arXiv subjects

Bozhen Zhou

Publications and source records attributed to Bozhen Zhou.

11 recordsLinked to original sources

arXiv2026

Quantum-classical crossover in fault-tolerant quantum dynamics simulation

While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of $p=10^{-3}$, fault-tolerant simulation requires approximately 2 hours and $3.7 \times 10^5$ physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of $p=10^{-4}$ leads to at least an order of magnitude reduction in qubit count ($3.1 \times 10^4$ physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.

quant-ph↗

arXiv2026

Trotter Scars: Trotter Error Suppression in Quantum Simulation

Recent studies have shown that Trotter errors are highly initial-state dependent and that standard upper bounds often substantially overestimate them. However, the mechanism underlying anomalously small Trotter errors and a systematic route to identifying error-resilient states remain unclear. Using interaction-picture perturbation theory, we derive an analytical expression for the leading-order Trotter error in the eigenbasis of the Hamiltonian. Our analysis shows that initial states supported on spectrally commensurate energy ladders exhibit strongly suppressed error growth together with persistent Loschmidt revivals. We refer to such states as Trotter scars. To identify such states, we further introduce a model-agnostic variational framework. Its loss function can be built from Trotterized dynamics alone, which allows the search to reach system sizes beyond exact diagonalization. The optimized states at small sizes moreover follow regular patterns that extend to larger sizes. We demonstrate our theory in three spin models, where the optimized states exhibit the predicted persistent Loschmidt revivals and strongly suppressed error growth. We further conducted experiments on a $17$-qubit superconducting quantum processor and successfully realized the Trotter-scar states and demonstrated the Trotter error suppression in quantum simulations.

quant-ph↗

arXiv2025

Dissipation-induced Half Quantized Conductance in One-dimensional Topological Systems

Quantized conductance from topologically protected edge states is a hallmark of two-dimensional topological phases. In contrast, edge states in one-dimensional (1D) topological systems cannot transmit current across the insulating bulk, rendering their topological nature invisible in transport. In this work, we investigate the transport properties of the Su-Schrieffer-Heeger model with gain and loss, and show that the zero-energy conductance exhibits qualitatively distinct behaviors between the topologically trivial and nontrivial phases, depending on the hybridization and dissipation strengths. Crucially, we analytically demonstrate that the conductance can become half-quantized in the topologically nontrivial phase, a feature absent in the trivial phase. We further show that the half quantization predominantly originates from transport channels involving gain/loss and edge states. Our results uncover a new mechanism for realizing quantized transport in 1D topological systems and highlight the nontrivial role of dissipation in enabling topological signatures in open quantum systems.

cond-mat.mes-hall↗

arXiv2024

Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions

The fidelity is widely used to detect quantum phase transitions, which is characterized by either a sharp change of fidelity or the divergence of fidelity susceptibility in the thermodynamical limit when the phase-driving parameter is across the transition point. In this work, we unveil that the occurrence of exact zeros of fidelity in finite-size systems can be applied to detect quantum phase transitions. In general, the fidelity $\mathcal{F}(γ,\tildeγ)$ always approaches zero in the thermodynamical limit, due to the Anderson orthogonality catastrophe, no matter whether the parameters of two ground states ($γ$ and $\tildeγ$) are in the same phase or different phases, and this makes it difficult to distinguish whether an exact zero of fidelity exists by finite-size analysis. To overcome the influence of orthogonality catastrophe, we study finite-size systems with twist boundary conditions, which can be introduced by applying a magnetic flux, and demonstrate that exact zeros of fidelity can be always accessed by tuning the magnetic flux when $γ$ and $\tildeγ$ belong to different phases. On the other hand, no exact zero of fidelity can be observed if $γ$ and $\tildeγ$ are in the same phase. We demonstrate the applicability of our theoretical scheme by studying concrete examples, including the Su-Schrieffer-Heeger model, Creutz model and Haldane model. Our work provides a practicable way to detect quantum phase transitions via the calculation of fidelity of finite-size systems.

quant-ph↗

arXiv2024

Spread complexity and dynamical transition in multimode Bose-Einstein condensates

We study the spread complexity in two-mode Bose-Einstein condensations and unveil that the long-time average of the spread complexity $\overline{C}_{K}$ can probe the dynamical transition from self-trapping to Josephson oscillation. When the parameter $ω$ increases over a critical value $ω_{c}$, we reveal that the spread complexity exhibits a sharp transition from lower to higher value, with the corresponding phase space trajectory changing from self-trapping to Josephson oscillation. Moreover, we scrutinize the eigen-spectrum and uncover the relation between the dynamical transition and the excited state quantum phase transition, which is characterized by the emergence of singularity in the density of states at critical energy $E_{c}$. In the thermodynamical limit, the cross point of $E_{c}(ω)$ and the initial energy $E_{0}(ω)$ determines the dynamical transition point $ω_{c}$. Furthermore, we show that the different dynamical behavior for the initial state at a fixed point can be distinguished by the long-time average of the spread complexity, when the fixed point changes from unstable to stable. Finally, we also examine the sensitivity of $\overline{C}_{K}$ for the triple-well bosonic model which exibits the transition from chaotic dynamics to regular dynamics.

cond-mat.quant-gas↗

arXiv2023

Dynamical singularity of the rate function for quench dynamics in finite-size quantum systems

The dynamical quantum phase transition is characterized by the emergence of nonanalytic behaviors in the rate function, corresponding to the occurrence of exact zero points of the Loschmidt echo in the thermodynamical limit. In general, exact zeros of the Loschmidt echo are not accessible in a finite-size quantum system except for some fine-tuned quench parameters. In this work, we study the realization of the dynamical singularity of the rate function for finite-size systems under the twist boundary condition, which can be introduced by applying a magnetic flux. By tuning the magnetic flux, we illustrate that exact zeros of the Loschmidt echo can be always achieved when the postquench parameter is across the underlying equilibrium phase transition point, and thus the rate function of a finite-size system is divergent at a series of critical times. We demonstrate our theoretical scheme by calculating the Su-Schrieffer-Heeger model and the Creutz model in detail and exhibit its applicability to more general cases. Our result unveils that the emergence of dynamical singularity in the rate function can be viewed as a signature for detecting dynamical quantum phase transition in finite-size systems. We also unveil that the critical times in our theoretical scheme are independent on the systems size, and thus it provides a convenient way to determine the critical times by tuning the magnetic flux to achieve the dynamical singularity of the rate function.

quant-ph↗

arXiv2022

Signature of nonequilibrium quantum phase transition in the long time average of Loschmidt echo

We unveil the role of the long time average of Loschmidt echo in the characterization of nonequilibrium quantum phase transitions by studying sudden quench processes across quantum phase transitions in various quantum systems. While the dynamical quantum phase transitions are characterized by the emergence of a series of zero points at critical times during time evolution, we demonstrate that nonequilibrium quantum phase transitions can be identified by nonanalyticities in the long time average of Loschmidt echo. The nonanalytic behaviours are illustrated by a sharp change in the long time average of Loschmidt echo or the corresponding rate function or the emergence of divergence in the second derivative of rate function when the driving quench parameter crosses the phase transition points. The connection between the second derivative of rate function and fidelity susceptibility is also discussed.

quant-ph↗

arXiv2022

Localization, multifractality, and many-body localization in periodically kicked quasiperiodic lattices

We study the combined effect of quasiperiodic disorder, driven and interaction in the periodically kicked Aubry-André model. In the non-interacting limit, by analyzing the quasienergy spectrum statistics, we verify the existence of a dynamical localization transition in the high-frequency region, whereas the spectrum statistics becomes intricate in the low-frequency region due to the emergence of the extended/localized-to-multifractal edges in the quasienergy spectrum, which separate the multifractal states from the extended (localized) states. When the interaction is introduced, we find the periodically kicked incommensurate potential can lead to a transition from ergodic to many-body-localization phase in the high-frequency region. However, the many-body localization phase vanishes in the low-frequency region even for strong quasiperiodic disorder. Our studies demonstrate that the periodically kicked Aubry-André model displays rich dynamical phenomena and the driving frequency plays an important role in the formation of many-body localization in addition to the disorder strength.

cond-mat.dis-nn↗

arXiv2022

Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization

We carry out a systematical study of the size scaling of Liouvillian gap in boundary-dissipated one-dimensional quasiperiodic and disorder systems. By treating the boundary-dissipation operators as a perturbation, we derive an analytical expression of the Liouvillian gap, which indicates clearly the Liouvillian gap being proportional to the minimum of boundary densities of eigenstates of the underlying Hamiltonian, and thus give a theoretical explanation why the Liouvillian gap has different size scaling relation in the extended and localized phase. While the Liouvillian gap displays a power-law size scaling $Δ_{g}\propto L^{- 3}$ in the extended phase, our analytical result unveils that the Liouvillian gap fulfills an exponential scaling relation $Δ_{g}\propto e^{- κL}$ in the localized phase, where $κ$ takes the largest Lyapunov exponent of localized eigenstates of the underlying Hamiltonian. By scrutinizing the extended Aubry-André-Harper model, we numerically confirm that the Liouvillian gap fulfills the exponential scaling relation and the fitting exponent $κ$ coincides pretty well with the analytical result of Lyapunov exponent. The exponential scaling relation is further verified numerically in other one-dimensional quasiperiodic and random disorder models. We also study the relaxation dynamics and show the inverse of Liouvillian gap giving a reasonable timescale of asymptotic convergence to the steady state.

cond-mat.dis-nn↗

arXiv2022

Observation of critical phase transition in a generalized Aubry-André-Harper model on a superconducting quantum processor with tunable couplers

Quantum simulation enables study of many-body systems in non-equilibrium by mapping to a controllable quantum system, providing a new tool for computational intractable problems. Here, using a programmable quantum processor with a chain of 10 superconducting qubits interacted through tunable couplers, we simulate the one-dimensional generalized Aubry-André-Harper model for three different phases, i.e., extended, localized and critical phases. The properties of phase transitions and many-body dynamics are studied in the presence of quasi-periodic modulations for both off-diagonal hopping coefficients and on-site potentials of the model controlled respectively by adjusting strength of couplings and qubit frequencies. We observe the spin transport for initial single- and multi-excitation states in different phases, and characterize phase transitions by experimentally measuring dynamics of participation entropies. Our experimental results demonstrate that the newly developed tunable coupling architecture of superconducting processor extends greatly the simulation realms for a wide variety of Hamiltonians, and may trigger further investigations on various quantum and topological phenomena.

quant-ph↗

arXiv2021

Exact zeros of the Loschmidt echo and quantum speed limit time for the dynamical quantum phase transition in finite-size systems

We study exact zeros of Loschmidt echo and quantum speed limit time for dynamical quantum phase transition in finite size systems. Our results illustrate that exact zeros of Loschmidt echo exist even in finite size quantum systems when the postquench parameter takes some discrete values in regions with the corresponding equilibrium phase different from the initial phase. As the system size increases and tends to infinity, the discrete parameters distribute continuously in the parameter regions. We further analyze the time for the appearance of the first exact zero of Loschmidt echo which is known as the quantum speed limit time $τ_{\text{QSL}}$. We demonstrate that the maximal value of $τ_{\text{QSL}}$ is proportional to $L$ and approaches infinity in the thermodynamical limit, when we quench the initial non-critical state to the critical phase. We also calculate the minimal value of $τ_{\text{QSL}}$ and find that its behavior is dependent on the phase of initial state.

quant-ph↗