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arXiv:2605.04155

Nonstabilizerness Mpemba Effects

Zhenyu Xiao, Hao-Kai Zhang, Shuo Liu

quant-phcond-mat.stat-mechSubmitted May 5, 2026• Announced May 7, 2026• 0 citations
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Abstract

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 $\mathrm{U(1)}$-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 $\mathrm{SU(2)}$-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.

Comments
4.5 pages, 3 figures

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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.
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.
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 quantum Mpemba effect is the counterintuitive phenomenon whereby a quantum state initially farther from equilibrium relaxes faster than one initially closer to it. We demonstrate this effect in random Clifford circuits with a conserved U(1)\mathrm{U}(1)U(1) charge, using the entanglement asymmetry to characterize relaxation through dynamical symmetry restoration. Exact numerical simulations show that an initially more asymmetric state can become locally more symmetric than an initially less asymmetric one. We explain this behavior by mapping the dynamics onto a charge-conserving quantum automaton, in which the decay of the entanglement asymmetry is controlled by the statistics of encounters between two particle species evolving according to a symmetric simple exclusion process. This mapping yields an analytic expression for the entanglement asymmetry and provides a simple microscopic mechanism for the quantum Mpemba effect: stronger initial symmetry breaking corresponds to a denser particle configuration, which enhances the frequency of particle encounters and thereby accelerates symmetry restoration.
Symmetries shape the quantum-information dynamics of many-body systems, but their effect on nonstabilizerness, the resource complementary to entanglement, is less understood. We compute the stabilizer Rényi entropy, a measure of nonstabilizerness, in U(1)\mathrm{U}(1)U(1)-symmetric one-dimensional random circuits. The disorder-averaged dynamics is captured by a four-replica tensor network, which we evaluate by S4S_4S4​-adapted infinite time-evolving block decimation (iTEBD) directly in the thermodynamic limit. Together with a hydrodynamic argument, our results identify a diffusive universality class for the late-time approach of nonstabilizerness to its random-state value, with the stabilizer Rényi entropy gap closing as 1/t1/t1/t. The same scaling is verified in an energy-conserving nonintegrable Ising chain. More broadly, our framework provides a hydrodynamic perspective on nonstabilizerness generation and offers insight into the design of approximate Haar-random states in Hamiltonian dynamics.
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.
Entanglement asymmetry, which serves as a diagnostic tool for symmetry breaking and a proxy for thermalization, has recently been proposed and studied in the context of symmetry restoration for quantum many-body systems undergoing a quench. In this Letter, we investigate symmetry restoration in various symmetric random quantum circuits, particularly focusing on the U(1) symmetry case. In contrast to nonsymmetric random circuits where the U(1) symmetry of a small subsystem can always be restored at late times, we reveal that symmetry restoration can fail in U(1)-symmetric circuits for certain weak symmetry-broken initial states in finite-size systems. In the early-time dynamics, we observe an intriguing quantum Mpemba effect implying that symmetry is restored faster when the initial state is more asymmetric. Furthermore, we also investigate the entanglement asymmetry dynamics for SU(2) and Z_{2} symmetric circuits and identify the presence and absence of the quantum Mpemba effect for the corresponding symmetries, respectively. A unified understanding of these results is provided through the lens of quantum thermalization with conserved charges.