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Researcher profile

Yufei Zhao

Yufei Zhao contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.COmath.MGComputational ComplexityInformation Theorymath.ITmath.NTComputer Visioneess.SPmath.AGmath.CAmath.FAmath.GRmath.SPquant-ph

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Published work

18 published item(s)

preprint2026arXiv

Rydberg Atomic Quantum Receivers for Classical Wireless Communications and Sensing: Their Models and Performance

The significant progress of quantum sensing technologies offer numerous radical solutions for measuring a multitude of physical quantities at an unprecedented precision. Among them, Rydberg atomic quantum receivers (RAQRs) emerge as an eminent solution for detecting the electric field of radio frequency (RF) signals, exhibiting great potential in assisting classical wireless communications and sensing. So far, most experimental studies have aimed for the proof of physical concepts to reveal its promise, while the practical signal model of RAQR-aided wireless communications and sensing remained under-explored. Furthermore, the performance of RAQR-based wireless receivers and their advantages over classical RF receivers have not been fully characterized. To fill these gaps, we introduce the RAQR to the wireless community by presenting an end-to-end reception scheme. We then develop a corresponding equivalent baseband signal model relying on a realistic reception flow. Our scheme and model provide explicit design guidance to RAQR-aided wireless systems. We next study the performance of RAQR-aided wireless systems based on our model, and compare them to classical RF receivers. The results show that Doppler broadening-free RAQRs are capable of achieving a substantial received signal-to-noise ratio (SNR) gain of over $27$ decibel (dB) and $40$ dB in the photon shot limit and standard quantum limit regimes, respectively.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

SwiftI2V: Efficient High-Resolution Image-to-Video Generation via Conditional Segment-wise Generation

High-resolution image-to-video (I2V) generation aims to synthesize realistic temporal dynamics while preserving fine-grained appearance details of the input image. At 2K resolution, it becomes extremely challenging, and existing solutions suffer from various weaknesses: 1) end-to-end models are often prohibitively expensive in memory and latency; 2) cascading low-resolution generation with a generic video super-resolution tends to hallucinate details and drift from input-specific local structures, since the super-resolution stage is not explicitly conditioned on the input image. To this end, we propose SwiftI2V, an efficient framework tailored for high-resolution I2V. Following the widely used two-stage design, it addresses the efficiency--fidelity dilemma by first generating a low-resolution motion reference to reduce token costs and ease the modeling burden, then performing a strongly image-conditioned 2K synthesis guided by the motion to recover input-faithful details with controlled overhead. Specifically, to make generation more scalable, SwiftI2V introduces Conditional Segment-wise Generation (CSG) to synthesize videos segment-by-segment with a bounded per-step token budget, and adopts bidirectional contextual interaction within each segment to improve cross-segment coherence and input fidelity. On VBench-I2V at 2K resolution, SwiftI2V achieves performance comparable to end-to-end baselines while reducing total GPU-time by 202x. Particularly, it enables practical 2K I2V generation on a single datacenter GPU (e.g., H800) or consumer GPU (e.g., RTX 4090).

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preprint2022arXiv

Enumerating k-SAT functions

How many $k$-SAT functions on $n$ boolean variables are there? What does a typical such function look like? Bollobás, Brightwell, and Leader conjectured that, for each fixed $k \ge 2$, the number of $k$-SAT functions on $n$ variables is $(1+o(1))2^{\binom{n}{k} + n}$, or equivalently: a $1-o(1)$ fraction of all $k$-SAT functions are unate, i.e., monotone after negating some variables. They proved a weaker version of the conjecture for $k=2$. The conjecture was confirmed for $k=2$ by Allen and $k=3$ by Ilinca and Kahn. We show that the problem of enumerating $k$-SAT functions is equivalent to a Turán density problem for partially directed hypergraphs. Our proof uses the hypergraph container method. Furthermore, we confirm the Bollobás--Brightwell--Leader conjecture for $k=4$ by solving the corresponding Turán density problem. Our solution applies a recent result of Füredi and Maleki on the minimum triangular edge density in a graph of given edge density. In an appendix (by Nitya Mani and Edward Yu), we further confirm the $k=5$ case of the conjecture via a brute force computer search.

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preprint2022arXiv

Equiangular lines with a fixed angle

Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle. Fix $0 < α< 1$. Let $N_α(d)$ denote the maximum number of lines through the origin in $\mathbb{R}^d$ with pairwise common angle $\arccos α$. Let $k$ denote the minimum number (if it exists) of vertices in a graph whose adjacency matrix has spectral radius exactly $(1-α)/(2α)$. If $k < \infty$, then $N_α(d) = \lfloor k(d-1)/(k-1) \rfloor$ for all sufficiently large $d$, and otherwise $N_α(d) = d + o(d)$. In particular, $N_{1/(2k-1)}(d) = \lfloor k(d-1)/(k-1) \rfloor$ for every integer $k\ge 2$ and all sufficiently large $d$. A key ingredient is a new result in spectral graph theory: the adjacency matrix of a connected bounded degree graph has sublinear second eigenvalue multiplicity.

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preprint2022arXiv

Joints of varieties

We generalize the Guth--Katz joints theorem from lines to varieties. A special case says that $N$ planes (2-flats) in 6 dimensions (over any field) have $O(N^{3/2})$ joints, where a joint is a point contained in a triple of these planes not all lying in some hyperplane. More generally, we prove the same bound when the set of $N$ planes is replaced by a set of 2-dimensional algebraic varieties of total degree $N$, and a joint is a point that is regular for three varieties whose tangent planes at that point are not all contained in some hyperplane. Our most general result gives upper bounds, tight up to constant factors, for joints with multiplicities for several sets of varieties of arbitrary dimensions (known as Carbery&#39;s conjecture). Our main innovation is a new way to extend the polynomial method to higher dimensional objects, relating the degree of a polynomial and its orders of vanishing on a given set of points on a variety.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

On the number of error correcting codes

We show that for a fixed $q$, the number of $q$-ary $t$-error correcting codes of length $n$ is at most $2^{(1 + o(1)) H_q(n,t)}$ for all $t \leq (1 - q^{-1})n - C_q\sqrt{n \log n}$ (for sufficiently large constant $C_q$), where $H_q(n, t) = q^n / V_q(n,t)$ is the Hamming bound and $V_q(n,t)$ is the cardinality of the radius $t$ Hamming ball. This proves a conjecture of Balogh, Treglown, and Wagner, who showed the result for $t = o(n^{1/3} (\log n)^{-2/3})$.

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preprint2022arXiv

Removal lemmas and approximate homomorphisms

We study quantitative relationships between the triangle removal lemma and several of its variants. One such variant, which we call the triangle-free lemma, states that for each $ε>0$ there exists $M$ such that every triangle-free graph $G$ has an $ε$-approximate homomorphism to a triangle-free graph $F$ on at most $M$ vertices (here an $ε$-approximate homomorphism is a map $V(G) \to V(F)$ where all but at most $ε|V(G)|^2$ edges of $G$ are mapped to edges of $F$). One consequence of our results is that the least possible $M$ in the triangle-free lemma grows faster than exponential in any polynomial in $ε^{-1}$. We also prove more general results for arbitrary graphs, as well as arithmetic analogues over finite fields, where the bounds are close to optimal.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A reverse Sidorenko inequality

Let $H$ be a graph allowing loops as well as vertex and edge weights. We prove that, for every triangle-free graph $G$ without isolated vertices, the weighted number of graph homomorphisms $\hom(G, H)$ satisfies the inequality \[ \hom(G, H ) \le \prod_{uv \in E(G)} \hom(K_{d_u,d_v}, H )^{1/(d_ud_v)}, \] where $d_u$ denotes the degree of vertex $u$ in $G$. In particular, one has \[ \hom(G, H )^{1/|E(G)|} \le \hom(K_{d,d}, H )^{1/d^2} \] for every $d$-regular triangle-free $G$. The triangle-free hypothesis on $G$ is best possible. More generally, we prove a graphical Brascamp-Lieb type inequality, where every edge of $G$ is assigned some two-variable function. These inequalities imply tight upper bounds on the partition function of various statistical models such as the Ising and Potts models, which includes independent sets and graph colorings. For graph colorings, corresponding to $H = K_q$, we show that the triangle-free hypothesis on $G$ may be dropped; this is also valid if some of the vertices of $K_q$ are looped. A corollary is that among $d$-regular graphs, $G = K_{d,d}$ maximizes the quantity $c_q(G)^{1/|V(G)|}$ for every $q$ and $d$, where $c_q(G)$ counts proper $q$-colorings of $G$. Finally, we show that if the edge-weight matrix of $H$ is positive semidefinite, then \[ \hom(G, H) \le \prod_{v \in V(G)} \hom(K_{d_v+1}, H )^{1/(d_v+1)}. \] This implies that among $d$-regular graphs, $G = K_{d+1}$ maximizes $\hom(G, H)^{1/|V(G)|}$. For 2-spin Ising models, our results give a complete characterization of extremal graphs: complete bipartite graphs maximize the partition function of 2-spin antiferromagnetic models and cliques maximize the partition function of ferromagnetic models. These results settle a number of conjectures by Galvin-Tetali, Galvin, and Cohen-Csikvári-Perkins-Tetali, and provide an alternate proof to a conjecture by Kahn.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Testing linear-invariant properties

Fix a prime $p$ and a positive integer $R$. We study the property testing of functions $\mathbb F_p^n\to[R]$. We say that a property is testable if there exists an oblivious tester for this property with one-sided error and constant query complexity. Furthermore, a property is proximity oblivious-testable (PO-testable) if the test is also independent of the proximity parameter $ε$. It is known that a number of natural properties such as linearity and being a low degree polynomial are PO-testable. These properties are examples of linear-invariant properties, meaning that they are preserved under linear automorphisms of the domain. Following work of Kaufman and Sudan, the study of linear-invariant properties has been an important problem in arithmetic property testing. A central conjecture in this field, proposed by Bhattacharyya, Grigorescu, and Shapira, is that a linear-invariant property is testable if and only if it is semi subspace-hereditary. We prove two results, the first resolves this conjecture and the second classifies PO-testable properties. (1) A linear-invariant property is testable if and only if it is semi subspace-hereditary. (2) A linear-invariant property is PO-testable if and only if it is locally characterized. Our innovations are two-fold. We give a more powerful version of the compactness argument first introduced by Alon and Shapira. This relies on a new strong arithmetic regularity lemma in which one mixes different levels of Gowers uniformity. This allows us to extend the work of Bhattacharyya, Fischer, Hatami, Hatami, and Lovett by removing the bounded complexity restriction in their work. Our second innovation is a novel recoloring technique called patching. This Ramsey-theoretic technique is critical for working in the linear-invariant setting and allows us to remove the translation-invariant restriction present in previous work.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Tower-type bounds for Roth&#39;s theorem with popular differences

Green developed an arithmetic regularity lemma to prove a strengthening of Roth&#39;s theorem on arithmetic progressions in dense sets. It states that for every $ε> 0$ there is some $N_0(ε)$ such that for every $N \ge N_0(ε)$ and $A \subset [N]$ with $|A| = αN$, there is some nonzero $d$ such that $A$ contains at least $(α^3 - ε) N$ three-term arithmetic progressions with common difference $d$. We prove that the minimum $N_0(ε)$ in Green&#39;s theorem is an exponential tower of 2s of height on the order of $\log(1/ε)$. Both the lower and upper bounds are new. It shows that the tower-type bounds that arise from the use of a regularity lemma in this application are quantitatively necessary.

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preprint2019arXiv

Induced arithmetic removal: complexity 1 patterns over finite fields

We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. Informally speaking, we show that given a fixed collection of $r$-colored complexity 1 arithmetic patterns over $\mathbb F_q$, every coloring $ϕ\colon \mathbb F_q^n \setminus\{0\} \to [r]$ with $o(1)$ density of every such pattern can be recolored on an $o(1)$-fraction of the space so that no such pattern remains.

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preprint2019arXiv

Triforce and Corners

May the $\mathit{triforce}$ be the 3-uniform hypergraph on six vertices with edges $\{123&#39;,12&#39;3,1&#39;23\}$. We show that the minimum triforce density in a 3-uniform hypergraph of edge density $δ$ is $δ^{4-o(1)}$ but not $O(δ^4)$. Let $M(δ)$ be the maximum number such that the following holds: for every $ε> 0$ and $G = \mathbb{F}_2^n$ with $n$ sufficiently large, if $A \subseteq G \times G$ with $A \ge δ|G|^2$, then there exists a nonzero &#34;popular difference&#34; $d \in G$ such that the number of &#34;corners&#34; $(x,y), (x+d,y), (x,y+d) \in A$ is at least $(M(δ) - ε)|G|^2$. As a corollary via a recent result of Mandache, we conclude that $M(δ) = δ^{4-o(1)}$ and $M(δ) = ω(δ^4)$. On the other hand, for $0 < δ< 1/2$ and sufficiently large $N$, there exists $A \subseteq [N]^3$ with $|A|\geδN^3$ such that for every $d \ne 0$, the number of corners $(x,y,z), (x+d,y,z),(x,y+d,z),(x,y,z+d) \in A$ is at most $δ^{c \log (1/δ)} N^3$. A similar bound holds in higher dimensions, or for any configuration with at least 5 points or affine dimension at least 3.

0 citations0 reviewsNo code linkedOpen access