arXiv subjects

Pei Wu

Publications and source records attributed to Pei Wu.

At least 19 recordsLinked to original sources

arXiv2026

PureSuperQMA(exp) = BellPureSymQMA(poly) = QMA via Dimension-Free Bosonic Argmax

Pure-state consistency problems naturally lead to quantum proof systems in which a single pure witness must satisfy many acceptance constraints. The corresponding class $\mathsf{PureSuperQMA}$ was previously known to lie between $\mathsf{QMA}$ and $\mathsf{QMA}(2)$, and Kamminga and Rudolph (ITCS'26) conjectured that both containments are strict. In this paper, we prove the following surprising complexity collapses $$ \mathsf{QMA} = \mathsf{PureSuperQMA} = \mathsf{PureSuperQMA}(\text{exp}) = \mathsf{BellPureSymQMA}(\text{poly}) $$ Here $\mathsf{PureSuperQMA}(\text{exp})$ allows exponentially many checks which are uniformly indexed and efficiently generated, while requiring an inverse-polynomial violation margin and an inverse-polynomial fraction of violated checks for the NO cases. $\mathsf{BellPureSymQMA}(\text{poly})$ is a related model that requires the prover to give the verifier polynomially many copies of a pure state, which the verifier measures separately with logarithmic output length for each local measurement, before processing the outcomes jointly. The main technical ingredient is a dimension-free stability bound for symmetric tensor states. Our simulations use polynomially many witness registers and combine a random-pair SWAP test with a permutation-invariant lift of the original verification procedure. The key step is to show that, on the symmetric subspace, the extremal verification value is close to that of some tensor-power witness with dimension-independent error. Applying this argument to the two verification models yields both simulations. As a consequence, exact $k$-local pure-state consistency is $\mathsf{QMA}$-complete for every fixed $k\ge2$, and so are the corresponding exact bosonic and fermionic pure $N$-representability problems.

quant-ph↗

arXiv2026

On the maximum size of 2-weakly compatible split systems

We consider a Tur\'an-type problem arising in phylogenetics: determining the maximum size of a 2-weakly compatible split system. This compatibility condition arises in the reconstruction of phylogenetic networks from quartet weights. It was previously shown that a 2-weakly compatible split system has size at most \[ 3\binom{n}{4}+\binom{n}{2}. \] We prove that the maximum size is $O(n^{5/2})$.

math.CO↗

arXiv2026

A counterexample to the Anstee-Sali's conjecture

This note propose a counterexample to the Anstee--Sali conjecture for forbidden configurations. The basic candidate is the $4$-uniform family \[ F_2=\{xyab,xybc,xycd,xyda\} \] on six vertices: a fixed two-vertex core $\{x,y\}$ joined to the four edges of a $4$-cycle. We give an explicit certificate that every four-fold product whose factors are of type $I$, $I^c$, or $T$ contains $F_2$, while $I^3$ avoids it. Thus, $X(F_2)=4$, so the conjecture predicts $\operatorname{forb}(m,F_2)=\Theta(m^3)$. On the other hand, a result of Mubayi on complete multipartite hypergraphs implies \[ \operatorname{forb}(m,F_2)=\Omega(m^{7/2}), \] which is asymptotically larger than $m^3$. The example was found by GPT-5.6 Sol.

math.CO↗

arXiv2026

Optimal Quantum de Finetti Theorems via Argmax Rounding

We prove optimal finite quantum de Finetti upper bounds. Given a bosonic state $\rho_N\in D(\mathrm{Sym}^N(\mathbb C^d))$, there is a probability measure $\nu$ on the unit sphere such that \[ \left\| \rho_N^{(2)}-\int |u\rangle\langle u|^{\otimes 2}\,d\nu(u) \right\|_1 \le \frac{\sqrt{d-1}}{N-1}. \] By purification, the bosonic theorem also gives the optimal $O(d/N)$ upper bound for arbitrary exchangeable states. These results settle the dimension dependence left open by Christandl, K\"onig, Mitchison, and Renner (CMP 2007). The proof casts de Finetti approximation as sum-of-squares rounding and applies the argmax method of Jeronimo, Wu, and Xu (manuscript 2026). More generally, $t$-site marginals satisfy $O(t\sqrt d/N)$ bosonic and $O(td/N)$ permutation-invariant bounds. Our proof formulates de Finetti approximation as the integrality gap of a symmetric-extension semidefinite program and rounds an optimum by the argmax principle. The sharp bounds have several consequences. For every fixed $\varepsilon\in(0,1)$, we construct a channel with input dimension $D=\exp(O_\varepsilon(\sqrt d\log d))=\exp(o(d))$ whose outputs are $\varepsilon$-close to separable states of local dimension $d$ and whose image contains every such separable state, thereby refuting Watrous's disentangler conjecture. We also obtain deterministic $\exp(\widetilde O(\sqrt d/\varepsilon))$-time algorithms for explicit Best Separable State without perfect completeness and for trace-distance separability testing. Finally, spectral truncation gives the first dimension-free bosonic de Finetti theorem in Hilbert--Schmidt distance, with the optimal rate $\Theta(N^{-1/2})$ when the dimension may grow.

quant-ph↗

arXiv2026

An Argmax Principle for Sum-of-Squares Relaxations on the Sphere

We develop an argmax principle for analyzing sum-of-squares relaxations of optimization problems over the unit sphere. Given a feasible pseudo-expectation, we form a polynomial of high-order pseudo-moments, such as $\Phi_k(u)=\widetilde{\mathbb E}\langle x,u\rangle^{2k}$. Our guiding principle is that its maximizers are rounding candidates: their local and global optimality conditions reveal the reweighed pseudo-expectation inequalities governing SoS convergence. This viewpoint unifies several problems previously analyzed by rather different techniques. We obtain three results. First, for Best Separable State, we give a degree-$O(\sqrt{n/\epsilon})$ SoS analysis for approximating $h_{\mathrm{sep}}(P)$ in the perfect-completeness regime, improving and simplifying Barak, Kothari and Steurer (STOC'17). The dependence is essentially tight for inverse-linear gap under the Exponential-Time Hypothesis, matching hardness from $\mathrm{QMA}(2)$ protocols. Second, for the matrix $2\to4$ norm, degree-$O(\sqrt n/\epsilon)$ SoS gives a multiplicative $(1+\epsilon)$ approximation. Barak et al. (STOC'12) previously gave a comparable-time constant-gap decision algorithm; our result gives a multiplicative guarantee and extends to a family of $p\to q$ norms with even $q$. Finally, for degree-$d$ polynomial optimization, we recover the convergence theorem of Bhattiprolu et al. (FOCS'17) with a shorter, more direct proof: degree-$k$ SoS gives approximation ratio $O_d((n/k)^{d/2-1})$. The paper introduces no new relaxation. Instead, the high-moment argmax gives a common way to read an SoS solution, unifying previously separate convergence analyses and yielding sharper bounds or simpler proofs.

cs.CC↗

arXiv2026

An Optimal Analysis of the Product Test

Product testing, i.e., deciding whether a pure multipartite quantum state is fully unentangled across a specified tensor decomposition, serves as a bridge between quantum property testing, unentangled quantum proof systems, and tensor optimization. Despite being a fundamental property testing task and having many applications, the product test's exact (worst-case) acceptance probability curve has yet to be fully determined. In this work, we determine this curve exactly. Let $\omega$ be the maximum squared overlap of the input with a product state, and let $\mathrm{PT}_n(\omega)$ be the largest possible acceptance probability of the product test over all $n$-partite pure states with product overlap $\omega$, allowing arbitrary finite local dimensions. We prove that, for every $n\ge 2 $ and every $\omega\in(0,1] $, $$ \mathrm{PT}_n(\omega)=\frac12\left(1+m\omega^2+(1-m\omega)^2\right), $$ where $m=\lfloor1/\omega\rfloor $. The formula recovers the previously known tight section of the curve for $\omega\ge 1/2 $, resolves all low-overlap regimes $\omega<1/2 $, and implies $\mathrm{PT}_n(\omega)\to 1/2 $ as $\omega\to 0$ answering an open problem in [Soleimanifar and Wright, SODA 2022]. As a complexity-theoretic application, our results improve the one-shot soundness parameter in the Harrow-Montanaro reduction from $\mathsf{QMA}(k)$ to $\mathsf{QMA}(2)$. Our techniques, built upon those of Soleimanifar and Wright, allow us to resolve these open questions while remaining surprisingly elementary.

quant-ph↗

arXiv2026

The power of unentanglement without destructive interference

Stoquasticity, originating in sign-problem-free physical systems, gives rise to $\sf StoqMA$, introduced by Bravyi, Bessen, and Terhal (2006), a quantum-inspired intermediate class between $\sf MA$ and $\sf AM$. Unentanglement similarly gives rise to ${\sf QMA}(2)$, introduced by Kobayashi, Matsumoto, and Yamakami (CJTCS 2009), which generalizes $\sf QMA$ to two unentangled proofs and still has only the trivial $\sf NEXP$ upper bound. In this work, we initiate a systematic study of the power of unentanglement without destructive interference via ${\sf StoqMA}(2)$, the class of unentangled stoquastic Merlin--Arthur proof systems. Beyond its complexity-theoretic interest, ${\sf StoqMA}(2)$ is connected to the optimality of non-negative tensor optimization algorithms. We highlight: 1. ${\sf NP} \subseteq {\sf StoqMA}(2)$ with $\widetilde{O}(\sqrt{n})$-qubit proofs and completenes $1-2^{-{\rm polylog}(n)}$. Conversely, the Sum-of-Squares algorithm of Barak, Kelner, and Steurer (STOC 2014) gives an exponential-time upper bound for ${\sf StoqMA}(2)$. Our tightened analysis shows the optimality of our protocol and the BKS algorithm under ETH. 2. For ${\sf StoqMA}(2)_1$, the parameter dependence in the general ETH-optimal time bound can be exponentially improved, or the bound achieved simultaneously with polynomial space. 3. For logarithmic-size proofs, ${\sf NP} \subseteq {\sf StoqMA}(2)_{\log}$ with completeness $1-O(n^{-2})$ and vanishing gap, while ${\sf StoqMA}(2)_{\log} \subseteq {\sf MA}$. Consequently, quantum-inspired randomness enables \emph{exponentially} shorter unentangled proofs even under the assumption ${\sf MA}={\sf NP}$. Our lower bounds are obtained by stoquastizing the short-proof ${\sf QMA}(2)$ protocols using distribution testing techniques. Our upper bounds for the nearly perfect completeness case are proved via our rectangular closure testing framework.

quant-ph↗

arXiv2026

Mimic Human Cognition, Master Multi-Image Reasoning: A Meta-Action Framework for Enhanced Visual Understanding

While Multimodal Large Language Models (MLLMs) excel at single-image understanding, they exhibit significantly degraded performance in multi-image reasoning scenarios. Multi-image reasoning presents fundamental challenges including complex inter-relationships between images and scattered critical information across image sets. Inspired by human cognitive processes, we propose a Cognition-Inspired Meta-Action Framework (CINEMA), which decomposes multi-image reasoning into five structured meta-actions: Global, Focus, Hint, Think, and Answer, explicitly modeling the sequential cognitive steps humans naturally employ. For cold-start training, we introduce a Retrieval-Based Tree Sampling strategy that generates high-quality meta-action trajectories to bootstrap the model with reasoning patterns. During reinforcement learning, we adopt a two-stage paradigm: an exploration phase with Diversity-Preserving Strategy to avoid entropy collapse, followed by an annealed exploitation phase with DAPO to gradually strengthen exploitation. To train our model, we construct a dataset of 56k cold-start and 58k reinforcement learning instances spanning multi-image, multi-frame, and single-image tasks. We conduct extensive evaluations on multi-image reasoning benchmarks, video understanding benchmarks, and single-image benchmarks, achieving competitive state-of-the-art performance on several key benchmarks. Our model surpasses GPT-4o on the MUIR and MVMath benchmarks and notably outperforms specialized video reasoning models on video understanding benchmarks, demonstrating the effectiveness and generalizability of our human cognition-inspired reasoning framework.

cs.CV↗

arXiv2025

Logo-VGR: Visual Grounded Reasoning for Open-world Logo Recognition

Recent advances in multimodal large language models (MLLMs) have been primarily evaluated on general-purpose benchmarks, while their applications in domain-specific scenarios, such as intelligent product moderation, remain underexplored. To address this gap, we introduce an open-world logo recognition benchmark, a core challenge in product moderation. Unlike traditional logo recognition methods that rely on memorizing representations of tens of thousands of brands-an impractical approach in real-world settings-our proposed method, Logo-VGR, enables generalization to large-scale brand recognition with supervision from only a small subset of brands. Specifically, we reformulate logo recognition as a comparison-based task, requiring the model to match product images with candidate logos rather than directly generating brand labels. We further observe that existing models tend to overfit by memorizing brand distributions instead of learning robust multimodal reasoning, which results in poor performance on unseen brands. To overcome this limitation, Logo-VGR introduces a new paradigm of domain-specific multimodal reasoning: Logo Perception Grounding injects domain knowledge, and Logo-Guided Visual Grounded Reasoning enhances the model's reasoning capability. Experimental results show that Logo-VGR outperforms strong baselines by nearly 10 points in OOD settings, demonstrating superior generalization.

cs.CV↗

arXiv2025

Dyna3DGR: 4D Cardiac Motion Tracking with Dynamic 3D Gaussian Representation

Accurate analysis of cardiac motion is crucial for evaluating cardiac function. While dynamic cardiac magnetic resonance imaging (CMR) can capture detailed tissue motion throughout the cardiac cycle, the fine-grained 4D cardiac motion tracking remains challenging due to the homogeneous nature of myocardial tissue and the lack of distinctive features. Existing approaches can be broadly categorized into image based and representation-based, each with its limitations. Image-based methods, including both raditional and deep learning-based registration approaches, either struggle with topological consistency or rely heavily on extensive training data. Representation-based methods, while promising, often suffer from loss of image-level details. To address these limitations, we propose Dynamic 3D Gaussian Representation (Dyna3DGR), a novel framework that combines explicit 3D Gaussian representation with implicit neural motion field modeling. Our method simultaneously optimizes cardiac structure and motion in a self-supervised manner, eliminating the need for extensive training data or point-to-point correspondences. Through differentiable volumetric rendering, Dyna3DGR efficiently bridges continuous motion representation with image-space alignment while preserving both topological and temporal consistency. Comprehensive evaluations on the ACDC dataset demonstrate that our approach surpasses state-of-the-art deep learning-based diffeomorphic registration methods in tracking accuracy. The code will be available in https://github.com/windrise/Dyna3DGR.

cs.CV↗

arXiv2025

UB-Mesh: a Hierarchically Localized nD-FullMesh Datacenter Network Architecture

As the Large-scale Language Models (LLMs) continue to scale, the requisite computational power and bandwidth escalate. To address this, we introduce UB-Mesh, a novel AI datacenter network architecture designed to enhance scalability, performance, cost-efficiency and availability. Unlike traditional datacenters that provide symmetrical node-to-node bandwidth, UB-Mesh employs a hierarchically localized nD-FullMesh network topology. This design fully leverages the data locality of LLM training, prioritizing short-range, direct interconnects to minimize data movement distance and reduce switch usage. Although UB-Mesh's nD-FullMesh topology offers several theoretical advantages, its concrete architecture design, physical implementation and networking system optimization present new challenges. For the actual construction of UB-Mesh, we first design the UB-Mesh-Pod architecture, which is based on a 4D-FullMesh topology. UB-Mesh-Pod is implemented via a suite of hardware components that serve as the foundational building blocks, including specifically-designed NPU, CPU, Low-Radix-Switch (LRS), High-Radix-Switch (HRS), NICs and others. These components are interconnected via a novel Unified Bus (UB) technique, which enables flexible IO bandwidth allocation and hardware resource pooling. For networking system optimization, we propose advanced routing mechanism named All-Path-Routing (APR) to efficiently manage data traffic. These optimizations, combined with topology-aware performance enhancements and robust reliability measures like 64+1 backup design, result in 2.04x higher cost-efficiency, 7.2% higher network availability compared to traditional Clos architecture and 95%+ linearity in various LLM training tasks.

cs.AR↗

arXiv2024

Quantum Algorithms on Edge Lists: Hiding, Shuffling, and Cycle Finding

The edge list model is arguably the simplest input model for graphs, where the graph is specified by a list of its edges. In this model, we study the quantum query complexity of three variants of the triangle finding problem. The first asks whether there exists a triangle containing a target edge and raises general questions about the hiding of a problem's input among irrelevant data. The second asks whether there exists a triangle containing a target vertex and raises general questions about the shuffling of a problem's input. The third asks whether there exists a triangle; this problem bridges the $3$-distinctness and $3$-sum problems, which have been extensively studied by both cryptographers and complexity theorists. We provide tight or nearly tight results for these problems as well as some first answers to the general questions they raise. Furthermore, given any graph with low maximum degree, such as a typical random sparse graph, we prove that the quantum query complexity of finding a length-$k$ cycle in its length-$m$ edge list is $m^{3/4-1/(2^{k+2}-4)\pm o(1)}$, which matches the best-known upper bound for the quantum query complexity of $k$-distinctness on length-$m$ inputs up to an $m^{o(1)}$ factor. We prove the lower bound by developing new techniques within Zhandry's recording query framework [CRYPTO '19] as generalized by Hamoudi and Magniez [ToCT '23]. These techniques extend the framework to treat any non-product distribution that results from conditioning a product distribution on the absence of rare events. We prove the upper bound by adapting Belovs's learning graph algorithm for $k$-distinctness [FOCS '12]. Finally, assuming a plausible conjecture concerning only cycle finding, we show that the lower bound can be lifted to an essentially tight lower bound on the quantum query complexity of $k$-distinctness, which is a long-standing open question.

quant-ph↗

arXiv2024

Coherence in Property Testing: Quantum-Classical Collapses and Separations

Understanding the power and limitations of classical and quantum information and how they differ is a fundamental endeavor. In property testing of distributions, a tester is given samples over a typically large domain $\{0,1\}^n$. An important property is the support size both of distributions [Valiant and Valiant, STOC'11], as well, as of quantum states. Classically, even given $2^{n/16}$ samples, no tester can distinguish distributions of support size $2^{n/8}$ from $2^{n/4}$ with probability better than $2^{-\Theta(n)}$, even promised they are flat. Quantum states can be in a coherent superposition of states of $\{0,1\}^n$, so one may ask if coherence can enhance property testing. Flat distributions naturally correspond to subset states, $|\phi_S \rangle=1/\sqrt{|S|}\sum_{i\in S}|i\rangle$. We show that coherence alone is not enough, Coherence limitations: Given $2^{n/16}$ copies, no tester can distinguish subset states of size $2^{n/8}$ from $2^{n/4}$ with probability better than $2^{-\Theta(n)}$. The hardness persists even with multiple public-coin AM provers, Classical hardness with provers: Given $2^{O(n)}$ samples from a distribution and $2^{O(n)}$ communication with AM provers, no tester can estimate the support size up to factors $2^{\Omega(n)}$ with probability better than $2^{-\Theta(n)}$. Our result is tight. In contrast, coherent subset state proofs suffice to improve testability exponentially, Quantum advantage with certificates: With poly-many copies and subset state proofs, a tester can approximate the support size of a subset state of arbitrary size. Some structural assumption on the quantum proofs is required since we show, Collapse of QMA: A general proof cannot improve testability of any quantum property whatsoever. We also show connections to disentangler and quantum-to-quantum transformation lower bounds.

quant-ph↗

arXiv2024

Quantum Merlin-Arthur with an internally separable proof

We find a modification to QMA where having one quantum proof is strictly less powerful than having two unentangled proofs, assuming EXP $\ne$ NEXP. This gives a new route to prove QMA(2) = NEXP that overcomes the primary drawback of a recent approach [arXiv:2402.18790 , arXiv:2306.13247] (QIP 2024). Our modification endows each proof with a form of *multipartite* unentanglement: after tracing out one register, a small number of qubits are separable from the rest of the state.

quant-ph↗

arXiv2024

Pseudorandom and Pseudoentangled States from Subset States

Pseudorandom states (PRS) are an important primitive in quantum cryptography. In this paper, we show that subset states can be used to construct PRSs. A subset state with respect to $S$, a subset of the computational basis, is \[ \frac{1}{\sqrt{|S|}}\sum_{i\in S} |i\rangle. \] As a technical centerpiece, we show that for any fixed subset size $|S|=s$ such that $s = 2^n/ω(\mathrm{poly}(n))$ and $s=ω(\mathrm{poly}(n))$, where $n$ is the number of qubits, a random subset state is information-theoretically indistinguishable from a Haar random state even provided with polynomially many copies. This range of parameter is tight. Our work resolves a conjecture by Ji, Liu and Song. Since subset states of small size have small entanglement across all cuts, this construction also illustrates a pseudoentanglement phenomenon.

quant-ph↗

arXiv2024

The Power of Unentangled Quantum Proofs with Non-negative Amplitudes

Quantum entanglement is a fundamental property of quantum mechanics and plays a crucial role in quantum computation and information. We study entanglement via the lens of computational complexity by considering quantum generalizations of the class NP with multiple unentangled quantum proofs, the so-called QMA(2) and its variants. The complexity of QMA(2) is a longstanding open problem, and only the trivial bounds QMA $\subseteq$ QMA(2) $\subseteq$ NEXP are known. In this work, we study the power of unentangled quantum proofs with non-negative amplitudes, a class which we denote $\text{QMA}^+(2)$. In this setting, we are able to design proof verification protocols for problems both using logarithmic size quantum proofs and having a constant probability gap in distinguishing yes from no instances. In particular, we design global protocols for small set expansion, unique games, and PCP verification. As a consequence, we obtain NP $\subseteq \text{QMA}^+_{\log}(2)$ with a constant gap. By virtue of the new constant gap, we are able to ``scale up'' this result to $\text{QMA}^+(2)$, obtaining the full characterization $\text{QMA}^+(2)$=NEXP by establishing stronger explicitness properties of the PCP for NEXP. One key novelty of these protocols is the manipulation of quantum proofs in a global and coherent way yielding constant gaps. Previous protocols (only available for general amplitudes) are either local having vanishingly small gaps or treat the quantum proofs as classical probability distributions requiring polynomially many proofs thereby not implying non-trivial bounds on QMA(2). Finally, we show that QMA(2) is equal to $\text{QMA}^+(2)$ provided the gap of the latter is a sufficiently large constant. In particular, if $\text{QMA}^+(2)$ admits gap amplification, then QMA(2)=NEXP.

quant-ph↗

arXiv2024

Dimension Independent Disentanglers from Unentanglement and Applications

Quantum entanglement is a key enabling ingredient in diverse applications. However, the presence of unwanted adversarial entanglement also poses challenges in many applications. In this paper, we explore methods to "break" quantum entanglement. Specifically, we construct a dimension-independent k-partite disentangler (like) channel from bipartite unentangled input. We show: For every $d,\ell\ge k$, there is an efficient channel $Λ: \mathbb{C}^{d\ell} \otimes \mathbb{C}^{d\ell} \to \mathbb{C}^{dk}$ such that for every bipartite separable state $ρ_1\otimes ρ_2$, the output $Λ(ρ_1\otimesρ_2)$ is close to a k-partite separable state. Concretely, for some distribution $μ$ on states from $\mathbb{C}^d$, $$ \left\|Λ(ρ_1 \otimes ρ_2) - \int | ψ\rangle \langle ψ|^{\otimes k} dμ(ψ)\right\|_1 \le \tilde O \left(\left(\frac{k^{3}}{\ell}\right)^{1/4}\right). $$ Moreover, $Λ(| ψ\rangle \langle ψ|^{\otimes \ell}\otimes | ψ\rangle \langle ψ|^{\otimes \ell}) = | ψ\rangle \langle ψ|^{\otimes k}$. Without the bipartite unentanglement assumption, the above bound is conjectured to be impossible. Leveraging our disentanglers, we show that unentangled quantum proofs of almost general real amplitudes capture NEXP, greatly relaxing the nonnegative amplitudes assumption in the recent work of QMA^+(2)=NEXP. Specifically, our findings show that to capture NEXP, it suffices to have unentangled proofs of the form $| ψ\rangle = \sqrt{a} | ψ_+ \rangle + \sqrt{1-a} | ψ_- \rangle$ where $| ψ_+ \rangle$ has non-negative amplitudes, $| ψ_- \rangle$ only has negative amplitudes and $| a-(1-a) | \ge 1/poly(n)$ with $a \in [0,1]$. Additionally, we present a protocol achieving an almost largest possible gap before obtaining QMA^R(k)=NEXP$, namely, a 1/poly(n) additive improvement to the gap results in this equality.

quant-ph↗

arXiv2023

Production of the triply heavy $Ω_{ccc}$ and $Ω_{bbb}$ baryons at $e^+e^-$ colliders

Non-relativistic quantum chromodynamics (NRQCD) factorization formulism is an important approach to investigate the production of the heavy quarkonium. In this paper, we study the production of the $Ω_{ccc}$ and $Ω_{bbb}$ at the $e^+e^-$ collider, using the NRQCD factorization formulism. We calculate the total and differential cross sections exactly of the processes, $e^+e^-\rightarrow γ^*/Z^*\rightarrow Ω_{ccc}\bar{c}\bar{c}\bar{c}$ and $e^+e^-\rightarrow γ^*/Z^*\rightarrow Ω_{bbb}\bar{b}\bar{b}\bar{b}$, in the leading order at the $e^+e^-$ colliders with different energies. The results show that it is hard to observe them at the $e^+e^-$ collider directly.

hep-ph↗