arXiv subjects

Qiyu Liu

Publications and source records attributed to Qiyu Liu.

16 recordsLinked to original sources

arXiv2026

Universal correlations in the Abelian sandpile model

We numerically study the bulk correlation functions in the two-dimensional Abelian sandpile model, aiming both to compare with the predictions of logarithmic conformal field theory and to extend the analysis to lattices where analytical methods are difficult to apply. Wilson's algorithm efficiently generates large-scale uniform spanning trees in parallel, which can be mapped to independent recurrent configurations via the Majumdar--Dhar burning bijection, eliminating sample autocorrelations and yielding fast convergence. On the square (single-sublattice) and honeycomb (two-sublattice) lattices our results agree well with the analytical predictions. For the kagome lattice we provide the first systematic numerical study of the bulk correlation functions, and cross-check the bulk height-1 probability against a closed-form analytical expression that we also derive here via the lattice Green function.

math-ph↗

arXiv2026

Cache-Aware I/O Cost Modeling for Disk-Based Learned Indexes

Learned indexes have shown attractive space-time trade-offs in main-memory settings, yet a principled I/O cost model for their disk-resident deployments is still missing, which is a prerequisite for index tuning and query optimization. The practically employed page buffer makes the problem even harder: under typical cache policies, many of the logical page references issued by the index are served by the buffer rather than reaching disk, so the effective physical I/O depends jointly on the workload, the cache policy, and the index configuration. In this paper, we propose CAM, the \textit{first} cache-aware I/O cost model for learned indexes that takes practical cache eviction policies into consideration. CAM is not tied to a particular learned index design: it estimates page access distributions without full trace replay for mainstream learned index designs, and then combines them with I/O cost models to estimate effective physical I/Os. This formulation enables principled knob tuning by explicitly modeling the trade-off between index footprint and buffer capacity. We instantiate CAM for disk-based PGM-index and RMI, and further apply the same modeling principle to learned-index-based joins through a hybrid strategy that adaptively chooses point or range probes based on local key density. Extensive experiments on real benchmarks show that CAM provides \textit{accurate and efficient} I/O estimation across diverse workloads: CAM-guided tuning improves PGM throughput by \textbf{1.17$\times$} over multicriteria PGM tuning and improves RMI throughput by \textbf{1.66$\times$} over CDFShop with I/O-related considerations. For learned-index-based joins, our hybrid strategy improves end-to-end performance by up to \textbf{8.8$\times$} over disk-based index nested-loop join.

cs.DB↗

arXiv2026

Continuous unitary transformations using tensor network representations access the full many-body localized spectrum

We develop variational continuous unitary transformations (VCUTs), which integrate Wegner-Wilson flow equations with tensor network techniques to approximately diagonalize many-body localized (MBL) Hamiltonians. The diagonalizing unitary is represented as a matrix product operator whose bond dimension controls the accuracy. For the disordered Heisenberg chain, VCUTs accurately reproduces the full spectrum across the ergodic-to-MBL crossover at small system sizes and scales to $L = 48$ sites. Beyond eigenenergies, the method can track the spatial entanglement structure of the diagonalizing unitary $U(l)$ at each flow step, enabling identification of local integrals of motion deep in the MBL phase.

cond-mat.dis-nn↗

arXiv2026

A biased-erasure cavity qubit with hardware-efficient quantum error detection

Erasure qubits are beneficial for quantum error correction due to their relaxed threshold requirements. While dual-rail erasure qubits have been demonstrated with a strong error hierarchy in circuit quantum electrodynamics, biased-erasure qubits -- where erasures originate predominantly from one logical basis state -- offer further advantages. Here, we realize a hardware-efficient biased-erasure qubit encoded in the vacuum and two-photon Fock states of a single microwave cavity. The qubit exhibits an erasure bias ratio of over 265. By using a transmon ancilla for logical measurements and mid-circuit erasure detections, we achieve logical state assignment errors below 1% and convert over 99.3% leakage errors into detected erasures. After postselection against erasures, we achieve effective logical relaxation and dephasing rates of $(6.2~\mathrm{ms})^{-1}$ and $(3.1~\mathrm{ms})^{-1}$, respectively, which exceed the erasure error rate by factors of 31 and 15, establishing a strong error hierarchy within the logical subspace. These postselected error rates indicate a coherence gain of about 6.0 beyond the break-even point set by the best physical qubit encoded in the two lowest Fock states in the cavity. Moreover, randomized benchmarking with interleaved erasure detections reveals a residual logical gate error of 0.29%. This work establishes a compact and hardware-efficient platform for biased-erasure qubits, promising concatenations into outer-level stabilizer codes toward fault-tolerant quantum computation.

quant-ph↗

arXiv2025

CARPO: Leveraging Listwise Learning-to-Rank for Context-Aware Query Plan Optimization

Efficient data processing is increasingly vital, with query optimizers playing a fundamental role in translating SQL queries into optimal execution plans. Traditional cost-based optimizers, however, often generate suboptimal plans due to flawed heuristics and inaccurate cost models, leading to the emergence of Learned Query Optimizers (LQOs). To address challenges in existing LQOs, such as the inconsistency and suboptimality inherent in pairwise ranking methods, we introduce CARPO, a generic framework leveraging listwise learning-to-rank for context-aware query plan optimization. CARPO distinctively employs a Transformer-based model for holistic evaluation of candidate plan sets and integrates a robust hybrid decision mechanism, featuring Out-Of-Distribution (OOD) detection with a top-k fallback strategy to ensure reliability. Furthermore, CARPO can be seamlessly integrated with existing plan embedding techniques, demonstrating strong adaptability. Comprehensive experiments on TPC-H and STATS benchmarks demonstrate that CARPO significantly outperforms both native PostgreSQL and Lero, achieving a Top-1 Rate of 74.54% on the TPC-H benchmark compared to Lero's 3.63%, and reducing the total execution time to 3719.16 ms compared to PostgreSQL's 22577.87 ms.

cs.DB↗

arXiv2025

Investigating Stark many-body localization with continuous unitary transformation flows

We investigate the ergodicity-to-localization transition in interacting fermion systems subjected to a spatially uniform electric field. For that we employ the recently proposed Tensorflow Equations (TFE), a type of continuous unitary flow equations. This enables us to iteratively determine an approximate diagonal basis of the quantum many-body system. We present improvements to the method, which achieves good accuracy at small to intermediate interaction strengths, even in the absence of an electric field or disorder. Then, we examine two quantities that reveal the fate of Stark MBL in 1D and 2D. First, we investigate the structure of the resulting basis to determine the crossover between ergodic and localized regimes with respect to electric field strength. Second, we simulate long-time dynamics at infinite temperature. Our results in 1D show a localization transition at non-zero field for finite interaction that vanishes with increasing system size leading to localization at infinitesimally small field even in the presence of interactions. In 2D we find less clear signatures of localization and strong finite size effects. We establish that the TFE work accurately up to intermediate times but cannot capture higher order effects in interaction strength that lead to delocalization at longer times in finite-size Stark MBL systems.

cond-mat.dis-nn↗

arXiv2025

Relaxation dynamics of a quantum spin coupled to a topological edge state

A classical impurity spin coupled to the spinful Su-Schrieffer-Heeger (SSH) chain is known to exhibit complex switching dynamics with incomplete spin relaxation. Here, we study the corrections that result from a full quantum treatment of the impurity spin. We find that in the topologically trivial case, the quantum spin behaves similarly to the classical one due to the absence of the Kondo effect for the trivial insulator. In the topological case, the quantum spin is significantly less likely to relax: It can be stuck at a pre-relaxation plateau with a sizable deviation from the expected relaxed value, and there is a large parameter regime where it does not relax at all but features an anomalously large Larmor frequency. Furthermore, we find an additional quantum effect where the pre-relaxation plateau can be hyperpolarized, i.e., the spin is stuck at a polarization value larger than the ground-state expectation value. This is possible due to the (incomplete) Kondo screening of the quantum spin, which is absent in the classical case. Our results are obtained via the ground state density matrix renormalization group (DMRG) algorithm and the time-dependent variational principle (TDVP), where the charge-SU(2) symmetry of the problem was exploited. Furthermore, we introduce and benchmark a method to predict the dynamics from the given numerical data based on the sparse identification of nonlinear dynamics (SINDy). This allows us to prolong the simulation timescale by a factor of 2.5, up to a maximal time of $10^3$ inverse hoppings.

cond-mat.str-el↗

arXiv2025

Piecewise Linear Approximation in Learned Index Structures: Theoretical and Empirical Analysis

A growing trend in the database and system communities is to augment conventional index structures, such as B+-trees, with machine learning (ML) models. Among these, error-bounded Piecewise Linear Approximation ($ε$-PLA) has emerged as a popular choice due to its simplicity and effectiveness. Despite its central role in many learned indexes, the design and analysis of $ε$-PLA fitting algorithms remain underexplored. In this paper, we revisit $ε$-PLA from both theoretical and empirical perspectives, with a focus on its application in learned index structures. We first establish a fundamentally improved lower bound of $Ω(κ\cdot ε^2)$ on the expected segment coverage for existing $ε$-PLA fitting algorithms, where $κ$ is a data-dependent constant. We then present a comprehensive benchmark of state-of-the-art $ε$-PLA algorithms when used in different learned data structures. Our results highlight key trade-offs among model accuracy, model size, and query performance, providing actionable guidelines for the principled design of future learned data structures.

cs.DB↗

arXiv2024

Learned Data Compression: Challenges and Opportunities for the Future

Compressing integer keys is a fundamental operation among multiple communities, such as database management (DB), information retrieval (IR), and high-performance computing (HPC). Recent advances in \emph{learned indexes} have inspired the development of \emph{learned compressors}, which leverage simple yet compact machine learning (ML) models to compress large-scale sorted keys. The core idea behind learned compressors is to \emph{losslessly} encode sorted keys by approximating them with \emph{error-bounded} ML models (e.g., piecewise linear functions) and using a \emph{residual array} to guarantee accurate key reconstruction. While the concept of learned compressors remains in its early stages of exploration, our benchmark results demonstrate that an SIMD-optimized learned compressor can significantly outperform state-of-the-art CPU-based compressors. Drawing on our preliminary experiments, this vision paper explores the potential of learned data compression to enhance critical areas in DBMS and related domains. Furthermore, we outline the key technical challenges that existing systems must address when integrating this emerging methodology.

cs.DB↗

arXiv2024

Why Are Learned Indexes So Effective but Sometimes Ineffective?

Learned indexes have attracted significant research interest due to their ability to offer better space-time trade-offs compared to traditional B+-tree variants. Among various learned indexes, the PGM-Index based on error-bounded piecewise linear approximation is an elegant data structure that has demonstrated \emph{provably} superior performance over conventional B+-tree indexes. In this paper, we explore two interesting research questions regarding the PGM-Index: (a) \emph{Why are PGM-Indexes theoretically effective?} and (b) \emph{Why do PGM-Indexes underperform in practice?} For question~(a), we first prove that, for a set of $N$ sorted keys, the PGM-Index can, with high probability, achieve a lookup time of $O(\log\log N)$ while using $O(N)$ space. To the best of our knowledge, this is the \textbf{tightest bound} for learned indexes to date. For question~(b), we identify that querying PGM-Indexes is highly memory-bound, where the internal error-bounded search operations often become the bottleneck. To fill the performance gap, we propose PGM++, a \emph{simple yet effective} extension to the original PGM-Index that employs a mixture of different search strategies, with hyper-parameters automatically tuned through a calibrated cost model. Extensive experiments on real workloads demonstrate that PGM++ establishes a new Pareto frontier. At comparable space costs, PGM++ speeds up index lookup queries by up to $\mathbf{2.31\times}$ and $\mathbf{1.56\times}$ when compared to the original PGM-Index and state-of-the-art learned indexes.

cs.DB↗

arXiv2024

How Good Are Multi-dimensional Learned Indices? An Experimental Survey

Efficient indexing is fundamental for multi-dimensional data management and analytics. An emerging tendency is to directly learn the storage layout of multi-dimensional data by simple machine learning models, yielding the concept of Learned Index. Compared with the conventional indices used for decades (e.g., kd-tree and R-tree variants), learned indices are empirically shown to be both space- and time-efficient on modern architectures. However, there lacks a comprehensive evaluation of existing multi-dimensional learned indices under a unified benchmark, which makes it difficult to decide the suitable index for specific data and queries and further prevents the deployment of learned indices in real application scenarios. In this paper, we present the first in-depth empirical study to answer the question of how good multi-dimensional learned indices are. Six recently published indices are evaluated under a unified experimental configuration including index implementation, datasets, query workloads, and evaluation metrics. We thoroughly investigate the evaluation results and discuss the findings that may provide insights for future learned index design.

cs.DB↗

arXiv2021

Direct Visualization of Gigahertz Acoustic Wave Propagation in Suspended Phononic Circuits

We report direct visualization of gigahertz-frequency Lamb waves propagation in aluminum nitride phononic circuits by transmission-mode microwave impedance microscopy (TMIM). Consistent with the finite-element modeling, the acoustic eigenmodes in both a horn-shaped coupler and a sub-wavelength waveguide are revealed in the TMIM images. Using fast Fourier transform filtering, we quantitatively analyze the acoustic loss of individual Lamb modes along the waveguide and the power coupling coefficient between the waveguide and the parabolic couplers. Our work provides insightful information on the propagation, mode conversion, and attenuation of acoustic waves in piezoelectric nanostructures, which is highly desirable for designing and optimizing phononic devices for microwave signal processing and quantum information transduction.

cond-mat.mes-hall↗

arXiv2019

Scalable Community Detection over Geo-Social Network

We consider a community finding problem called Co-located Community Detection (CCD) over geo-social networks, which retrieves communities that satisfy both high structural tightness and spatial closeness constraints. To provide a solution that benefits from existing studies on community detection, we decouple the spatial constraint from graph structural constraint and propose a uniform CCD framework which gives users the freedom to choose customized measurements for social cohesiveness (e.g., $k$-core or $k$-truss). For the spatial closeness constraint, we apply the bounded radius spatial constraint and develop an exact algorithm together with effective pruning rules. To further improve the efficiency and make our framework scale to a very large scale of data, we propose a near-linear time approximation algorithm with a constant approximation ratio ($\sqrt{2}$). We conduct extensive experiments on both synthetic and real-world datasets to demonstrate the efficiency and effectiveness of our algorithms.

cs.DB↗

arXiv2019

Electromechanical Brillouin scattering in integrated optomechanical waveguides

In the well-known stimulated Brillouin scattering (SBS) process, spontaneous acoustic phonons in materials are stimulated by laser light and scatter the latter into a Stokes sideband. SBS becomes more pronounced in optical fibers and has been harnessed to amplify optical signals and even achieve lasing. Exploitation of SBS has recently surged on integrated photonics platforms as simultaneous confinement of photons and phonons in waveguides leads to drastically enhanced interaction. Instead of being optically stimulated, coherent phonons can also be electromechanically excited with very high efficiency as has been exploited in radiofrequency acoustic filters. Here, we demonstrate electromechanically excited Brillouin scattering in integrated optomechanical waveguides made of piezoelectric material aluminum nitride (AlN). Acoustic phonons of 16 GHz in frequency are excited with nanofabricated electromechanical transducers to scatter counter-propagating photons in the waveguide into a single anti-Stokes sideband. We show that phase-matching conditions of Brillouin scattering can be tuned by varying both the optical wavelength and the acoustic frequency to realize tunable single-sideband modulation. Combining Brillouin scattering photonics with nanoelectromechanical systems, our approach provides an efficient interface between microwave and optical photons that will be important for microwave photonics and potentially quantum transduction.

physics.optics↗

arXiv2015

Acousto-optic modulation of a photonic crystal nanocavity with Lamb waves in microwave K band

Integrating nanoscale electromechanical transducers and nanophotonic devices potentially can enable new acousto-optic devices to reach unprecedented high frequencies and modulation efficiency. Here, we demonstrate acousto-optic modulation of a photonic crystal nanocavity using Lamb waves with frequency up to 19 GHz, reaching the microwave K band. The devices are fabricated in suspended aluminum nitride membrane. Excitation of acoustic waves is achieved with interdigital transducers with periods as small as 300 nm. Confining both acoustic wave and optical wave within the thickness of the membrane leads to improved acousto-optic modulation efficiency in the new devices than that obtained in previous surface acoustic wave devices. Our system demonstrates a novel scalable optomechanical platform where strong acousto-optic coupling between cavity-confined photons and high frequency traveling phonons can be explored.

physics.optics↗

arXiv2015

Nanophotonic cavity optomechanics with propagating phonons in microwave Ku band

Sideband-resolved coupling between multiple photonic nanocavities and propagating mechanical waves in microwave Ku-band is demonstrated. Coherent and strong photon-phonon interaction is manifested with optomechanically induced transparency and absorption, and phase-coherent interaction in multiple cavities. Inside an echo chamber it is shown that a phonon pulse can interact with an embedded nanocavity for multiple times. Our device provides a scalable platform to optomechanically couple phonons and photons for microwave photonics and quantum photonics.

physics.optics↗