arXiv subjects

Yidong Zhou

Publications and source records attributed to Yidong Zhou.

At least 19 recordsLinked to original sources

arXiv2026

The optimal $\chi$-bound for $\{P_6, \text{dart}, K_4\}$-free graphs

A \textit{diamond} is a graph obtained from $K_4$ by removing an edge, and a \textit{dart} is a graph obtained from a diamond by adding a pendant edge to a vertex of degree 3. We prove that every $\{P_6, \text{dart}, K_4\}$-free graph is 6-colorable. This improves the previous bound of 7 due to Hong and Xu \cite{HongXu2025} and resolves their open question on the optimality of the bound. Our result also extends a theorem of Karthick and Mishra~\cite{KarthickMishra2018}, who proved 6-colorability for the class of $\{P_6, \text{diamond}, K_4\}$-free graphs.

math.CO↗

arXiv2026

SQD-Enabled Circuit Compression for Resource-Efficient Quantum Chemistry

Sample-based Quantum Diagonalization (SQD) recovers ground-state energies by classically diagonalizing a Hamiltonian in the subspace spanned by quantum samples, requiring only bitstrings with sufficient ground-state overlap rather than an accurate variational energy. We reveal and exploit this underexplored robustness property: how much non-Clifford and variational expressivity can be removed from the sampling circuit before SQD accuracy degrades? We answer through two complementary compression techniques: gradient-based operator pruning, which discards low-impact excitation operators, and Clifford rounding, which snaps remaining parameters to the nearest Clifford angle. Both of these techniques can be applied to a VQE ansatz on a qubit-reduced Hamiltonian. A systematic ablation study across 21 molecules shows that median SQD error stays within chemical accuracy even at 50\% compression on both axes, while simulation speedup reaches $33\times$. Hardware validation on 6 molecules on IBM quantum hardware confirms up to $2.8\times$ transpiled-depth reduction with zero loss in SQD accuracy. Our implementation can be found at: https://github.com/zkysfls/cs-vqe-sqd

quant-ph↗

arXiv2026

Q-Score: A Quantum-Native Scoring Function for Molecular Docking

Molecular docking predicts how a small molecule binds to a protein and is a key bottleneck in drug discovery. Classical scoring functions sum empirical pairwise contacts, blind to quantum-mechanical effects like orbital charge transfer that govern binding specificity. We introduce Q-Score, encoding GNN-predicted orbital donor-acceptor energies into a weighted graph and scoring binding by solving a maximum-weight vertex clique problem via Digitized-Counterdiabatic QAOA. Each interaction anchor maps to one qubit and compatibility constraints become edges. Across 11 protein targets, DC-QAOA recovers the exact optimum on 8 at 10 qubits. On 1000 AI-generated molecules, Q-Score is orthogonal to classical scoring with Spearman rho of 0.05, driven by orbital quality with rho of 0.90, and free of molecular-weight bias, enriching for strong orbital interactions at twice the random rate. DC-QAOA achieves a mean approximation ratio of 0.94 with 52 percent exact. Execution of 1000 circuits on IBM Eagle confirms 6-qubit solvability on NISQ hardware.

physics.chem-ph↗

arXiv2026

Coset Ensemble Decoder for Quantum Error Correction with Algorithm-Hardware Co-Design

Reliable large-scale quantum computation relies on fault-tolerant architectures, where quantum error correction (QEC) continuously extracts and decodes error syndromes in real time. A critical component in QEC is the decoder, a classical subsystem that must simultaneously deliver high logical accuracy and ultra-low latency. This paper presents a novel algorithm-hardware co-design that improves the accuracy-latency trade-off over existing approaches such as vanilla Minimum-Weight Perfect Matching (MWPM) and Union-Find (UF) decoders. At the algorithmic level, we introduce coset ensemble decoding, which improves UF decoding by explicitly exploiting logically equivalent cosets. Our method performs ensemble forest exploration to generate multiple coset-consistent candidates and aggregates them to approximate coset-level maximum-likelihood decoding. We further reduce computational and memory complexity via reverse-order elimination and lossless graph compression, without sacrificing accuracy. At the hardware level, we design a domain-specific architecture that temporally reuses resources, avoiding the code-distance-proportional resource growth in prior spatial architectures. Several optimizations, such as multi-bank memory hashing and hierarchical ID mapping, are proposed to mitigate pipeline stalls and memory conflicts under highly concurrent access patterns. Under a circuit-level depolarizing noise model, our co-design approach achieves a better accuracy-latency trade-off than prior MWPM- and UF-based decoders, while reducing FPGA LUT consumption by up to 8.2 times compared with reported UF-based decoder resources. The tunable candidate number further exposes a flexible design knob, enabling users to tailor decoding performance to the requirements of different fault-tolerant workloads. Our implementation is publicly available at https://github.com/IMSeonL/coset-ensemble-decoder.

cs.AR↗

arXiv2026

Deep Single-Index Fr\'echet Regression

Predicting outputs that are located in non-Euclidean spaces, such as probability distributions, networks, and symmetric positive-definite matrices, is becoming increasingly important in modern data analysis, particularly when inputs are high-dimensional. We propose DeSI (Deep Single-Index Fr\'echet Regression), a semiparametric framework for regression with metric space-valued outputs and multivariate inputs that assumes a single-index structure for the conditional Fr\'echet mean. DeSI estimates an interpretable index direction, which quantifies the relative importance of inputs, using a deep neural network, and performs Fr\'echet regression along the resulting one-dimensional index in the target metric space. This structure mitigates the curse of dimensionality while retaining interpretability, which stands in contrast to standard deep neural networks. We establish theoretical guarantees for DeSI, including uniform approximation and convergence rates, and demonstrate its strong predictive performance through simulations on distributions, networks, and symmetric positive-definite matrices, as well as an application to compositional mood data from New Jersey.

stat.ML↗

arXiv2026

Erd\H{o}s-Hajnal conjecture beyond five-vertex graphs

In 1989, Erd\H{o}s and Hajnal conjectured that for any graph $H$, there is a constant $c=c(H)>0$ such that every $n$-vertex graph $G$ with no induced copies of $H$ contains a clique or an independent set of size at least $n^{c}$. This conjecture, known as the Erd\H{o}s-Hajnal conjecture, is a central open problem in combinatorics and listed as one of the top 10 Erd\H{o}s problems by Bloom on the Erd\H{o}s problem website https://www.erdosproblems.com/. In a recent breakthrough, Nguyen, Scott and Seymour proved that Erd\H{o}s-Hajnal conjecture holds for the case when $H$ is the five-vertex path, which, combined with known results, implies that Erd\H{o}s-Hajnal conjecture holds for every five-vertex graph. In this paper, we extend the iterative sparsification framework recently developed by Nguyen, Scott and Seymour. We introduce a generalized niceness condition relaxing their nice condition, a novel intermediate property concerning combs and a general structural lemma (which may be of independent interest) that is sufficient to deduce the Erd\H{o}s-Hajnal conjecture. This framework simultaneously recovers the recent result on the five-vertex path (PLMS 2026) and the classical result on the bull graph by Chudnovsky and Safra (JCTB 2008) as special cases, thereby unifying these two previously independent strands, and further proves the conjecture for two new cases: the E-graph (which contains the five-vertex path) and the Bird graph (which contains both the five-vertex path and the bull). These are the first two six-vertex graphs whose validity does not follow from the known operations (see Alon-Pach-Solymosi, Combinatorica 2001, and Nguyen-Scott-Seymour, TAMS 2026) that preserve the Erd\H{o}s-Hajnal property.

math.CO↗

arXiv2026

Compiler Framework for Directional Transport in Zoned Neutral Atom Systems with AOD Assistance: A Hybrid Remote CZ Approach

We present a directional-transport (DT)-based remote CZ gate and compiler for zoned neutral-atom arrays that overcomes movement-bound entanglement limitations. Current AOD-based shuttling faces row/column non-crossing constraints, device-speed limits, and hardware-restricted range - bottlenecks for long-distance connectivity. Our approach reserves AODs for channel setup and micro-tuning while making DT the default for remote entanglement. Under antiblockade, a detuning-modulated pi-pulse sequence drives directional transport of a Rydberg excitation along a dynamic and resettable ancilla corridor, realizing a CZ gate between stationary, non-adjacent qubits. This cuts entangling-stage duration by approximately 50 to 90 percent versus AOD-only baselines and enables long-distance connectivity beyond objective-limited shuttling.

quant-ph↗

arXiv2026

The optimal chromatic bound for even-hole-free graphs without induced seven-vertex paths

The class of even-hole-free graphs has been extensively studied on its own and on its relation to perfect graphs. In this paper, we study the $χ$-boundedness of even-hole-free graphs which itself is an important topic in graph theory. In particular, we prove that every even-hole-free graph $G$ without induced 7-vertex paths satisfies $χ(G)\le \lceil\frac{5}{4}ω(G)\rceil$, where $χ(G)$ and $ω(G)$ denote the chromatic number and clique number of $G$, respectively. This bound is optimal. Our result strictly extends the result of Karthick and Maffary \cite{KM19} on even-hole-free graphs without induced 6-vertex paths, and implies that even-hole-free graphs without induced 7-vertex paths satisfy Reed's Conjecture. Our proof relies on a heavy structural analysis on a maximal substructure called a nice blowup of a five-cycle and can be viewed for graphs in which all holes are of length five (graphs with all holes having the same length gain increasing interest in recent years \cite{COOK202496}). Our result gives a partial answer to a conjecture of Wang and Wu \cite{WW25} on graphs in which all holes are of length 5. One of the key technical ingredients is a technical lemma proved via clique cutset argument combined with the idea of Infinite Descent Method (often used in number theory).

math.CO↗

arXiv2026

Reinforcement Learning for Enhanced Advanced QEC Architecture Decoding

The advent of promising quantum error correction (QEC) codes with efficient resource utilization and high-performance fault-tolerant quantum memories signifies a critical step towards realizing practical quantum computation. While surface codes have been a dominant approach, their limitations have spurred the development of more advanced QEC architectures. These advanced codes often present increased complexity, demanding innovative decoding methodologies. This work investigates the application of reinforcement learning (RL) techniques, including hybrid and multi-agent approaches, to enhance the decoding of various advanced QEC architectures. By leveraging the ability of RL to learn optimal strategies from noisy syndrome measurements, we explore the potential for achieving improved logical error rates and scalability compared to traditional decoding methods. Our approach examines the adaptation of reinforcement learning to exploit the structural properties of these modern QEC models. We also explore the benefits of combining different RL algorithms to address the multifaceted nature of the decoding problem, considering factors such as code degeneracy and real-world noise characteristics. With our proposed method, we are able to demonstrate that an autonomously trained agent can derive decoding schemes for the complex decoding requirement of advanced QEC architectures.

quant-ph↗

arXiv2025

Three-coloring triangle-free graphs without long forbidden paths

A graph $G$ is $k$-vertex-critical if $χ(G)=k$, but $χ(G')<k$ for every proper induced subgraph $G'$ of $G$. For a family of graphs $\mathcal{F}$, $G$ is $\mathcal{F}$-free if no graph $F \in \mathcal{F}$ is an induced subgraph of $G$. We show that there are exactly three 4-vertex-critical $\{P_7,C_3\}$-free graphs containing an induced $C_7$, thereby settling the first of the two cases of a conjecture by Goedgebeur and Schaudt [J.~Graph Theory, 87:188--207, 2018]. Moreover, we show that all $\{P_5+P_1,C_3\}$-free graphs are $3$-colorable and by combining our result with known results from the literature, we completely characterize the maximum chromatic number of $\{F,C_3\}$-free graphs if $F$ is a six-vertex induced subgraph of $P_7$. Finally, we construct an infinite family of $4$-vertex-critical $\{4K_2,C_3\}$-free graphs. These graphs are also $\{P_{11},C_3\}$-free and this is the first value of $t$ for which an infinite family of $4$-vertex-critical $\{P_{t},C_3\}$-free graphs is known.

math.CO↗

arXiv2025

3-Coloring $P_t$-Free Graphs With Only One Prescribed Induced Odd Cycle Length

A graph is $P_t$-free if it contains no induced subgraph isomorphic to a $t$-vertex path. A graph is not bipartite if and only if it contains an induced subgraph isomorphic to a $k$-vertex cycle, where $k$ is odd. We focus on the 3-coloring problem for $P_t$-free graphs that have only one prescribed induced odd cycle length. For any integer $t$ and any odd integer $k$, let $\mathcal{G}_{t,k}$ be the class of graphs that are $P_{t}$-free and all their induced odd cycles must be $C_k$. In this paper, we present a polynomial-time algorithm that solves the 3-coloring problem for any graph in $\mathcal{G}_{10,7}$.

math.CO↗

arXiv2025

Quantum-machine-assisted Drug Discovery

Drug discovery is lengthy and expensive, with traditional computer-aided design facing limits. This paper examines integrating quantum computing across the drug development cycle to accelerate and enhance workflows and rigorous decision-making. It highlights quantum approaches for molecular simulation, drug-target interaction prediction, and optimizing clinical trials. Leveraging quantum capabilities could accelerate timelines and costs for bringing therapies to market, improving efficiency and ultimately benefiting public health.

quant-ph↗

arXiv2025

Sensitivity Analysis when Generalizing Causal Effects from Multiple Studies to a Target Population: Motivation from the ECHO Program

Unobserved effect modifiers can induce bias when generalizing causal effect estimates to target populations. In this work, we extend a sensitivity analysis framework assessing the robustness of study results to unobserved effect modification that adapts to various generalizability scenarios, including multiple (conditionally) randomized trials, observational studies, or combinations thereof. This framework is interpretable and does not rely on distributional or functional assumptions about unknown parameters. We demonstrate how to leverage the multi-study setting to detect violation of the generalizability assumption through hypothesis testing, showing with simulations that the proposed test achieves high power under real-world sample sizes. Finally, we apply our sensitivity analysis framework to analyze the generalized effect estimate of secondhand smoke exposure on birth weight using cohort sites from the Environmental influences on Child Health Outcomes (ECHO) study.

stat.ME↗

arXiv2025

Wasserstein Transfer Learning

Transfer learning is a powerful paradigm for leveraging knowledge from source domains to enhance learning in a target domain. However, traditional transfer learning approaches often focus on scalar or multivariate data within Euclidean spaces, limiting their applicability to complex data structures such as probability distributions. To address this limitation, we introduce a novel transfer learning framework for regression models whose outputs are probability distributions residing in the Wasserstein space. When the informative subset of transferable source domains is known, we propose an estimator with provable asymptotic convergence rates, quantifying the impact of domain similarity on transfer efficiency. For cases where the informative subset is unknown, we develop a data-driven transfer learning procedure designed to mitigate negative transfer. The proposed methods are supported by rigorous theoretical analysis and are validated through extensive simulations and real-world applications. The code is available at https://github.com/h7nian/WaTL

cs.LG↗

arXiv2025

Sliced Wasserstein Regression

While statistical modeling of distributional data has gained increased attention, the case of multivariate distributions has been somewhat neglected despite its relevance in various applications. This is because the Wasserstein distance, commonly used in distributional data analysis, poses challenges for multivariate distributions. A promising alternative is the sliced Wasserstein distance, which offers a computationally simpler solution. We propose distributional regression models with multivariate distributions as responses paired with Euclidean vector predictors. The foundation of our methodology is a slicing transform from the multivariate distribution space to the sliced distribution space for which we establish a theoretical framework, with the Radon transform as a prominent example. We introduce and study the asymptotic properties of sample-based estimators for two regression approaches, one based on utilizing the sliced Wasserstein distance directly in the multivariate distribution space, and a second approach based on a new slice-wise distance, employing a univariate distribution regression for each slice. Both global and local Fréchet regression methods are deployed for these approaches and illustrated in simulations and through applications. These include joint distributions of excess winter death rates and winter temperature anomalies in European countries as a function of base winter temperature and also data from finance.

stat.ME↗

arXiv2025

End-to-End Deep Learning for Predicting Metric Space-Valued Outputs

Many modern applications involve predicting structured, non-Euclidean outputs such as probability distributions, networks, and symmetric positive-definite matrices. These outputs are naturally modeled as elements of general metric spaces, where classical regression techniques that rely on vector space structure no longer apply. We introduce E2M (End-to-End Metric regression), a deep learning framework for predicting metric space-valued outputs. E2M performs prediction via weighted Fr\'echet means over training outputs, where the weights are learned by a neural network conditioned on the input. This construction provides a principled mechanism for geometry-aware prediction that avoids surrogate embeddings and restrictive parametric assumptions, while fully preserving the intrinsic geometry of the output space. We establish theoretical guarantees, including a universal approximation theorem that characterizes the expressive capacity of the model and a convergence analysis of the entropy-regularized training objective. Through extensive simulations involving probability distributions, networks, and symmetric positive-definite matrices, we show that E2M consistently achieves state-of-the-art performance, with its advantages becoming more pronounced at larger sample sizes. Applications to human mortality distributions and New York City taxi networks further demonstrate the flexibility and practical utility of this framework.

stat.ML↗

arXiv2025

Fréchet Geodesic Boosting

Gradient boosting has become a cornerstone of machine learning, enabling base learners such as decision trees to achieve exceptional predictive performance. While existing algorithms primarily handle scalar or Euclidean outputs, increasingly prevalent complex-structured data, such as distributions, networks, and manifold-valued outputs, present challenges for traditional methods. Such non-Euclidean data lack algebraic structures such as addition, subtraction, or scalar multiplication required by standard gradient boosting frameworks. To address these challenges, we introduce Fréchet geodesic boosting (FGBoost), a novel approach tailored for outputs residing in geodesic metric spaces. FGBoost leverages geodesics as proxies for residuals and constructs ensembles in a way that respects the intrinsic geometry of the output space. Through theoretical analysis, extensive simulations, and real-world applications, we demonstrate the strong performance and adaptability of FGBoost, showcasing its potential for modeling complex data.

stat.ML↗

arXiv2025

Regression Discontinuity Designs for Functional Data and Random Objects in Geodesic Spaces

Regression discontinuity designs (RDDs) are widely used for causal inference in observational studies with cutoff-based treatment assignment, primarily for Euclidean outcomes. We propose the geodesic regression discontinuity design (GRDD), which extends RDDs to complex non-Euclidean outcomes, including networks, compositional data, functional data, and other random objects in geodesic metric spaces. Since algebraic operations are unavailable in such spaces, we define the causal effect at the cutoff as the geodesic connecting the local Fr\'echet means of untreated and treated outcomes, recovering the classical local average treatment effect in the scalar case. Estimation is conducted intrinsically via local Fr\'echet regression to preserve geometric validity and interpretability. For inference, we adopt an extrinsic approach by embedding the metric space into a Hilbert space, enabling tractable asymptotic analysis. We establish asymptotic normality and develop bootstrap-based procedures for hypothesis testing and confidence intervals for the treatment effect magnitude. We also propose a data-adaptive bandwidth selection method tailored to RDDs in metric spaces and study its empirical performance. Applications include compositional voting outcomes in UK elections and daily CO concentration curves after the Taipei metro introduction, and we extend the framework to fuzzy designs with imperfect compliance.

stat.ME↗