arXiv subjects

Lily Wang

Publications and source records attributed to Lily Wang.

11 recordsLinked to original sources

arXiv2026

A polynomial-time approximation scheme for minimum-weight decoding of topological codes

Two-dimensional topological translationally invariant (2D TTI) stabilizer codes lie at the heart of fault-tolerant quantum computation, but using them requires solving the decoding problem. Minimum-weight decoding of these codes was recently shown to be NP-hard, even in basic settings, such as the color code with Pauli $Z$ errors and the toric code with Pauli $X$, $Y$ and $Z$ errors. Here, we prove that minimum-weight decoding of 2D TTI codes nonetheless admits a polynomial-time approximation scheme (PTAS), i.e., for any constant $\varepsilon>0$, a recovery operator of weight within a multiplicative factor of $1+\varepsilon$ of the minimum can be found in polynomial time. Our approach builds on Arora's PTAS for Euclidean problems, such as the traveling salesman problem, and applies when decoding can be cast in terms of point-like excitations connected by string-like errors. It therefore extends beyond two dimensions, covering certain higher-dimensional topological codes and quantum memories, including the toric code with phenomenological or circuit-level noise.

quant-ph↗

arXiv2026

The color code, the surface code, and the transversal CNOT: NP-hardness of minimum-weight decoding

The decoding problem is a ubiquitous algorithmic task in fault-tolerant quantum computing, and solving it efficiently is essential for scalable quantum computing. Here, we prove that minimum-weight decoding is NP-hard in three quintessential settings: (i) the color code with Pauli $Z$ errors, (ii) the surface code with Pauli $X$, $Y$ and $Z$ errors, and (iii) the surface code with a transversal CNOT gate, Pauli $Z$ and measurement bit-flip errors. Our results show that computational intractability already arises in basic and practically relevant decoding problems central to both quantum memories and logical circuit implementations, highlighting a sharp computational complexity separation between minimum-weight decoding and its approximate realizations.

quant-ph↗

arXiv2026

Check-weight-constrained quantum codes: Bounds and examples

Quantum low-density parity-check (qLDPC) codes can be implemented by measuring only low-weight checks, making them compatible with noisy quantum hardware and central to the quest to build noise-resilient quantum computers. A fundamental open question is how constraints on check weight limit the achievable parameters of qLDPC codes. Here, we study stabilizer and subsystem codes with constrained check weight, combining analytical arguments with numerical optimization to establish strong upper bounds on their parameters. We show that stabilizer codes with checks of weight at most three cannot have nontrivial distance. We also prove tight tradeoffs between rate and distance for broad families of CSS stabilizer and subsystem codes with checks of weight at most four and two, respectively. Notably, our bounds are applicable to general qLDPC codes, as they rely only on check-weight constraints without assuming geometric locality or special graph connectivity. In the finite-size regime, we derive numerical upper bounds using linear programming techniques and identify explicit code constructions that approach these limits, delineating the landscape of practically relevant qLDPC codes with tens or hundreds of physical qubits.

quant-ph↗

arXiv2025

The FACTS Leaderboard: A Comprehensive Benchmark for Large Language Model Factuality

We introduce The FACTS Leaderboard, an online leaderboard suite and associated set of benchmarks that comprehensively evaluates the ability of language models to generate factually accurate text across diverse scenarios. The suite provides a holistic measure of factuality by aggregating the performance of models on four distinct sub-leaderboards: (1) FACTS Multimodal, which measures the factuality of responses to image-based questions; (2) FACTS Parametric, which assesses models' world knowledge by answering closed-book factoid questions from internal parameters; (3) FACTS Search, which evaluates factuality in information-seeking scenarios, where the model must use a search API; and (4) FACTS Grounding (v2), which evaluates whether long-form responses are grounded in provided documents, featuring significantly improved judge models. Each sub-leaderboard employs automated judge models to score model responses, and the final suite score is an average of the four components, designed to provide a robust and balanced assessment of a model's overall factuality. The FACTS Leaderboard Suite will be actively maintained, containing both public and private splits to allow for external participation while guarding its integrity. It can be found at https://www.kaggle.com/benchmarks/google/facts .

cs.CL↗

arXiv2025

Light Edge Fault Tolerant Graph Spanners

There has recently been significant interest in fault tolerant spanners, which are spanners that still maintain their stretch guarantees after some nodes or edges fail. This work has culminated in an almost complete understanding of the three-way tradeoff between stretch, sparsity, and number of faults tolerated. However, despite some progress in metric settings, there have been no results to date on the tradeoff in general graphs between stretch, lightness, and number of faults tolerated. We initiate the study of light edge fault tolerant (EFT) graph spanners, obtaining the first such results. First, we observe that lightness can be unbounded if we use the traditional definition (normalizing by the MST). We then argue that a natural definition of fault-tolerant lightness is to instead normalize by a min-weight fault tolerant connectivity preserver; essentially, a fault-tolerant version of the MST. However, even with this, we show that it is still not generally possible to construct $f$-EFT spanners whose weight compares reasonably to the weight of a min-weight $f$-EFT connectivity preserver. In light of this lower bound, it is natural to then consider bicriteria notions of lightness, where we compare the weight of an $f$-EFT spanner to a min-weight $(f' > f)$-EFT connectivity preserver. The most interesting question is to determine the minimum value of $f'$ that allows for reasonable lightness upper bounds. Our main result is a precise answer to this question: $f' = 2f$. In particular, we show that the lightness can be untenably large (roughly $n/k$ for a $k$-spanner) if one normalizes by the min-weight $(2f-1)$-EFT connectivity preserver. But if one normalizes by the min-weight $2f$-EFT connectivity preserver, then we show that the lightness is bounded by just $O(f^{1/2})$ times the non-fault tolerant lightness (roughly $n^{1/k}$, for a $(1+ε)(2k-1)$-spanner).

cs.DS↗

arXiv2025

The FACTS Grounding Leaderboard: Benchmarking LLMs' Ability to Ground Responses to Long-Form Input

We introduce FACTS Grounding, an online leaderboard and associated benchmark that evaluates language models' ability to generate text that is factually accurate with respect to given context in the user prompt. In our benchmark, each prompt includes a user request and a full document, with a maximum length of 32k tokens, requiring long-form responses. The long-form responses are required to be fully grounded in the provided context document while fulfilling the user request. Models are evaluated using automated judge models in two phases: (1) responses are disqualified if they do not fulfill the user request; (2) they are judged as accurate if the response is fully grounded in the provided document. The automated judge models were comprehensively evaluated against a held-out test-set to pick the best prompt template, and the final factuality score is an aggregate of multiple judge models to mitigate evaluation bias. The FACTS Grounding leaderboard will be actively maintained over time, and contains both public and private splits to allow for external participation while guarding the integrity of the leaderboard. It can be found at https://www.kaggle.com/facts-leaderboard.

cs.CL↗

arXiv2024

Improved Shortest Path Restoration Lemmas for Multiple Edge Failures: Trade-offs Between Fault-tolerance and Subpaths

The restoration lemma is a classic result by Afek, Bremler-Barr, Kaplan, Cohen, and Merritt [PODC '01], which relates the structure of shortest paths in a graph $G$ before and after some edges in the graph fail. Their work shows that, after one edge failure, any replacement shortest path avoiding this failing edge can be partitioned into two pre-failure shortest paths. More generally, this implies an additive tradeoff between fault tolerance and subpath count: for any $f, k$, we can partition any $f$-edge-failure replacement shortest path into $k+1$ subpaths which are each an $(f-k)$-edge-failure replacement shortest path. This generalized result has found applications in routing, graph algorithms, fault tolerant network design, and more. Our main result improves this to a multiplicative tradeoff between fault tolerance and subpath count. We show that for all $f, k$, any $f$-edge-failure replacement path can be partitioned into $O(k)$ subpaths that are each an $(f/k)$-edge-failure replacement path. We also show an asymptotically matching lower bound. In particular, our results imply that the original restoration lemma is exactly tight in the case $k=1$, but can be significantly improved for larger $k$. We also show an extension of this result to weighted input graphs, and we give efficient algorithms that compute path decompositions satisfying our improved restoration lemmas.

cs.DS↗

arXiv2023

EspalomaCharge: Machine learning-enabled ultra-fast partial charge assignment

Atomic partial charges are crucial parameters in molecular dynamics (MD) simulation, dictating the electrostatic contributions to intermolecular energies, and thereby the potential energy landscape. Traditionally, the assignment of partial charges has relied on surrogates of \textit{ab initio} semiempirical quantum chemical methods such as AM1-BCC, and is expensive for large systems or large numbers of molecules. We propose a hybrid physical / graph neural network-based approximation to the widely popular AM1-BCC charge model that is orders of magnitude faster while maintaining accuracy comparable to differences in AM1-BCC implementations. Our hybrid approach couples a graph neural network to a streamlined charge equilibration approach in order to predict molecule-specific atomic electronegativity and hardness parameters, followed by analytical determination of optimal charge-equilibrated parameters that preserves total molecular charge. This hybrid approach scales linearly with the number of atoms, enabling, for the first time, the use of fully consistent charge models for small molecules and biopolymers for the construction of next-generation self-consistent biomolecular force fields. Implemented in the free and open source package \texttt{espaloma\_charge}, this approach provides drop-in replacements for both AmberTools \texttt{antechamber} and the Open Force Field Toolkit charging workflows, in addition to stand-alone charge generation interfaces. Source code is available at \url{https://github.com/choderalab/espaloma_charge}.

cs.LG↗

arXiv2021

On Some Variants of Euclidean K-Supplier

The $k$-Supplier problem is an important location problem that has been actively studied in both general and Euclidean metrics. Many of its variants have also been studied, primarily on general metrics. We study two variants of $k$-Supplier, namely Priority $k$-Supplier and $k$-Supplier with Outliers, in Euclidean metrics. We obtain $(1+\sqrt{3})$-approximation algorithms for both variants, which are the first improvements over the previously-known factor-$3$ approximation (that is known to be best-possible for general metrics). We also study the Matroid Supplier problem on Euclidean metrics, and show that it cannot be approximated to a factor better than $3$ (assuming $P\ne NP$); so the Euclidean metric offers no improvement in this case.

cs.DS↗

arXiv2020

Online Generalized Network Design Under (Dis)Economies of Scale

We consider a general online network design problem where a sequence of N requests arrive over time, each of which needs to use some subset of the available resources E. The cost incurred by any resource e is some function $f_e$ of the total load $L_e$ on that resource. The objective is to minimize the total cost $\sum_{e\in E} f_e(L_e)$. We focus on cost functions that exhibit (dis)economies of scale, that are of the form $f_e(x) = σ_e + ξ_e\cdot x^{α_e}$ if $x>0$ (and zero if $x=0$), where the exponent $α_e\ge 1$. Optimization problems under these functions have received significant recent attention due to applications in energy-efficient computing. Our main result is a deterministic online algorithm with tight competitive ratio $Θ\left(\max_{e\in E} \left(\frac{σ_e}{ξ_e}\right)^{1/α_e}\right)$ when $α_e$ is constant for all $e\in E$. This framework is applicable to a variety of network design problems in undirected and directed graphs, including multicommodity routing, Steiner tree/forest connectivity and set-connectivity. In fact, our online competitive ratio even matches the previous-best (offline) approximation ratio for generalized network design.

cs.DS↗

arXiv2008

Single-Index Model-Assisted Estimation In Survey Sampling

A model-assisted semiparametric method of estimating finite population totals is investigated to improve the precision of survey estimators by incorporating multivariate auxiliary information. The proposed superpopulation model is a single-index model which has proven to be a simple and efficient semiparametric tool in multivariate regression. A class of estimators based on polynomial spline regression is proposed. These estimators are robust against deviation from single-index models. Under standard design conditions, the proposed estimators are asymptotically design-unbiased, consistent and asymptotically normal. An iterative optimization routine is provided that is sufficiently fast for users to analyze large and complex survey data within seconds. The proposed method has been applied to simulated datasets and MU281 dataset, which have provided strong evidence that corroborates with the asymptotic theory.

stat.ME↗