reach its instantaneous equilibrium with a uniform phase. Instead, domains of different broken-symmetry states are formed, leading to the excitation of topological defects such as domain walls and vortices. For slow driving protocols, the Kibble-Zurek mechanism (KZM) provides a universal framework for describing this process: the density of defects scales as a power law of the driving rate, with an exponent determined by the universality class of the phase transition2. The mechanism, originally conceived for continuous phase transitions, was recently extended to phase transitions with tunable order3–5. Its applicability to classical and quantum phase transitions has been verified in numerous theoretical and experimental studies, and recent quantum simulation experiments with Rydberg atoms6 and superconducting circuits7–12 have demonstrated the quantum Kibble-Zurek mechanism (QKZM) in new regimes. While most demonstrations have realized the one-dimensional (1D) transverse-field Ising model (TFIM), recent work has also explored two-dimensional (2D) interacting systems13,14 for which classical simulations are difficult15. Connections between the phenomenology of QKZM and quantum speed limits have deepened its theoretical foundations16,17. However, the QKZM applies only in the near-adiabatic regime, when the defect density is small. The power-law scaling with quench rate breaks down in fast quenches, where the defect density saturates into a plateau that depends on the quench depth rather than rate18–20. The QKZM and its extensions not only provide a universal description of nonequilibrium critical phenomena but are also relevant in the practical pursuit of quantum computing relying on the adiabatic theorem. For systems with a finite energy gap above the ground state, a driving rate below the gap is known to preserve adiabaticity. At a quantum phase transition, however, the gap closes in the thermodynamic limit and excitations become inevitable. Excitations along the adiabatic path are detrimental in applications such as quantum optimization21 and quantum state preparation22,23, where they reduce the fidelity of the final state24. 1 Kipu Quantum GmbH, Berlin, Germany. 2Department of Physical Chemistry, University of the Basque Country EHU, Bilbao, Spain. 3Department of Physics and Materials Science, University of Luxembourg, Luxembourg, Luxembourg. 4Donostia International Physics Center, San Sebastian, Spain. e-mail: ; ; ; npj Quantum Information | (2026)12:47 1 Article https://doi.org/10.1038/s41534-026-01208-z Fig. 1 | A schematic illustration of the initial and final states resulting from CDassisted evolution and digitized annealing without CD. a The spin system is driven across a phase transition from the paramagnetic to the ferromagnetic phase. Counterdiabatic evolution results in fewer kinks in the magnetization in the final state at time t = T. b The time-dependent factors in the Hamiltonian _ . The magnitude of the coefficient jλðtÞα _ HðλÞ ¼ HðλÞ þ λA λ 1 ðtÞj of the CD Hamiltonian is largest at the critical point where excitations have the lowest energy cost and are most likely to occur. In one dimension, the critical point g = J is crossed at t/T = 0.5. The scheduling function λ(t) = t/T is chosen as linear, and the vertical lines indicate that time is discretized into steps of size δt. c The circuit that implements the CD evolution. The colored boxes correspond to a single time step with tm = mδt, and omitting the green boxes results in the implementation of digitized annealing. The black squares denote Hadamard gates, and Rx ðθÞ ¼ expði θ2 XÞ, Rzz ðθÞ ¼ expði θ2 Z  ZÞ, Ryz ðθÞ ¼ expði θ2 Y  ZÞ, and Rzy ðθÞ ¼ expði θ2 Z  YÞ are single- and two-qubit gates with the Pauli matrices X, Y, and Z. In adiabatic quantum computing, an easy-to-prepare ground state of an initial Hamiltonian is evolved adiabatically to that of a final Hamiltonian encoding the solution25. When the Hamiltonian parameters are changed sufficiently slowly, the system remains in its instantaneous ground state. However, the time scale required for adiabaticity typically exceeds the coherence time of current and near-term quantum computers, making adiabatic quantum computing infeasible. The Kibble-Zurek scaling governing the slow crossing of a quantum critical point explicitly reflects these challenges, given that the power-law dependence of the defect density on the driving time scale, the quench time T, is governed by an exponent that generally takes fractional values smaller than 1. For instance, for a 1D Ising chain, the defect density scales as 1/T1/226–28: reducing it by a factor of 10 requires quench times 100 times longer. It is thus necessary to find driving schemes that (...truncated)