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arXiv:2512.13143

Quantum critical dynamics and emergent universality in decoherent digital quantum processors

Brendan Rhyno, Swarnadeep Majumder, Smitha Vishveshwara, Khadijeh Najafi

quant-phcond-mat.stat-mechcond-mat.str-elSubmitted Dec 15, 2025• Announced Dec 16, 2025• 0 citations• Revised Mar 29, 2026 (v2)

v1 · Dec 15, 2025 v2 · Mar 29, 2026

Abstract

Understanding how noise influences nonequilibrium quantum critical dynamics is essential for both fundamental physics and the development of practical quantum technologies. While the quantum Kibble-Zurek (QKZ) mechanism predicts universal scaling during quenches across a critical point, real quantum systems exhibit complex decoherence that can substantially modify these behaviors, ranging from altering critical scaling to completely suppressing it. By considering a specific case of nondemolishing noise, we first show how decoherence can reshape universal scaling and verify these theoretical predictions using numerical simulations of spin chains across a wide range of noise strengths. Then, we study linear quenches in the transverse-field Ising model on IBM superconducting processors where the noise model is unknown. Using large system sizes of 80-120 qubits, we measure equal-time connected correlations, defect densities, and excess energies across various quench times. Surprisingly, unlike earlier observations where noise-induced defect production masked universal behavior at long times, we observe clear scaling relations, pointing towards persistent universal structure shaped by decoherence. The extracted scaling exponents differ from both ideal QKZ predictions and analytic results for simplified noise models, suggesting the emergence of a distinct noise-influenced universality regime. Our results, therefore, point toward the possibility of using universal dynamical scaling as a high-level descriptor of quantum hardware, complementary to conventional gate-level performance metrics.

Comments: 22 pages, 8 figures

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When a system is swept through a quantum critical point (QCP), the Kibble-Zurek mechanism predicts that the average number of topological defects follows a universal power-law scaling with the ramp time scale. This scaling behavior is determined by the equilibrium critical exponents of the underlying phase transition. We show that the correspondence between Kibble-Zurek scaling and quantum criticality does not hold generally. In particular, the defect density can exhibit a suppression faster than the Kibble-Zurek prediction even when the quench crosses a critical point, while conventional Kibble-Zurek scaling may persist for quenches through a non-critical point. Our results, based on models representative of a broad class of quasi-one-dimensional Fermi systems, identify the dynamical conditions under which universal defect scaling emerges and clarify the relation between defect generation and equilibrium criticality.

We analyze mechanisms for universal out-of-equilibrium dynamics near criticality by exploring the effect of randomized quantum resetting (QR) under a finite-time quench across a quantum phase transition. Using the transverse-field Ising chain as a generic model and exploiting its exact solution, QR is found to cause a crossover of the scaling of the topological defect density with the time scale

τ

of the quench, from Kibble-Zurek to anti-Kibble-Zurek scaling as

τ

increases. This reflects a competition between non-adiabatic quench-driven excitations and QR, giving rise to local minima of the defect densities at optimal annealing times. These times and the corresponding local minima are shown to scale as universal power laws with the rate of QR. Additional results for the scaling of the mean excess energy suggest that a system driven across a quantum critical point exhibits the same scaling behavior under a linear quench with QR as with uncorrelated noise.

We present a formulation for investigating quench dynamics across quantum phase transitions in the presence of decoherence. We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. We generalize the well-studied universal Kibble-Zurek behavior for linear temporal drive across the critical point. We identify a strong decoherence regime wherein the decoherence time is shorter than the standard correlation time, which varies as the inverse gap above the groundstate. In this regime, we find that the freeze-out time

\bar{t}\simτ^{{2νz}/({1+2νz})}

for when the system falls out of equilibrium and the associated freeze-out length

\barξ\simτ^{ν/({1+2νz})}

show power-law scaling with respect to the quench rate

\bar{t}\simτ^{{2νz}/({1+2νz})}

, where the exponents depend on the correlation length exponent

ν

and the dynamical exponent

z

associated with the transition. The universal exponents differ from those of standard Kibble-Zurek scaling. We explicitly demonstrate this scaling behavior in the instance of a topological transition in a Chern insulator system. We show that the freeze-out time scale can be probed from the relaxation of the Hall conductivity. Furthermore, on introducing disorder to break translational invariance, we demonstrate how quenching results in regions of imbalanced excitation density characterized by an emergent length scale which also shows universal scaling. We perform numerical simulations to confirm our analytical predictions and corroborate the scaling arguments that we postulate as universal to a host of systems.

We present a formulation for investigating quench dynamics across quantum phase transitions in the presence of decoherence. We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. We generalize the well-studied universal Kibble-Zurek behavior for linear temporal drive across the critical point. We identify a strong decoherence regime wherein the decoherence time is shorter than the standard correlation time, which varies as the inverse gap above the groundstate. In this regime, we find that the freeze-out time \bar{t}\sim\tau^{{2\nu z}/({1+2\nu z})} t - ∼ τ 2 ν z / ( 1 + 2 ν z ) for when the system falls out of equilibrium and the associated freeze-out length \bar{\xi}\sim\tau^{\nu/({1+2\nu z})} ξ ‾ ∼ τ ν / ( 1 + 2 ν z ) show power-law scaling with respect to the quench rate 1/\tau 1 / τ , where the exponents depend on the correlation length exponent \nu ν and the dynamical exponent z z associated with the transition. The universal exponents differ from those of standard Kibble-Zurek scaling. We explicitly demonstrate this scaling behavior in the instance of a topological transition in a Chern insulator system. We show that the freeze-out time scale can be probed from the relaxation of the Hall conductivity. Furthermore, on introducing disorder to break translational invariance, we demonstrate how quenching results in regions of imbalanced excitation density characterized by an emergent length scale which also shows universal scaling. We perform numerical simulations to confirm our analytical predictions and corroborate the scaling arguments that we postulate as universal to a host of systems.