arXiv subjects

Hongzheng Zhao

Publications and source records attributed to Hongzheng Zhao.

At least 19 recordsLinked to original sources

arXiv2026

Quantum simulation of circular cluster interactions in a linear spin chain

The preparation of ground states of Hamiltonians with symmetries that are fundamentally different than those of the underlying device is a central challenge for quantum technologies. Here, we address this challenge with an analog protocol for the iconic generalized cluster Hamiltonian with the translational symmetry resultant from periodic boundary conditions based on a magnetization-preserving interaction on a linear geometry with open boundary conditions. Our results show that this goal can be achieved in a control duration that scales only moderately with the number of spins and Hamiltonian interaction complexity.

quant-ph↗

arXiv2026

Reinforcement Learning to Harness Approximation Errors for Long-Time Quantum Simulation

Accurate digital quantum simulation at long times is limited by the accumulation of errors inherent to approximate simulation. Here we introduce RL-Trotter, a reinforcement-learning framework that treats unavoidable approximation errors as resources for error correction rather than merely imperfections to suppress. We show that low-dimensional information from conservation laws, such as the energy and energy variance, provides a sufficient learning signal to guide the agent, which learns to adapt a single scalar---the next Trotter step size---without access to the target wave function. By optimizing the entire long-time evolution rather than individual steps, RL-Trotter discovers self-correcting sequences in which later errors compensate for those accumulated earlier, increasing the accuracy of the long-time dynamics. The learned policies are intrinsically robust to measurement noise, substantially reducing measurement overhead. They also generalize to previously unseen, physically similar initial states and transfer from small, classically simulable systems to systems an order of magnitude larger. This enables a practical protocol based on classical pretraining followed by direct deployment or limited fine-tuning on quantum hardware. Our results establish a broader perspective for quantum algorithms: errors in approximate evolution can be orchestrated into resources for accurate and resource-efficient quantum dynamics.

quant-ph↗

arXiv2026

From stable periodic orbits to many-body chaos: doubly tunable prethermalization via engineering of an emergent band structure

We uncover a family of many-body periodic orbits in a periodically driven (Floquet) spin system away from the high-frequency limit. While linear stability analysis predicts that perturbed many-body trajectories remain close to stable periodic orbits, thermodynamic principles dictate that Floquet heating will ultimately set in. Our work aims to resolve the tension between these two expectations. In particular, we show that perturbations away from the stable periodic orbits feature a description akin to a quasiparticle band structure. A long-lived prethermal regime appears when modes around the gapless point are slowly populated. The dispersion determines the prethermal lifetime, and we show how band engineering leads to a "doubly tunable" parametric dependence of the prethermal lifetime $R^{-W}$, with $R$ the width in momentum space of the quasiparticle distribution and $W$ the exponent of the dispersion around the gapless point. Our results not only establish a powerful route toward stabilizing non-equilibrium phases of matter in driven many-body systems but also establish a conceptual bridge between periodic orbits in 'low-dimensional' nonlinear systems and many-body chaos.

cond-mat.stat-mech↗

arXiv2026

Anomalous Floquet Heating from Sparse Long-Range Interactions

Regular lattices of interacting particles under a periodic drive typically heat with rate $γ\sim e^{-\mathcal{O}(ω)}$ which is exponentially suppressed in drive frequency $ω$. Here, we show that sparse infinite-range interactions, which have recently become accessible in quantum simulators, can lead to anomalous heating with rate $γ\sim e^{-\mathcal{O}(\sqrtω)}$. This anomaly originates from the broad distribution of coordination numbers across the network: as the driving frequency increases, heating becomes dominated by sites with larger coordination numbers, making the characteristic local energy scale relevant for heating grow with frequency. For small-world networks, we develop an analytic theory that thoroughly matches our large scale numerics. Finally, we discuss how network topology can serve as a control knob for engineering non-equilibrium phases of matter. Our results uncover a new mechanism for Floquet heating and suggest new routes toward stabilizing nonequilibrium phases in driven systems with programmable interaction networks.

cond-mat.stat-mech↗

arXiv2026

Emergent Self-Similar Quantum Revivals in Spiral Drives

We uncover a distinct form of nonequilibrium temporal order: self-similar quantum revivals in a many-body system driven by quasiperiodic spiral kicks, where the system recurrently returns close to its initial state at a hierarchically nested sequence of times. We demonstrate that both the fidelity and entanglement entropy exhibit this self-similar temporal structure. It originates from an emergent dynamical attractor, which we identify, such that all momentum modes eventually fall into the same closed orbits at self-similar times. We analytically justify this behavior and show that, for special momentum modes, this attractor arises as a consequence of a generalized spin echo process, and more generally we prove its existence using quasiperiodic SU(2) cocycles. Interestingly, the dynamics between consecutive revivals supports either volume- or area-law entanglement scaling, tunable via the driving parameters. In the presence of integrability-breaking perturbations, the system eventually heats up, but a long-lived prethermal regime with algebraically tunable lifetime occurs before heating sets in. Our results establish self-similar quantum revivals as a new paradigm for nonequilibrium quantum matter and provide a realistic route for its observation in current quantum simulators.

quant-ph↗

arXiv2026

Engineering long-range and multi-body interactions via global kinetic constraints

Long-range and multi-body interactions are crucial for quantum simulation and quantum computation. Yet, their practical realization using elementary pairwise interactions remains an outstanding challenge. We propose an experimental scheme based on the Bose-Hubbard system with a periodic driving of the on-site energy and global-range density-density interactions, a setup readily implementable via cold atoms in optical lattices with cavity-mediated interactions. Optimally chosen driving parameters can induce global kinetic constraints, where tunneling rates are selectively suppressed depending on the particle number imbalance between all even and odd sites. This mechanism, together with the flexible tunability of local tunneling rates, provides efficient implementation schemes of a family of global controlled gates for quantum computation. We illustrate this scheme for the $N$-qubit Toffoli gate, circumventing the need for a two-body gate decomposition, and elaborate on the efficient preparation of entangled many-body states.

quant-ph↗

arXiv2026

Protecting Quantum Simulations of Lattice Gauge Theories through Engineered Emergent Hierarchical Symmetries

We present a strategy for the quantum simulation of many-body lattice models with constrained Hilbert spaces. We focus on lattice gauge theories (LGTs), which underlie a wide range of phenomena in particle physics, condensed matter, and quantum information. In present-day quantum computing platforms, perfect restrictions of the Hilbert space to the desired gauge sectors are beyond reach: for LGTs, violations of the local constraint are unavoidable, posing a formidable challenge for the emulation of the underlying physics. Here, we develop a Floquet-engineering framework that restructures departures from a target sector such that a series of emergent local symmetries occurs hierarchically in time and in a controllable way. This leads to a set of approximate dynamical selection rules that strongly restrict inter-sector couplings, resulting in a pronounced, symmetry-controlled hierarchy of lifetimes for the state population to spread among sectors. Concretely, this protects $U(1)$ LGTs against violations of the {defining} local symmetry. While some sectors remain very long-lived, others are destabilized on shorter timescales. We numerically verify our theory for the one-dimensional $U(1)$ quantum link model. In addition, we reveal that `defects', whose movement accounts for violations of the gauge constraint, are kinetically constrained, becoming mobile only through the assistance of intra-sector dynamics, which we describe using an effective quantum marble model. Our results can thus be used to extend the lifetime, in the spirit of passive error correction, of quantum simulations of complex many-body problems when emergent or desired local symmetries are only implemented approximately.

quant-ph↗

arXiv2026

Prethermal gauge structure and surface growth in $\mathbb{Z}_2$ lattice gauge theories

Universal aspects of thermalization in interacting many-body systems are challenging to derive microscopically, especially in kinetically constrained models, yet their numerical study beyond $(1+1)$D remains notoriously difficult. Here, we numerically study the mean-field dynamics of a $(2+1)$D spin system with thousands of spins and show that experimentally-feasible two-body Ising interactions can stabilize a prethermal $\mathbb{Z}_2$ lattice gauge structure with dynamical matter, manifested by a separation of timescales with a stable gauge-invariant plateau. Eventually, the metastable prethermal $\mathbb{Z}_2$ gauge structure breaks down via a proliferation of Gauss' law defects, similar to bubble formation in false vacuum decay. In this regime, we discover spatio-temporal correlations described by a non-linear surface growth consistent with the $(1+1)$D Kardar-Parisi-Zhang (KPZ) universality class, revealing a previously hidden feature in the thermalization of multi-point correlators. We benchmark our results in small systems against semi-classical discrete time Wigner approximation (DTWA) and exact diagonalization (ED), where the breakdown of DTWA signals the emergence of an extensive number of local symmetries that strongly influence the thermalization pathway. Our model provides a testbed for quantum simulators and is directly implementable in large-scale arrays of Rydberg atoms.

quant-ph↗

arXiv2026

Anomalous spin transport in integrable random quantum circuits

High-temperature spin transport in integrable quantum spin chains exhibits a rich dynamical phase diagram, including ballistic, superdiffusive, and diffusive regimes. While integrability is known to survive in static and periodically driven systems, its fate in the complete absence of time-translation symmetry, particularly in interacting random quantum circuits, has remained unclear. Here we construct integrable random quantum circuits built from inhomogeneous XXZ R-matrices. Remarkably, integrability is preserved for arbitrary sequences of gate layers, ranging from quasiperiodic to fully random, thereby explicitly breaking both continuous and discrete time-translation symmetry. Using large-scale time-dependent density-matrix renormalization group simulations at infinite temperature and half filling, we map out the resulting spin-transport phase diagram and identify ballistic, superdiffusive, and diffusive regimes controlled by the spectral parameters of the R-matrices. The spatiotemporal structure of spin correlations within each regime depends sensitively on the inhomogeneity, exhibiting spatial asymmetry and sharp peak structures tied to near-degenerate quasiparticle velocities. To account for these findings, we develop a generalized hydrodynamics framework adapted to time-dependent integrable circuits, yielding Euler-scale predictions for correlation functions, Drude weights, and diffusion bounds. This approach identifies the quasiparticles governing transport and quantitatively captures both the scaling exponents and fine structures of the correlation profiles observed numerically. Our results demonstrate that exact Yang-Baxter integrability is compatible with stochastic quantum dynamics and establish generalized hydrodynamics as a predictive framework for transport in time-dependent integrable systems.

cond-mat.stat-mech↗

arXiv2025

Floquet Superheating

Periodically driven many-body systems generally heat towards a featureless 'infinite-temperature' state. As an alternative to uniform heating in a clean system, here we establish a Floquet superheating regime, where fast heating nucleates at ''hot spots" generated by rare fluctuations in the local energy with respect to an appropriate effective Hamiltonian. Striking macroscopic consequences include exceptionally long-lived prethermalization and non-ergodic bimodal distributions of macroscopic observables. Superheating is predicated on a heating rate depending strongly on the local fluctuation; in our example, this is supplied by a sharp state-selective spin-echo, where the energy absorption is strongly suppressed for low-energy states, while thermal fluctuations open up excessive heating channels. A simple phenomenological theory is developed to show the existence of a critical droplet size, which incorporates heating by the driving field as well as the heat current out of the droplet. Our results shine light on a new heating mechanism and suggest new routes towards stabilizing non-equilibrium phases of matter in driven systems.

cond-mat.stat-mech↗

arXiv2025

Emergent long-tail dynamics in driven magnets with dynamical frustration

In this study, we show that dynamical frustration can spontaneously emerge in frustration-free magnetic systems under periodic driving. Specifically, we consider a classical spin system and demonstrate the emergence of spin-ice physics when drive-induced heating is well suppressed. In particular, we focus on the dynamics of magnetic monopole excitations, which, in sharp contrast to their equilibrium counterparts, exhibit a non-ergodic stochastic random-walk process with long-tailed, power-law distributed waiting times, where the power-law exponent is tunable by the system's effective temperature. Heating is accelerated at intermediate driving frequencies, and the system eventually heats up to an infinite-temperature state. However, the heating time is extremely sensitive to different initial-state realizations and also follows a long-tailed power-law distribution. We show that a drive-induced short-range attractive interaction between monopoles is responsible for the long-tailed distributions observed in both monopole and heating dynamics.

cond-mat.stat-mech↗

arXiv2025

Complex and tunable heating in conformal field theories with structured drives via classical ergodicity breaking

Emission and absorption of energy are fundamental aspects of non-equilibrium dynamics. The heating induced by driving a many-body system is perhaps the most straightforward diagnostic of the process of equilibration, or the lack thereof. Gapless systems are particularly susceptible to drive-induced heating, and the capacity to control such heating is of experimental importance. Our study addresses this challenge in the framework of conformal field theory (CFT), for which we study families of structured drives up to the aperiodic Thue-Morse sequence. Concretely, we consider a class of spatially inhomogeneous Hamiltonians, where the operator evolution is governed by a non-linear classical dynamical system $\mathcal{K}$. The existence of invariant regions and fixed points of $\mathcal{K}$ leads to different levels of ergodicity breaking. Upon bridging the gap between this dynamical system and the driven CFT, we classify various dynamical phases of matter, including the heating and non-heating phases, as well as a prethermal phase with a controllably slow heating rate. We further generalize the discussion to $η-$random multipolar driving, characterized by $η-$th order multipolar correlation in time. A ``triply tunable'' parametric dependence of the prethermal lifetime arises as $K^{-2(η-ξ)}$, where $K$ quantifies the deviation from the preimages of the fixed points of $\mathcal{K}$, the multipolar order $η$, and the order of the preimages $ξ$. Upon sacrificing Hermiticity by considering SU(2) deformed CFTs, we find another non-heating phase with a non-zero measure, inaccessible via purely unitary CFTs. This is underpinned by an emergent compact subspace in the generic $\mathrm{SL}(2,\mathbb{C})$ group structure, which we also identify in the transfer matrix in non-Hermitian systems with binary disorder.

quant-ph↗

arXiv2025

Stable time rondeau crystals in dissipative many-body systems

Driven systems offer the potential to realize a wide range of non-equilibrium phenomena that are inaccessible in static systems, such as the discrete time crystals. Time rondeau crystals with a partial temporal order have been proposed as a distinctive prethermal phase of matter in systems driven by structured random protocols. Yet, heating is inevitable in closed systems and time rondeau crystals eventually melt. We introduce dissipation to counteract heating and demonstrate stable time rondeau crystals, which persist indefinitely, in a many-body interacting system. A key ingredient is synchronization in the non-interacting limit, which allows for stable time rondeau order without generating excessive heating. The presence of many-body interaction competes with synchronization and a de-synchronization phase transition occurs at a finite interaction strength. This transition is well captured via a linear stability analysis of the underlying stochastic processes.

cond-mat.stat-mech↗

arXiv2025

Floquet-engineered Emergent Massive Nambu-Goldstone Modes

We present a general framework to implement massive Nambu-Goldstone quasi-particles in driven many-body systems. The underlying mechanism leverages an explicit Lie group structure imprinted into an effective Hamiltonian that governs the dynamics of slow degrees of freedom; the resulting emergent continuous symmetry is weakly explicitly broken, giving rise to a massive Nambu-Goldstone mode, with a spectral mass gap scaling linearly with the drive period. We discuss explicit and experimentally implementable realizations, such as Heisenberg-like spin models that support gapped spin-wave excitations. We provide a protocol to certify the existence of the massive Nambu-Goldstone mode from the dynamics of specific observables, and analyse the dispersion spectrum and their lifetime in the presence of weak explicit symmetry breaking.

quant-ph↗

arXiv2025

Preparation of cat states in many-body eigenbasis via non-local measurement

Engineered dissipation offers a promising route to prepare correlated quantum many-body states that are otherwise difficult to access using purely unitary protocols. However, creating superpositions of multiple many-body eigenstates with tunable properties remains a major challenge. We propose to periodically interrupt the many-body evolution by precisely removing a given many-body Fock state through a non-local post-selected measurement protocol. Upon tuning the measurement period, we show that a dark state manifold survives the removal, allowing us to filter the system and generate a coherent superposition within this manifold at long times. As a testbed, we study a non-integrable spin-1 XY chain featuring a solvable family of eigenstates that can differ macroscopically in quasi-particle excitations. Our protocol generates tunable superpositions of these eigenstates, including the spin-1 Greenberger-Horne-Zeilinger state and a generalized variant with tunable spatiotemporal order. Under perturbations, the system exhibits an exceptionally long-lived metastable regime where the engineered superpositions remain robust. Our work provides new insight into quantum state preparation via non-local measurements using tools available in current quantum simulators.

quant-ph↗

arXiv2025

Prethermalization by Random Multipolar Driving on a 78-Qubit Superconducting Processor

Time-dependent drives hold the promise of realizing non-equilibrium many-body phenomena that are absent in undriven systems. Yet, drive-induced heating normally destabilizes the systems, which can be parametrically suppressed in the high-frequency regime by using periodic (Floquet) drives. It remains largely unknown to what extent highly controllable quantum simulators can suppress heating in non-periodically driven systems. Using the 78-qubit superconducting quantum processor, Chuang-tzu 2.0, we report the experimental observation of long-lived prethermal phases in many-body systems with tunable heating rates, driven by structured random protocols, characterized by $n$-multipolar temporal correlations. By measuring both the particle imbalance and subsystem entanglement entropy, we monitor the entire heating process over 1,000 driving cycles and observe the existence of the prethermal plateau. The prethermal lifetime is `doubly tunable': one way by driving frequency, the other by multipolar order; it grows algebraically with the frequency with the universal scaling exponent $2n{+}1$. Using quantum state tomography on different subsystems, we demonstrate a non-uniform spatial entanglement distribution and observe a crossover from area-law to volume-law entanglement scaling. With 78 qubits and 137 couplers in a 2D configuration, the entire far-from-equilibrium heating dynamics are beyond the reach of simulation using tensor-network numerical techniques. Our work highlights superconducting quantum processors as a powerful platform for exploring universal scaling laws and non-equilibrium phases of matter in driven systems in regimes where classical simulation faces formidable challenges.

quant-ph↗

arXiv2025

Non-Hermitian delocalization in 1D via emergent compactness

Potential disorder in 1D leads to Anderson localization of the entire spectrum. Upon sacrificing hermiticity by adding non-reciprocal hopping, the non-Hermitian skin effect competes with localization. We find another route for delocalization, which involves imaginary potential disorder. While an entirely random potential generally still leads to localization, imposing minimal spatial structure to the disorder can protect delocalization: it endows the concomitant transfer matrix with an SU(2) structure, whose compactness in turn translates into an infinite localization length. The fraction of delocalized states can be tuned by the choice of boundary conditions.

cond-mat.dis-nn↗

arXiv2025

Engineering Hierarchical Symmetries

The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A particularly promising route is the use of driving protocols to engineer specific desired properties with a high degree of control and flexibility. Here, we present such a program for the tunable generation of sequences of symmetries on controllable timescales. Concretely, our general driving protocol for many-body systems generates a sequence of prethermal regimes, each exhibiting a lower symmetry than the preceding one. We provide an explicit construction of effective Hamiltonians exhibiting these symmetries, which imprints emergent quasiconservation laws hierarchically, enabling us to engineer the respective symmetries and concomitant orders in nonequilibrium matter. We provide explicit examples, including spatiotemporal and topological phenomena, as well as a spin chain realizing the symmetry ladder $\text{SU(2)}{\rightarrow}\text{U(1)} {\rightarrow} \mathbb{Z}_2{\rightarrow} E$. Our results have direct applications in experiments with quantum simulators.

quant-ph↗