arXiv subjects

Yuan Qiu

Publications and source records attributed to Yuan Qiu.

At least 19 recordsLinked to original sources

arXiv2026

Anisotropic Rabi Model as a Noise Biased Qubit

We present the quantum anisotropic Rabi model as a potential resource for a noise biased qubit. The system-environment coupling can be biased by tuning the relative strengths of the rotating-wave and counter-rotating-wave interactions, characterized by the anisotropy parameter $\eta$. This anisotropy selectively suppresses dominant decoherence pathways, thereby enabling the construction of a protected logical qubit in the ultrastrong and deep-strong coupling regimes. The logical states (formed by the ground and first excited states of the anisotropic Rabi model) possess coherence times that are enhanced compared to the isotropic case. Moreover, we construct a set of universal gate operations within the logical-state subspace and demonstrate that the gate operations associated with different values of $\eta$ exhibit robustness against external noise. These findings are expected to inspire applications and research directions for the anisotropic Rabi model with promising potential impacts.

quant-ph↗

arXiv2026

Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations

AI-driven flood digital twins demand fast hydrodynamic surrogates for ensemble forecasting and observation assimilation. Yet even GPU-accelerated two-dimensional shallow water equation (SWE) solvers still require $\sim 55$ minutes per $96$-hour run on a $\sim 4.2$-million-active-cell metropolitan basin (the Des~Plaines River basin at $30\,\mathrm{m}$ resolution), making such workloads prohibitive at native resolution. We present the Conditional Latent Dynamics Network (CLDNet): a low-dimensional latent neural ODE driven by rainfall, paired with a coordinate-based decoder conditioned on static terrain (elevation, slope, Manning roughness) that reconstructs depth and discharge at arbitrary query points. Pointwise decoding decouples memory from grid size and handles irregular watersheds natively, enabling metropolitan-scale training on a single compute node and direct queries at exact gauge coordinates without raster snapping. We evaluate CLDNet on a synthetic $250{,}000$-cell Texas benchmark and on a new Des~Plaines case study of $114$ real-rainfall Stage~IV storms whose reference simulator we validate against United States Geological Survey (USGS) gauges at the April~2013 flood-of-record (Nash--Sutcliffe efficiency $0.57$--$0.94$ on mean-recentered water-surface elevation). CLDNet roughly halves the relative root-mean-squared error of an unconditional baseline, outperforms regular-grid VAE--ConvLSTM and FNO baselines on the Texas benchmark (both presuppose a Cartesian grid and do not apply to the irregular Des~Plaines watershed), reaches a critical success index of $\approx 86\%$ at the $0.5\,\mathrm{m}$ inundation threshold, and produces a full $96$-hour basin-wide forecast in $\sim 29$ seconds -- a $\sim 115\times$ speedup.

cs.LG↗

arXiv2026

Entanglement generation of arbitrary squeezed Fock states

We propose an efficient and robust protocol for the generation of entanglement between a superconducting qubit and a squeezed cavity. By applying a parametric drive to the cavity coupled to the qubit, the dynamical evolution of the system is precisely described by an anisotropic Rabi model within a squeezed reference frame. Utilizing high-order time-averaging methods, we analytically derive the resonance conditions and the effective Rabi frequency for the high-order three-photon process. By implementing an adiabatic passage, slowly tuning the cavity frequency across the resonance, the system is steered into a maximally entangled state, e.g., between the three-photon state $\ket{g,3}$ and the qubit excited state $\ket{e,0}$ in the squeezed picture. Numerical simulation results confirm the high fidelity and robustness of the proposed protocol. Our method provides a practical pathway for generating complex non-Gaussian entangled states, which are of significant value for fault-tolerant quantum computation and quantum metrology beyond the standard quantum limit.

quant-ph↗

arXiv2026

Interpretable Battery Aging without Extra Tests via Neural-Assisted Physics-based Modelling

State of health (SoH) is widely used for battery management, but it is a single scalar and offers limited interpretability. Two batteries with similar SoH can exhibit very different degradation behaviors and the lack of interpretability hinders optimal battery operation. In this paper, we propose IBAM for interpretable battery aging modelling with a neural-assisted physics-based framework. IBAM outputs a 2-D aging fingerprint without extra diagnostic tests and uses only routine logs from the battery management system. The fingerprint offers great interpretability by capturing a battery's curve-wide polarization voltage loss and the tail loss near the end-of-discharge. IBAM first creates a physics-based battery model based on a fractional-order equivalent circuit model, and then extracts per-cycle fingerprints from the model using a two-stage least-squares method. IBAM further anchors fingerprints on the SoH axis with physics-guided regression, where the per-cycle SoH is estimated via a bidirectional gated recurrent unit with customized multi-channel voltage features. Across batteries with short-, medium-, and long-lifespans, IBAM consistently yields the best physics model fidelity at different aging stages, and provides clear interpretations of degradation mechanisms and fingerprint patterns about batteries of different lifespans. The resulting fingerprints support interpretable battery health assessment and can inform battery control choices.

eess.SP↗

arXiv2026

Reinforcement Learning for Fast and Robust Longitudinal Qubit Readout

Longitudinal coupling offers a compelling pathway for quantum nondemolition (QND) readout, but pulse design is constrained by hardware limitations such as the coupling strength and the photon number required to stay within the linear regime. We develop a reinforcement learning framework to optimize the longitudinal coupling waveform under such constraints. Building upon the theoretical foundation of shortcuts to adiabaticity (STA), we parameterize an auxiliary trajectory with cubic B-splines and reconstruct the physical control. At a fixed short readout time, the optimized pulse converges to a constraint saturating flat-top protocol and yields a approximately $50\%$ improvement in $\mathrm{SNR}$ over an STA baseline, while exhibiting enhanced robustness to parameter drifts. Simulation results demonstrate the efficacy of reinforcement learning in optimizing longitudinal readout pulses. The optimized protocol attains substantial performance gains and yields smooth, hardware-compatible waveforms governed by an interpretable ``saturate-and-hold'' mechanism.

quant-ph↗

arXiv2026

DP-S4S: Accurate and Scalable Select-Join-Aggregate Query Processing with User-Level Differential Privacy

Answering Select-Join-Aggregate queries with DP is a fundamental problem with important applications in various domains. The current SOTA methods ensure user-level DP (i.e., the adversary cannot infer the presence or absence of any given individual user with high confidence) and achieve instance-optimal accuracy on the query results. However, these solutions involve solving expensive optimization programs, which may incur prohibitive computational overhead for large databases. One promising direction to achieve scalability is through sampling, which provides a tunable trade-off between result utility and computational costs. However, applying sampling to differentially private SJA processing is a challenge for two reasons. First, it is unclear what to sample, in order to achieve the best accuracy within a given computational budget. Second, prior solutions were not designed with sampling in mind, and their mathematical tool chains are not sampling-friendly. To our knowledge, the only known solution that applies sampling to private SJA processing is S&E, a recent proposal that (i) samples users and (ii) combines sampling directly with existing solutions to enforce DP. We show that both are suboptimal designs; consequently, even with a relatively high sample rate, the error incurred by S&E can be 10x higher than the underlying DP mechanism without sampling. Motivated by this, we propose Differentially Private Sampling for Scale (DP-S4S), a novel mechanism that addresses the above challenges by (i) sampling aggregation units instead of users, and (ii) laying the mathematical foundation for SJA processing under RDP, which composes more easily with sampling. Further, DP-S4S can answer both scalar and vector SJA queries. Extensive experiments on real data demonstrate that DP-S4S enables scalable SJA processing on large datasets under user-level DP, while maintaining high result utility.

cs.DB↗

arXiv2026

Enhancing light-matter coupling for exploring chaos in the quantum Rabi model

Accessing chaos in the quantum Rabi model (QRM) usually requires operating far from resonance, combined with ultra- or deep-strong light-matter coupling. This makes direct experiments challenging. In this manuscript, we propose a solution to this challenge by employing an anti-squeezing transformation to the bosonic field. Specifically, we demonstrate that this transformation maps a weakly coupled, two-photon driven Jaynes-Cummings model (JCM) to an effective deep-strong-coupling QRM in the squeezed-light frame. Using out-of-time-order correlator, Husimi distribution, and linear entanglement entropy, we numerically probe chaos in this coupling-enhanced platform and observe the similar chaotic phenomena as in the ideal QRM. We also find the coupling-enhanced model can drive the system deeper into the chaotic regime. This establishes coupling-enhanced method as a practical approach to study QRM chaos without requiring intrinsic ultra-strong coupling.

quant-ph↗

arXiv2025

Variationally correct operator learning: Reduced basis neural operator with a posteriori error estimation

Minimizing PDE-residual losses is a common strategy to promote physical consistency in neural operators. However, standard formulations often lack variational correctness, meaning that small residuals do not guarantee small solution errors due to the use of non-compliant norms or ad hoc penalty terms for boundary conditions. This work develops a variationally correct operator learning framework by constructing first-order system least-squares (FOSLS) objectives whose values are provably equivalent to the solution error in PDE-induced norms. We demonstrate this framework on stationary diffusion and linear elasticity, incorporating mixed Dirichlet-Neumann boundary conditions via variational lifts to preserve norm equivalence without inconsistent penalties. To ensure the function space conformity required by the FOSLS loss, we propose a Reduced Basis Neural Operator (RBNO). The RBNO predicts coefficients for a pre-computed, conforming reduced basis, thereby ensuring variational stability by design while enabling efficient training. We provide a rigorous convergence analysis that bounds the total error by the sum of finite element discretization bias, reduced basis truncation error, neural network approximation error, and statistical estimation errors arising from finite sampling and optimization. Numerical benchmarks validate these theoretical bounds and demonstrate that the proposed approach achieves superior accuracy in PDE-compliant norms compared to standard baselines, while the residual loss serves as a reliable, computable a posteriori error estimator.

math.NA↗

arXiv2025

Dissecting the superradiant phase transition in the anisotropic Rabi model: Pattern competition and cavity-QED simulation

In this manuscript, we analyze the mechanism of the superradiant phase transition in the anisotropic Rabi model under the classical oscillator limit using the pattern picture. By expanding the anisotropic Rabi model Hamiltonian in operator space, we obtained three patterns, and we find that the phase transition arises from the competition between patterns. The difficulty in achieving the classical oscillator limit motivates our investigation into the quantum phase transition within a parametrically-driven Jaynes-Cummings model. This parametrically-driven Jaynes-Cummings model can reproduce the dynamics of an ultrastrong-coupling anisotropic Rabi model in a squeezed-light frame. According to the eigenenergies and eigenstates of the normal and superradiant phases of this equivalent anisotropic Rabi model, we find that the excitation energy of the normal phase and the superradiant phase vanishes at the critical point. The photon number becomes infinite beyond the critical point. These results indicate that the system undergoes a superradiant phase transition at the critical point.

quant-ph↗

arXiv2025

Approximate DBSCAN under Differential Privacy

This paper revisits the DBSCAN problem under differential privacy (DP). Existing DP-DBSCAN algorithms aim at publishing the cluster labels of the input points. However, we show that both empirically and theoretically, this approach cannot offer any utility in the published results. We therefore propose an alternative definition of DP-DBSCAN based on the notion of spans. We argue that publishing the spans actually better serves the purposes of visualization and classification of DBSCAN. Then we present a linear-time DP-DBSCAN algorithm achieving the sandwich quality guarantee in any constant dimensions, as well as matching lower bounds on the approximation ratio. A key building block in our algorithm is a linear-time algorithm for constructing a histogram under pure-DP, which is of independent interest. Finally, we conducted experiments on both synthetic and real-world datasets to verify the practical performance of our DP-DBSCAN algorithm.

cs.CR↗

arXiv2025

Adaptive Inner Speech-Text Alignment for LLM-based Speech Translation

Recent advancement of large language models (LLMs) has led to significant breakthroughs across various tasks, laying the foundation for the development of LLM-based speech translation systems. Existing methods primarily focus on aligning inputs and outputs across modalities while overlooking deeper semantic alignment within model representations. To address this limitation, we propose an Adaptive Inner Speech-Text Alignment (AI-STA) method to bridge the modality gap by explicitly aligning speech and text representations at selected layers within LLMs. To achieve this, we leverage the optimal transport (OT) theory to quantify fine-grained representation discrepancies between speech and text. Furthermore, we utilize the cross-modal retrieval technique to identify the layers that are best suited for alignment and perform joint training on these layers. Experimental results on speech translation (ST) tasks demonstrate that AI-STA significantly improves the translation performance of large speech-text models (LSMs), outperforming previous state-of-the-art approaches. Our findings highlight the importance of inner-layer speech-text alignment in LLMs and provide new insights into enhancing cross-modal learning.

cs.CL↗

arXiv2024

Omega theorem for fractional sigma function

The research in the subfield of analytic number theory around error term of summation of sigma functions possesses a history which can be dated back to the mid-19th century when Dirichlet provided an $O(\sqrt{n})$ estimation of error term of summation of $d(n)$. Later, G. Voronoi, G. Kolesnik, and M.N. Huxley (to name just a few) contributed more on the upper bound on the error term of summation of sigma functions. As for $\Omega$-theorems, G.H. Hardy was the first contributor. Later researchers on this topic include G.H. Hardy and T.H. Gronwall, but the amount of academic effort is much sparser than $O$-theorems. This research aims to provide a better $\Omega$-bound for the error term of summation of fractional sigma function $\sigma_{\alpha}(n)$ on the range $0 < \alpha < \frac{1}{2}$, obtaining the result $\Omega((x \ln x)^{\frac{1}{4}+\frac{\alpha}{2}})$.

math.NT↗

arXiv2024

Spontaneous emission in Casimir-Rabi oscillations through a weak optomechanical coupling

The dynamical Casimir effect (DCE) describes the energy conversion from a mechanical motion to the electromagnetic fields. When the mechanical oscillator is in a mechanically excited state, the free evolution due to the DCE produces radiation in the vacuum, in analogy with the spontaneous emission from an excited atom. In this manuscript, we investigate such a spontaneous radiation process by employing the quantum trajectory approach. When the dissipation rate of the system is very low, there can be a reversible energy exchange between the mirror in the excited state and the vacuum field, and this reversible exchange is called vacuum Casimir-Rabi oscillations. Multiple quantum trajectory simulations of this process show that the number of trajectories responsible for the generation of radiation can reach a significant value when the mechanical dissipation rate is less than the photon dissipation rate. We also find that two-photon (two/three-phonon) bundle emission occurs in photon (phonon) emission. In comparison to pure two-photon and three-phonon free dissipation, the probability of two-photon bundle emission and two-phonon bundle emission are observed to be marginally elevated as a consequence of the presence of the DCE. This pattern may assist in developing a deeper comprehension of the physical characteristics of photon and phonon emission in the DCE.

quant-ph↗

arXiv2024

Generating three-photon Rabi oscillations without a large-detuning condition

It is well known that in the quantum Rabi model, a three-photon resonance occurs when the cavity field bare frequency is about 1/3 of the atomic transition frequency. In this manuscript, we show that the resonance can also be generated in the absence of the 1/3 condition by employing an artificial atom with tunable transition frequency. To realize the protocol, the modulation frequency should be comparable to the cavity frequency in order to induce a counter-rotating interaction in the effective Hamiltonian. In this way, three-photon Rabi oscillations can be observed in a small-detuning regime, thus avoiding the excitation of high-energy states. We derive an effective Hamiltonian (equivalent to the anisotropic Rabi model Hamiltonian) to determine the magnitude of the energy splitting and the resonance position. Numerical simulations results show that the protocol not only generates a three-photon resonance, but also has a detectable output photon flux. We hope the protocol can be exploited for the realization of Fock-state sources and the generation of multiparticle entanglement.

quant-ph↗

arXiv2024

Derivative-enhanced Deep Operator Network

The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a derivative-enhanced deep operator network (DE-DeepONet), which leverages derivative information to enhance the solution prediction accuracy and provides a more accurate approximation of solution-to-parameter derivatives, especially when training data are limited. DE-DeepONet explicitly incorporates linear dimension reduction of high dimensional parameter input into DeepONet to reduce training cost and adds derivative loss in the loss function to reduce the number of required parameter-solution pairs. We further demonstrate that the use of derivative loss can be extended to enhance other neural operators, such as the Fourier neural operator (FNO). Numerical experiments validate the effectiveness of our approach.

cs.LG↗

arXiv2024

Sudden change of the photon output field marks phase transitions in the quantum Rabi model

The experimental observation of quantum phase transitions predicted by the quantum Rabi model in quantum critical systems is usually challenging due to the lack of signature experimental observables associated with them. Here, we describe a method to identify the dynamical critical phenomenon in the quantum Rabi model consisting of a three-level atom and a cavity at the quantum phase transition. Such a critical phenomenon manifests itself as a sudden change of steady-state output photons in the system driven by two classical fields, when both the atom and the cavity are initially unexcited. The process occurs as the high-frequency pump field is converted into the low-frequency Stokes field and multiple cavity photons in the normal phase, while this conversion cannot occur in the superradiant phase. The sudden change of steady-state output photons is an experimentally accessible measure to probe quantum phase transitions, as it does not require preparing the equilibrium state.

quant-ph↗

arXiv2023

Differential Privacy on Dynamic Data

A fundamental problem in differential privacy is to release a privatized data structure over a dataset that can be used to answer a class of linear queries with small errors. This problem has been well studied in the static case. In this paper, we consider the dynamic setting where items may be inserted into or deleted from the dataset over time, and we need to continually release data structures so that queries can be answered at any time. We present black-box constructions of such dynamic differentially private mechanisms from static ones with only a polylogarithmic degradation in the utility. For the fully-dynamic case, this is the first such result. For the insertion-only case, similar constructions are known, but we improve them over sparse update streams.

cs.CR↗

arXiv2022

Linear recurrences of order at most two in nontrivial small divisors and large divisors

For each positive integer $N$, define $$S'_N \ =\ \{1 < d < \sqrt{N}: d|N\}\mbox{ and }L'_N \ =\ \{\sqrt{N} < d < N : d|N\}.$$ Recently, Chentouf characterized all positive integers $N$ such that the set of small divisors $\{d\le \sqrt{N}: d|N\}$ satisfies a linear recurrence of order at most two. We nontrivially extend the result by excluding the trivial divisor $1$ from consideration, which dramatically increases the analysis complexity. Our first result characterizes all positive integers $N$ such that $S'_N$ satisfies a linear recurrence of order at most two. Moreover, our second result characterizes all positive $N$ such that $L'_N$ satisfies a linear recurrence of order at most two, thus extending considerably a recent result that characterizes $N$ with $L'_N$ being in an arithmetic progression.

math.NT↗