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arXiv:2610.08769

Observing the magic Mpemba effect in localized dynamics on a digital quantum computer

Han-Ze Li, Xianquan Yan, Yi-Rui Zhang, Jian-Xin Zhong, Shuo Liu, Ching Hua Lee

quant-phcond-mat.dis-nnSubmitted Oct 6, 2026• Announced Oct 7, 2026• 0 citations
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Abstract

The Mpemba effect challenges the intuition that states closer to equilibrium must relax faster. We ask whether an analogous magic-ordering reversal can occur in the generation of quantum magic (nonstabilizerness), a key resource for universal quantum computation: can a state with less initial magic overtake one with more and reach its asymptotic value sooner? Here, we uncover interaction-induced dephasing as a distinct mechanism for this magic Mpemba effect, requiring neither transport nor conventional thermalization. For tilted product states in an interacting $\ell$-bit model, a random-phase analysis predicts a reversal of the magic ordering: states with less initial magic attain higher saturated magic, independent of their spatial pattern. Exact simulations of the $\ell$-bit model and localized spin chains further show that these states also saturate earlier. We observe both features on IBM superconducting quantum processors. An effective $\ell$-bit implementation accesses long dephasing times at fixed circuit depth by encoding time in gate angles, while a microscopic spin model exhibits the reversal universally across initial patterns in the localized regime but only selectively in the ergodic regime. These results establish interaction-induced dephasing as a route to anomalous quantum-resource relaxation beyond transport-driven thermalizing dynamics.

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The Mpemba effect challenges the intuition that states closer to equilibrium must relax faster. We ask whether an analogous magic-ordering reversal can occur in the generation of quantum magic (nonstabilizerness), a key resource for universal quantum computation: can a state with less initial magic overtake one with more and reach its asymptotic value sooner? Here, we uncover interaction-induced dephasing as a distinct mechanism for this magic Mpemba effect, requiring neither transport nor conventional thermalization. For tilted product states in an interacting ℓ\ellℓ-bit model, a random-phase analysis predicts a reversal of the magic ordering: states with less initial magic attain higher saturated magic, independent of their spatial pattern. Exact simulations of the ℓ\ellℓ-bit model and localized spin chains further show that these states also saturate earlier. We observe both features on IBM superconducting quantum processors. An effective ℓ\ellℓ-bit implementation accesses long dephasing times at fixed circuit depth by encoding time in gate angles, while a microscopic spin model exhibits the reversal universally across initial patterns in the localized regime but only selectively in the ergodic regime. These results establish interaction-induced dephasing as a route to anomalous quantum-resource relaxation beyond transport-driven thermalizing dynamics.
Quantum state preparation can be strikingly counterintuitive: the fastest route to a target state need not start from the apparently closest initial condition. We uncover such a quantum Mpemba effect in the dynamical generation of quantum magic (nonstabilizerness), quantified by the stabilizer Rényi entropy, in U(1)\mathrm{U(1)}U(1)-symmetric random circuits initialized from tilted product states. States with lower initial magic can generate magic faster than states with higher initial magic. The acceleration is not determined solely by the conserved-charge distribution. Two initial-state families with identical initial magic and identical charge distribution exhibit qualitatively different magic-growth dynamics, depending also on the spatial structure of the initial state within each charge sector. Analogous magic Mpemba effects in SU(2)\mathrm{SU(2)}SU(2)-symmetric circuits and under nonintegrable Hamiltonian dynamics further show that the phenomenon is tied neither to Abelian symmetry nor to random-circuit dynamics, establishing quantum magic as a distinct arena for Mpemba physics.
Generating entanglement rapidly and reliably is essential for quantum information processing, communication, and metrology. Dissipative preparation is attractive because engineered reservoirs robustly drive a system toward an entangled target, yet relaxation can carry a substantial time cost. Here we formulate the entanglement Mpemba effect, whereby an initially less entangled state overtakes a more entangled state under the same open-system dynamics. This effect turns initial-state engineering into a route for faster preparation without altering the dissipative protocol. We derive a general criterion for the reversal from the relaxation spectrum, applicable even when entanglement evolves nonmonotonically. A reversal of deterministic local operations and classical communication (LOCC)-reachability preorder provides a measure-independent certificate of reversed entanglement order. Exactly solvable models show that initial-state selection can substantially shorten the time required to reach high entanglement. We further propose an experimentally relevant trapped-ion protocol that can realize the entanglement Mpemba effect.
The quantum Mpemba effect refers to the counterintuitive phenomenon in which a system initially farther from equilibrium relaxes faster than one prepared closer to it. Several mechanisms have been identified in open quantum systems to explain this behavior, including the strong Mpemba effect, non-Markovian memory, and initial system-reservoir entanglement. Here, we unveil a distinct mechanism rooted in the non-normal nature of the Liouvillian superoperator in Markovian dynamics. When the Liouvillian's eigenmodes are non-orthogonal, transient interference between decaying modes can induce anomalous early-time behavior-such as delayed thermalization or transient freezing-even though asymptotic decay rates remain unchanged. This differs fundamentally from strong Mpemba effects, which hinge on suppressed overlap with slow-decaying modes. We demonstrate this mechanism using a waveguide quantum electrodynamics model, where quantum emitters interact with the photonic modes of a one-dimensional waveguide. The directional and radiative nature of these couplings naturally introduces non-normality into the system's dynamics. As a result, certain initial states-despite being closer to equilibrium-can exhibit slower relaxation at short times. This work reveals a previously unexplored and universal source of Mpemba-like behavior in memoryless quantum systems, expanding the theoretical framework for anomalous relaxation and opening new avenues for control in engineered quantum platforms.
We construct a controllable imaginary-time Mpemba effect in quantum spin systems using spatially modulated local rotations without changing initial bipartite entanglement spectra and correlation magnitudes. This feature unambiguously isolates the redistribution of spectral weights as the sole driver of the anomalous relaxation. Using the compact-boson description, we reveal that these twists act as precise mode selectors: higher-harmonic twists exclusively populate high-energy standing waves, structurally bypassing slow-decaying infrared modes to accelerate convergence. We derive exact analytical crossing times for these reversals and demonstrate that intentionally reintroducing the slow-mode population systematically delays the ITME. This exact mechanism is validated beyond the fixed-point theory via calculations on interacting XXZ chains and ladders. Furthermore, a twelve-qubit simulation of variational quantum imaginary-time evolution reproduces the reversals and their controlled delay, providing a concrete route to realize this protocol in realistic quantum circuits. Ultimately, these results provide a strictly controllable and exact starting point for realizing and investigating the imaginary-time Mpemba effect, establishing a foundational paradigm to harness anomalous non-equilibrium relaxation in quantum ground-state preparations.
The Mpemba effect, where a state prepared farther from equilibrium relaxes faster to equilibrium than one prepared closer, has a quantum counterpart where relaxation is resolved by conserved charge. However, the fate of the quantum Mpemba effect in systems with long-range interactions remains an open question. Here, we study the quantum Mpemba effect in long-ranged, U(1)-symmetric random unitary circuits. Using annealed Rényi-2 entanglement asymmetry computed via replica tensor networks and exact diagonalization, we track the symmetry restoration from three types of tilted product states: ferromagnetic, antiferromagnetic, and ferromagnetic with a central domain wall. The quantum Mpemba effect is present for tilted ferromagnetic states at all interaction ranges, but absent for tilted antiferromagnetic states, and occurs for the domain-wall state only in effectively short-ranged circuits, where the Mpemba time tMt_{\rm M}tM​ is found to scale with the subsystem size NAN_ANA​ as tM ⁣∼ ⁣NA zt_{\rm M}\!\sim\!N_{A}^{\,z}tM​∼NAz​, with the dynamical exponent z=min⁡(α−1,2)z=\min(α-1,2)z=min(α−1,2). These results reveal how the quantum Mpemba effect is governed by the interplay between interaction range and initial-state charge bias in long-ranged chaotic systems.
The essence of the Mpemba effect is that nonequilibrium systems may relax faster the further they are from their equilibrium configuration. In the quantum realm, this phenomenon arises in closed systems dynamics and is witnessed by features of symmetry and entanglement. Here, we study the quantum Mpemba effect in charge-preserving random circuits, combining extensive numerical simulations and analytical arguments. We show that the more asymmetric certain classes of initial states (tilted ferromagnets) are, the faster they restore symmetry and reach the grand-canonical ensemble. Conversely, other classes of states (tilted antiferromagnets) do not show the Mpemba effect. We provide a simple and general mechanism underlying the effect, based on the spreading of nonconserved operators in terms of conserved densities. Grounded only in locality, unitarity, and symmetry, our analysis clarifies the emergence of Mpemba physics in chaotic quantum systems.