arXiv subjects

William He

Publications and source records attributed to William He.

15 recordsLinked to original sources

arXiv2026

Nearly Time-Optimal Pure State Tomography with Pauli Measurements

We give an algorithm for pure state tomography with near-optimal copy and time complexity using only single-qubit measurements. Specifically, given $\widetilde{O}(2^n/\epsilon)$ copies of an unknown $n$-qubit pure state $|\psi\rangle$, the algorithm performs only nonadaptive Pauli measurements, runs in time $\widetilde{O}(2^n/\epsilon)$, and outputs $|\widehat{\psi} \rangle$ with fidelity at least $1-\epsilon$ with $|\psi\rangle$ with high probability. This is the first algorithm for pure state tomography that achieves near-optimal running time.

quant-ph↗

arXiv2025

Mode Control and Dynamic Population Gratings in Quantum-Dot Lasers

Single-mode operation is essential for integrated semiconductor lasers, yet most solutions rely on regrowth, etched gratings, or other complex fabrication steps that limit scalability. We show that quantum-dot (QD) lasers can achieve stable single-mode lasing through a simple cavity design using dynamic population gratings (DPGs). Owing to the low lateral carrier diffusion of QDs, a strong standing-wave-induced carrier grating forms in a reverse-biased saturable absorber and provides self-aligned, mode-selective feedback not attainable in quantum-well devices. A single-ring laser achieves 46 dB side-mode suppression ratio (SMSR), while a dual-ring Vernier laser delivers ($>$ 46 nm) tuning range and up to 52.6 dB SMSR, with continuous-wave operation up to $80\,^{\circ}\mathrm{C}$. The laser remains single-mode under $-10.6$ dB external optical feedback and supports isolator-free data transmission at 32 Gbps. These results establish DPG-enabled QD lasers as a simple and scalable route to tunable, feedback-resilient on-chip light sources for communication, sensing, and reconfigurable photonic systems.

physics.optics↗

arXiv2025

A Classical Quadratic Speedup for Planted $k$XOR

A recent work of Schmidhuber et al (QIP, SODA, & Phys. Rev. X 2025) exhibited a quantum algorithm for the noisy planted $k$XOR problem running quartically faster than all known classical algorithms. In this work, we design a new classical algorithm that is quadratically faster than the best previous one, in the case of large constant $k$. Thus for such $k$, the quantum speedup of Schmidhuber et al. becomes only quadratic (though it retains a space advantage). Our algorithm, which also works in the semirandom case, combines tools from sublinear-time algorithms (essentially, the birthday paradox) and polynomial anticoncentration.

cs.DS↗

arXiv2025

Sampling and Identity-Testing Without Approximate Tensorization of Entropy

Certain tasks in high-dimensional statistics become easier when the underlying distribution satisfies a local-to-global property called approximate tensorization of entropy (ATE). For example, the Glauber dynamics Markov chain of an ATE distribution mixes fast and can produce approximate samples in a small amount of time, since such a distribution satisfies a modified log-Sobolev inequality. Moreover, identity-testing for an ATE distribution requires few samples if the tester is given coordinate conditional access to the unknown distribution, as shown by Blanca, Chen, \v{S}tefankovi\v{c}, and Vigoda (COLT 2023). A natural class of distributions that do not satisfy ATE consists of mixtures of (few) distributions that do satisfy ATE. We study the complexity of identity-testing and sampling for these distributions. Our main results are the following: 1. We show fast mixing of Glauber dynamics from a data-based initialization, with optimal sample complexity, for mixtures of distributions satisfying modified log-Sobolev inequalities. This extends work of Huang, Koehler, Lee, Mohanty, Rajaraman, Vuong, and Wu (STOC 2025, COLT 2025) for mixtures of distributions satisfying Poincar\'e inequalities. 2. Answering an open question posed by Blanca et al., we give efficient identity-testers for mixtures of ATE distributions in the coordinate-conditional sampling access model. We also give some simplifications and improvements to the original algorithm of Blanca et al.

math.ST↗

arXiv2025

Few Single-Qubit Measurements Suffice to Certify Any Quantum State

A fundamental task in quantum information science is state certification: testing whether a lab-prepared $n$-qubit state is close to a given hypothesis state. In this work, we show that every pure hypothesis state can be certified using only $O(n^2)$ single-qubit measurements applied to $O(n)$ copies of the lab state. Prior to our work, it was not known whether even subexponentially many single-qubit measurements could suffice to certify arbitrary states. This resolves the main open question of Huang, Preskill, and Soleimanifar (FOCS 2024, QIP 2024). Our algorithm also showcases the power of adaptive measurements: within each copy of the lab state, previous measurement outcomes dictate how subsequent qubit measurements are made. We show that the adaptivity is necessary, by proving an exponential lower bound on the number of copies needed for any nonadaptive single-qubit measurement algorithm.

quant-ph↗

arXiv2025

Pseudorandomness Properties of Random Reversible Circuits

Motivated by practical concerns in cryptography, we study pseudorandomness properties of permutations on $\{0,1\}^n$ computed by random circuits made from reversible $3$-bit gates (permutations on $\{0,1\}^3$). Our main result is that a random circuit of depth $\sqrt{n} \cdot \tilde{O}(k^3)$, with each layer consisting of $\Theta(n)$ random gates in a fixed two-dimensional nearest-neighbor architecture, yields approximate $k$-wise independent permutations. Our result can be seen as a particularly simple/practical block cipher construction that gives provable statistical security against attackers with access to $k$~input-output pairs within few rounds. The main technical component of our proof consists of two parts: 1. We show that the Markov chain on $k$-tuples of $n$-bit strings induced by a single random $3$-bit one-dimensional nearest-neighbor gate has spectral gap at least $1/n \cdot \tilde{O}(k)$. Then we infer that a random circuit with layers of random gates in a fixed one-dimensional gate architecture yields approximate $k$-wise independent permutations of $\{0,1\}^n$ in depth $n\cdot \tilde{O}(k^2)$ 2. We show that if the $n$ wires are layed out on a two-dimensional lattice of bits, then repeatedly alternating applications of approximate $k$-wise independent permutations of $\{0,1\}^{\sqrt n}$ to the rows and columns of the lattice yields an approximate $k$-wise independent permutation of $\{0,1\}^n$ in small depth. Our work improves on the original work of Gowers, who showed a gap of $1/\mathrm{poly}(n,k)$ for one random gate (with non-neighboring inputs); and, on subsequent work improving the gap to $\Omega(1/n^2k)$ in the same setting.

cs.CR↗

arXiv2024

Faster Mixing of Higher-Dimensional Random Reversible Circuits

We continue the study of the approximate $k$-wise independence of random reversible circuits as permutations of $\{\pm1\}^n$. Our main result is the first construction of a natural class of random reversible circuits with a sublinear-in-$n$ dependence on depth. Our construction is motivated by considerations in practical cryptography and is somewhat inspired by the design of practical block ciphers, such as DES and AES. Previous constructions of He and O'Donnell [HO24], which were built with gate architectures on one-dimensional lattices, suffered from an inherent linear-in-$n$ dependence on depth. The main novelty of our circuit model is a gate architecture built on higher-dimensional lattices.

cs.CC↗

arXiv2024

Improving Entity Recognition Using Ensembles of Deep Learning and Fine-tuned Large Language Models: A Case Study on Adverse Event Extraction from Multiple Sources

Adverse event (AE) extraction following COVID-19 vaccines from text data is crucial for monitoring and analyzing the safety profiles of immunizations. Traditional deep learning models are adept at learning intricate feature representations and dependencies in sequential data, but often require extensive labeled data. In contrast, large language models (LLMs) excel in understanding contextual information, but exhibit unstable performance on named entity recognition tasks, possibly due to their broad but unspecific training. This study aims to evaluate the effectiveness of LLMs and traditional deep learning models in AE extraction, and to assess the impact of ensembling these models on performance. In this study, we utilized reports and posts from the VAERS (n=621), Twitter (n=9,133), and Reddit (n=131) as our corpora. Our goal was to extract three types of entities: "vaccine", "shot", and "ae". We explored and fine-tuned (except GPT-4) multiple LLMs, including GPT-2, GPT-3.5, GPT-4, and Llama-2, as well as traditional deep learning models like RNN and BioBERT. To enhance performance, we created ensembles of the three models with the best performance. For evaluation, we used strict and relaxed F1 scores to evaluate the performance for each entity type, and micro-average F1 was used to assess the overall performance. The ensemble model achieved the highest performance in "vaccine", "shot", and "ae" with strict F1-scores of 0.878, 0.930, and 0.925, respectively, along with a micro-average score of 0.903. In conclusion, this study demonstrates the effectiveness and robustness of ensembling fine-tuned traditional deep learning models and LLMs, for extracting AE-related information. This study contributes to the advancement of biomedical natural language processing, providing valuable insights into improving AE extraction from text data for pharmacovigilance and public health surveillance.

cs.CL↗

arXiv2024

More Efficient $k$-wise Independent Permutations from Random Reversible Circuits via log-Sobolev Inequalities

We prove that the permutation computed by a reversible circuit with $\tilde{O}(nk\cdot \log(1/\varepsilon))$ random $3$-bit gates is $\varepsilon$-approximately $k$-wise independent. Our bound improves on currently known bounds in the regime when the approximation error $\varepsilon$ is not too small. We obtain our results by analyzing the log-Sobolev constants of appropriate Markov chains rather than their spectral gaps.

cs.CC↗

arXiv2024

Pseudorandom Permutations from Random Reversible Circuits

We study pseudorandomness properties of permutations on $\{0,1\}^n$ computed by random circuits made from reversible $3$-bit gates (permutations on $\{0,1\}^3$). Our main result is that a random circuit of depth $n \cdot \tilde{O}(k^2)$, with each layer consisting of $\approx n/3$ random gates in a fixed nearest-neighbor architecture, yields almost $k$-wise independent permutations. The main technical component is showing that the Markov chain on $k$-tuples of $n$-bit strings induced by a single random $3$-bit nearest-neighbor gate has spectral gap at least $1/n \cdot \tilde{O}(k)$. This improves on the original work of Gowers [Gowers96], who showed a gap of $1/\mathrm{poly}(n,k)$ for one random gate (with non-neighboring inputs); and, on subsequent work [HMMR05,BH08] improving the gap to $\Omega(1/n^2k)$ in the same setting. From the perspective of cryptography, our result can be seen as a particularly simple/practical block cipher construction that gives provable statistical security against attackers with access to $k$~input-output pairs within few rounds. We also show that the Luby--Rackoff construction of pseudorandom permutations from pseudorandom functions can be implemented with reversible circuits. From this, we make progress on the complexity of the Minimum Reversible Circuit Size Problem (MRCSP), showing that block ciphers of fixed polynomial size are computationally secure against arbitrary polynomial-time adversaries, assuming the existence of one-way functions (OWFs).

cs.CC↗

arXiv2024

ICAT: An Indoor Connected and Autonomous Testbed for Vehicle Computing

Indoor autonomous driving testbeds have emerged to complement expensive outdoor testbeds and virtual simulations, offering scalable and cost-effective solutions for research in navigation, traffic optimization, and swarm intelligence. However, they often lack the robust sensing and computing infrastructure for advanced research. Addressing these limitations, we introduce the Indoor Connected Autonomous Testbed (ICAT), a platform that not only tackles the unique challenges of indoor autonomous driving but also innovates vehicle computing and V2X communication. Moreover, ICAT leverages digital twins through CARLA and SUMO simulations, facilitating both centralized and decentralized autonomy deployments.

cs.RO↗

arXiv2023

Testing Junta Truncation

We consider the basic statistical problem of detecting truncation of the uniform distribution on the Boolean hypercube by juntas. More concretely, we give upper and lower bounds on the problem of distinguishing between i.i.d. sample access to either (a) the uniform distribution over $\{0,1\}^n$, or (b) the uniform distribution over $\{0,1\}^n$ conditioned on the satisfying assignments of a $k$-junta $f: \{0,1\}^n\to\{0,1\}$. We show that (up to constant factors) $\min\{2^k + \log{n\choose k}, {2^{k/2}\log^{1/2}{n\choose k}}\}$ samples suffice for this task and also show that a $\log{n\choose k}$ dependence on sample complexity is unavoidable. Our results suggest that testing junta truncation requires learning the set of relevant variables of the junta.

cs.CC↗

arXiv2023

Beyond the Quadratic Time Barrier for Network Unreliability

Karger (STOC 1995) gave the first FPTAS for the network (un)reliability problem, setting in motion research over the next three decades that obtained increasingly faster running times, eventually leading to a $\tilde{O}(n^2)$-time algorithm (Karger, STOC 2020). This represented a natural culmination of this line of work because the algorithmic techniques used can enumerate $\Theta(n^2)$ (near)-minimum cuts. In this paper, we go beyond this quadratic barrier and obtain a faster FPTAS for the network unreliability problem. Our algorithm runs in $m^{1+o(1)} + \tilde{O}(n^{1.5})$ time. Our main contribution is a new estimator for network unreliability in very reliable graphs. These graphs are usually the bottleneck for network unreliability since the disconnection event is elusive. Our estimator is obtained by defining an appropriate importance sampling subroutine on a dual spanning tree packing of the graph. To complement this estimator for very reliable graphs, we use recursive contraction for moderately reliable graphs. We show that an interleaving of sparsification and contraction can be used to obtain a better parametrization of the recursive contraction algorithm that yields a faster running time matching the one obtained for the very reliable case.

cs.DS↗

arXiv2022

Symmetric Formulas for Products of Permutations

We study the formula complexity of the word problem $\mathsf{Word}_{S_n,k} : \{0,1\}^{kn^2} \to \{0,1\}$: given $n$-by-$n$ permutation matrices $M_1,\dots,M_k$, compute the $(1,1)$-entry of the matrix product $M_1\cdots M_k$. An important feature of this function is that it is invariant under action of $S_n^{k-1}$ given by \[ (\pi_1,\dots,\pi_{k-1})(M_1,\dots,M_k) = (M_1\pi_1^{-1},\pi_1M_2\pi_2^{-1},\dots,\pi_{k-2}M_{k-1}\pi_{k-1}^{-1},\pi_{k-1}M_k). \] This symmetry is also exhibited in the smallest known unbounded fan-in $\{\mathsf{AND},\mathsf{OR},\mathsf{NOT}\}$-formulas for $\mathsf{Word}_{S_n,k}$, which have size $n^{O(\log k)}$. In this paper we prove a matching $n^{\Omega(\log k)}$ lower bound for $S_n^{k-1}$-invariant formulas computing $\mathsf{Word}_{S_n,k}$. This result is motivated by the fact that a similar lower bound for unrestricted (non-invariant) formulas would separate complexity classes $\mathsf{NC}^1$ and $\mathsf{Logspace}$. Our more general main theorem gives a nearly tight $n^{d(k^{1/d}-1)}$ lower bound on the $G^{k-1}$-invariant depth-$d$ $\{\mathsf{MAJ},\mathsf{AND},\mathsf{OR},\mathsf{NOT}\}$-formula size of $\mathsf{Word}_{G,k}$ for any finite simple group $G$ whose minimum permutation representation has degree~$n$. We also give nearly tight lower bounds on the $G^{k-1}$-invariant depth-$d$ $\{\mathsf{AND},\mathsf{OR},\mathsf{NOT}\}$-formula size in the case where $G$ is an abelian group.

cs.CC↗

arXiv2022

Steiner Connectivity Augmentation and Splitting-off in Poly-logarithmic Maximum Flows

We give an almost-linear time algorithm for the Steiner connectivity augmentation problem: given an undirected graph, find a smallest (or minimum weight) set of edges whose addition makes a given set of terminals $\tau$-connected (for any given $\tau > 0$). The running time of our algorithm is dominated by polylogarithmic calls to any maximum flow subroutine; using the recent almost-linear time maximum flow algorithm (Chen et al., FOCS 2022), we get an almost-linear running time for our algorithm as well. This is tight up to the polylogarithmic factor even for just two terminals. Prior to our work, an almost-linear (in fact, near-linear) running time was known only for the special case of global connectivity augmentation, i.e., when all vertices are terminals (Cen et al., STOC 2022). We also extend our algorithm to the closely related Steiner splitting-off problem, where the edges incident on a vertex have to be {\em split-off} while maintaining the (Steiner) connectivity of a given set of terminals. Prior to our work, a nearly-linear time algorithm was known only for the special case of global connectivity (Cen et al., STOC 2022). The only known generalization beyond global connectivity was to preserve all pairwise connectivities using a much slower algorithm that makes $n$ calls to an all-pairs maximum flow (or Gomory-Hu tree) subroutine (Lau and Yung, SICOMP 2013), as against polylog(n) calls to a (single-pair) maximum flow subroutine in this work.

cs.DS↗