Quantum phase transitions provide a controlled route for generating many-body excitations, but the dynamics after the critical point can be as important as the initial defect creation. Recent progress in quantum annealing has made it possible to access coherent nonequilibrium dynamics in programmable Ising systems with thousands of superconducting qubits. Here we use this capability to study a longitudinally biased quantum Ising chain, where Kibble--Zurek defect creation is followed by nonintegrable post-critical dynamics. The longitudinal bias confines kink--antikink excitations into mesonic bound states, so that the final spin configurations encode both the production of defects near the critical point and the subsequent evolution of the confined excitations. Using energy-scale rescaling and zero-noise extrapolation, we find that the defect density follows the expected biased Kibble--Zurek/Landau--Zener crossover and agrees with matrix-product-state simulations with uniform bias. In contrast, magnetization, spatial profiles, and minority-domain statistics reveal that mesonic evolution is interrupted by localization of the post-critical domain pattern. Matrix-product-state simulations with disorder reproduce this separation between robust defect creation and localized post-critical dynamics. Our results show that large-scale quantum annealers can probe the fate of critical excitations beyond defect counting.
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.
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.
Kibble-Zurek theory (KZ) stands out as the most robust theory of defect generation in the dynamics of phase transitions. KZ utilizes the structure of equilibrium states away from the transition point to estimate the excitations due to the transition using adiabatic and impulse approximations. Here we show, the actual nonequilibrium dynamics lead to a qualitatively different scenario from KZ, as far correlations between the defects (rather than their densities) are concerned. For a quantum Ising chain, we show, this gives rise to a Gaussian spatial decay in the domain wall (kinks) correlations, while KZ would predict an exponential fall. We propose a simple but general framework on top of KZ, based on the ``quantum coarsening'' dynamics of local correlators in the supposed impulse regime. We outline how our picture extends to generic interacting situations.
We revisit the quantum annealing problem in the non-Hermitian transverse-field Ising model. We determine, both analytically and numerically, the intrinsic transition probabilities and the resulting defect density. Our results reveal that, unlike the Hermitian case where defect production is dominated by modes near the gap-closing point, the non-Hermitian dynamics involve significant contributions from broad momentum sectors. We find that, depending on the dissipation strength, the defect density exhibits standard Kibble-Zurek scaling, anti-Kibble-Zurek behavior, and a suppression faster than the Kibble-Zurek prediction. We demonstrate that these deviations from the standard Kibble-Zurek scaling can be understood in terms of the underlying excitation probabilities. Specifically, the fast decay of the defect density originates from a vanishing excitation probability spanning a range of annealing times across all allowed modes, even at the gap-closing points. In contrast, the anti-Kibble-Zurek behavior arises from supplementary excitations facilitated by dissipation over a broad range of allowed modes, particularly those situated away from the gap-closing region.
We investigate defects in the two-dimensional transverse-field Ising ferromagnet on periodic
L×L lattices after quantum annealing from high to vanishing field. With exact numerical solutions for
L≤6, we observe the expected critical Kibble-Zurek (KZ) time scale
∝Lz+1/ν (with
z=1 and
1/ν≈1.59) at the quantum phase transition. We also observe KZ scaling of the ground-state fidelity at the end of the process. The excitations evolve by coarsening dynamics of confined defects, with a time scale
∝L2, and interface fluctuations of system-spanning defects, with life time
∝L3. We build on analogies with classical simulated annealing, where we characterize system-spanning defects in detail and find differences in the dynamic scales of domain walls with winding numbers
W=(1,0)/(0,1) (horizontal/vertical) and
W=(1,1) (diagonal). They decay on time scales
∝L3 (which applies also to system-spanning domains in systems with open boundaries) and
∝L3.4, respectively, when imposed in the ordered phase. As a consequence of
L3.4 exceeding the classical KZ scale
Lz+1/ν=L3.17 the probability of
W=(1,1) domains in SA scales with the KZ exponent even in the final
T=0 state. In QA, also the
W=(1,0)/(0,1) domains are controlled by the KZ time scale
L2.59. The
L3 scale can nevertheless be detected in the excited states, using a method that we develop that should also be applicable in QA experiments.
Demonstrating genuine many-body quantum coherence in large-scale quantum processors remains a central challenge for near-term quantum technologies. Recent experiments on D-Wave quantum annealers have investigated quenches of Ising chains and observed defect densities that show Kibble-Zurek scaling, consistent with coherent quantum dynamics. However, identical scaling can arise from classical or thermal processes. Here we propose the use of many-body coherent oscillations (MBCO) as a diagnostic for the identification of system-wide coherence in analog quantum simulators. Solving the time-dependent Schrodinger equation, we show that quenches of a staggered one-dimensional Ising chain across a quantum critical point produce oscillatory signatures in defect observables. We implement this model on the D-Wave Advantage quantum annealer. Using fast-anneal protocols, we find that, although defect densities follow Kibble-Zurek scaling, the expected oscillatory behavior is absent. We demonstrate that static disorder associated with individual qubits is not likely responsible for the absence of MBCO. Modest modifications to annealing schedules can dramatically enhance oscillation visibility. This work gives a general roadmap for the search for quantum coherence in noisy, large-scale quantum platforms.