Coecke Links Language Grammar to Quantum Circuits for AI Advantage

From Quantum Picturalism to Quantum NLP: Interpretable, Scalable, and Exponential Advantage — Ai4

Ai4

Mapping natural language syntax directly into quantum circuits provides exponential computational speedups and built-in interpretability that black-box deep learning models cannot achieve.

AI-assisted summary of From Quantum Picturalism to Quantum NLP: Interpretable, Scalable, and Exponential Advantage — original source. Check the original for full context.

Source published:

Detailed notes

## Background Published on YouTube by the Ai4 channel on August 15, 2026, this presentation features Bob Coecke, Founder and CEO of Relational Intelligence. According to the page description, the talk chronicles the twenty-year development of diagrammatic quantum picturalism and explains how natural language and quantum systems share an identical mathematical structure, resulting in scalable, interpretable Quantum Natural Language Processing (QNLP).

## TL;DR Bob Coecke traces the evolution of quantum picturalism from John von Neumann's early critique of Hilbert spaces to category-theoretic visual diagrams that secondary school students can master faster than traditional formalism. He recounts his pivotal breakthrough with linguist Jim Lambek, which established that quantum compositionality and grammatical structure share the exact same underlying architecture. By combining linguistic vectors with diagrammatic syntax, Coecke's team developed Quantum NLP, enabling discourse to be represented as language-neutral text circuits. This quantum-inspired compositional framework provides explainable AI, massive training data efficiency, and demonstrable exponential speedups on quantum hardware alongside scalable classical deployment.

## Atmosphere & style The presentation carries an engaging, iconoclastic, and accessible tone, blending deep mathematical insights with witty personal anecdotes and spontaneous humor. Coecke speaks with the warmth and conversational ease of an Oxford academic and industry veteran who genuinely enjoys dismantling quantum mysticism, playfully acknowledging slide glitches while passing physical visual textbooks through the audience. The talk transitions smoothly from philosophical reflections on Leibniz and Schrödinger to rigorous modern computing paradigms, creating an intellectually stimulating and refreshingly grounded look at the future of AI.

## Key takeaways - [00:04](https://www.youtube.com/watch?v=djCZTOUUkcc&t=4s) The deepest intersection between AI and quantum computing ('Quantum Meets AI') occurs because quantum mechanics and natural language processing share the exact same underlying compositional mathematics. - [01:27](https://www.youtube.com/watch?v=djCZTOUUkcc&t=87s) Traditional Hilbert space formalisms were renounced by John von Neumann in 1935, paving the way for compositionality and graphical tensor network approaches pioneered by Roger Penrose. - [04:25](https://www.youtube.com/watch?v=djCZTOUUkcc&t=265s) Quantum Picturalism uses monoidal category theory to make quantum mechanics fully visual, enabling secondary school students to outperform Oxford postgraduates on quantum physics exams. - [04:25](https://www.youtube.com/watch?v=djCZTOUUkcc&t=265s) Diagrammatic calculi like ZX-calculus are mathematically complete with respect to Hilbert space quantum mechanics and are widely adopted across industry leaders like IBM and Google. - [08:13](https://www.youtube.com/watch?v=djCZTOUUkcc&t=493s) Mathematician Jim Lambek discovered that diagrammatic quantum teleportation shares the exact mathematical grammar structure used in linguistic syntactic analysis. - [10:17](https://www.youtube.com/watch?v=djCZTOUUkcc&t=617s) Embedding native compositional language structures into quantum circuits significantly reduces the volume of training data required relative to traditional statistical deep learning models. - [12:14](https://www.youtube.com/watch?v=djCZTOUUkcc&t=734s) Quantum Natural Language Processing (QNLP) resolves long-standing AI challenges by unifying vector-based word meanings with grammatical sentence structures onto quantum circuits. - [14:17](https://www.youtube.com/watch?v=djCZTOUUkcc&t=857s) Classical bottom-up Fregean compositionality fails in deep neural networks, driving the need for top-down compositional interpretability and explainable AI (XAI) frameworks. - [16:35](https://www.youtube.com/watch?v=djCZTOUUkcc&t=995s) The 'mathematics of text structure' represents multi-sentence discourse as language-neutral circuits with entities as persistent wires and relational interactions as gates. - [18:47](https://www.youtube.com/watch?v=djCZTOUUkcc&t=1127s) Quantum-inspired circuit representations provide four simultaneous advantages: full interpretability, classical scalability, high energy efficiency, and an exponential speedup on quantum processors.

## Detailed walkthrough ### [00:04](https://www.youtube.com/watch?v=djCZTOUUkcc&t=4s) Defining the Intersection: AI Meets Quantum

Bob Coecke introduces himself as the CEO and founder of Relational Intelligence, following a twenty-year career as a professor at Oxford University and a five-year tenure as Chief Scientist at the quantum computing company Quantinuum. Addressing an AI conference audience, he sets out to demystify what bringing artificial intelligence and quantum computing together actually means. He outlines three distinct paradigms: 1. **AI for Quantum**: Using machine learning to optimize and speed up quantum computing research and algorithms—which he considers a practical "no-brainer." 2. **Quantum for AI**: Deploying quantum hardware to accelerate AI models. He notes that while he strongly believes in its future, AI is inherently an empirical discipline, and today's hardware is not yet mature enough to provide overwhelming empirical evidence of quantum advantage. 3. **Quantum Meets AI**: The deeper convergence where quantum mechanics and natural language processing share the exact same underlying mathematical architecture.

[01:27](https://www.youtube.com/watch?v=djCZTOUUkcc&t=87s) Compositionality: From von Neumann to Schrödinger and Penrose

The story of this convergence begins with the mathematical foundations of quantum theory. In 1932, John von Neumann published the standard mathematical framework for quantum mechanics based on Hilbert spaces. Remarkably, only three years later in 1935, von Neumann publicly denounced his own creation in a letter, writing: "I would like to make a confession which may seem [strange]... I do not absolutely believe in Hilbert space no more."

Around the same period, Erwin Schrödinger observed that when two physical systems enter into temporary physical interaction, their entanglement and combination represents not merely one feature among many, but rather "the characteristic trait of quantum theory." In computer science, this foundational phenomenon of putting systems together is known as compositionality. While traditional physics neglected compositionality for decades, Roger Penrose (a colleague of Coecke's in the Oxford Mathematics Department) realized during his undergraduate studies that drawing graphical tensor network diagrams provided far more intuitive, useful calculations than standard algebraic tensor index notation. Penrose’s graphical diagrams, introduced in notes and later published in a 1971 paper appendix, remained largely overlooked as a formal mathematical language for decades.

```mermaid flowchart TD accTitle: Evolution of Quantum Compositional Formalisms subgraph S1["Foundational Insights"] VN["John von Neumann (1935)<br/>'Denounces Hilbert Space'"] SC["Erwin Schrödinger<br/>'Interaction is the trait of Quantum'"] end

subgraph S2["Diagrammatic Bridge"] RP["Roger Penrose (1971)<br/>Graphical Tensor Diagrams"] MCT["Monoidal Category Theory<br/>Mathematics of Compositionality"] end

subgraph S3["Modern Quantum Picturalism"] QP["Quantum Picturalism<br/>(Coecke et al.)"] QNLP["Quantum Natural Language Processing<br/>(Quantum meets AI)"] end

VN --> MCT SC --> MCT RP --> QP MCT --> QP QP --> QNLP ```

[04:25](https://www.youtube.com/watch?v=djCZTOUUkcc&t=265s) Quantum Picturalism and Teaching Quantum to Schoolchildren

Around 2003–2004, Coecke began developing *Quantum Picturalism*—a complete reformulation of quantum theory grounded in monoidal category theory, a branch of mathematics traditionally dismissed by some pure mathematicians as "abstract nonsense." Monoidal category theory proves that compositionality across diverse domains—whether in quantum mechanics, AI, cooking, or human relationships—is mathematically equivalent to drawing pictures.

This work culminated in Coecke and Aleks Kissinger's 2017 textbook *Picturing Quantum Processes*, which has served as the foundational curriculum for Oxford University's postgraduate quantum computing course since roughly 2013. Coecke later co-authored *Quantum in Pictures* (with Stefano Gogioso), a visual guide designed for audiences without advanced mathematical backgrounds.

To demonstrate the power and accessibility of diagrammatic reasoning, Coecke and his team conducted an educational experiment covered by *The Guardian*, where secondary school students were taught quantum theory exclusively through pictures and videos. In a subsequent test, these high school pupils outperformed Oxford University postgraduate students who used standard algebraic methods. Coecke highlights ongoing global initiatives teaching this visual quantum language in places like Ghana. He notes with amusement that while he had updated his presentation slides with diagram samples that failed to load properly, he brought physical copies of the book to pass through the audience. Crucially, this visual framework has been mathematically proven to be fully complete with respect to Hilbert space quantum mechanics and is now widely adopted across major quantum computing industry players, including IBM and Google.

- **Foundational Equivalence**: Anything derivable or provable in traditional Hilbert space quantum mechanics can be proven diagrammatically via Quantum Picturalism. - **Widespread Industry Adoption**: Major quantum hardware and software ecosystems (such as IBM and Google) now utilize diagrammatic calculus (such as ZX-calculus) in compiler optimization and circuit design.

[08:13](https://www.youtube.com/watch?v=djCZTOUUkcc&t=493s) The McGill Breakthrough: Quantum Teleportation is Grammar

The conceptual leap connecting quantum physics to AI occurred around 2004–2005 during a category theory seminar at McGill University. Coecke was presenting his pictorial derivation of quantum teleportation when Jim Lambek—a pioneer of mathematical linguistics who developed pregroup grammars and algebraic systems for syntactic analysis in the 1950s—interrupted him.

Lambek pointed at the quantum teleportation diagrams and insisted, "Hey, Bob, this is grammar. This is grammar." Coecke initially pushed back, saying, "No, no, Jim. Jim, Jim, this is physics. This is quantum physics." Lambek doubled down, and when the two researchers sat down to analyze the underlying mathematics, they discovered that monoidal category theory unifies both fields under the exact same compositional architecture. The way words compose to form meaning in a sentence, and the way concepts interact in human cognition, mirrors how quantum physical systems compose and interact during processes like teleportation.

[10:17](https://www.youtube.com/watch?v=djCZTOUUkcc&t=617s) The Birth of Quantum NLP on Near-Term Quantum Hardware

By 2020, recognizing that the algebraic structure of natural language syntax matches quantum compositionality allowed researchers to run natural language processing tasks directly on NISQ-era quantum hardware. Coecke's team successfully executed Quantum Natural Language Processing (QNLP) on a small quantum processor with as few as six qubits, training models to answer questions accurately.

The critical insight behind this success is computational data efficiency. Traditional statistical AI approaches require vast troves of unstructured data to learn patterns. By contrast, embedding the natural compositional structure of language directly into native quantum circuits drastically reduces the amount of training data required to achieve meaningful representations. This breakthrough traced directly back to early foundational work, beginning with a 2008 paper that formulated the very first mathematically rigorous compositional distributional model of meaning.

[12:14](https://www.youtube.com/watch?v=djCZTOUUkcc&t=734s) Combining Meaning and Grammar: The Birth of Quantum NLP

Previous attempts to unite linguistic meaning and grammar—such as early work by Paul Smolensky—suffered from severe structural flaws. The core challenge in natural language processing was reconciling two distinct paradigms: word meanings, which modern machine learning represents as vectors, and grammar, the structural rules long studied by linguists. When mathematician Jim Lambek pointed out that the diagrammatic quantum formalism shared the exact same structure as natural language grammar, the solution became immediate. In quantum mechanics, what flows through systems are vectors; likewise, in natural language processing and modern large language models, words and meanings are represented as vectors. Despite having no initial background in AI or NLP, Bob Coecke recognized that the new quantum pictorial formalism was the natural framework to compose meaning and language.

In subsequent work, Coecke and his doctoral student proved in 2016 that executing this compositional language model on a quantum computer yielded a quantum advantage—initially a quadratic speedup. This led to pioneering experimental demonstrations of question answering executed directly on quantum hardware, alongside the release of `lambeq`, an open-source software package designed to convert natural language text into quantum circuits. Pointing to his t-shirt, Coecke notes that his new company, Relational Intelligence, is currently re-engineering this software stack from the ground up to deliver a vastly improved platform.

```mermaid flowchart LR accTitle: Quantum NLP Synthesis accDescription: Flow showing how vector semantics and grammatical structure combine via quantum picturalism into quantum circuits.

subgraph Language ["Natural Language"] V["Word Meanings<br/>(Vectors)"] G["Grammar Structure<br/>(Linguistics)"] end

subgraph QNLP ["Quantum Picturalism"] D["Diagrammatic Tensor Calculus<br/>(Wires & Boxes)"] end

subgraph Execution ["Implementation"] QC["Quantum Circuits / lambeq<br/>(Exponential Advantage)"] end

V --> D G --> D D --> QC ```

- **Origins of QNLP:** Direct mapping of vector-based semantics into grammatical diagrammatic calculi identified by Jim Lambek. - **Hardware demonstrations:** Successful execution of question-answering tasks on physical quantum devices following the 2016 theoretical framework. - **Software evolution:** Transitioning from the original `lambeq` library to a redesigned software platform at Relational Intelligence.

---

[14:17](https://www.youtube.com/watch?v=djCZTOUUkcc&t=857s) Rethinking Compositionality for AI and Quantum Systems

Compositionality is the foundational principle underpinning modern information technology; without it, complex systems like smartphones could not function. In linguistics, standard compositionality is traditionally attributed to Gottlob Frege: if you know the meanings of the parts and the rules governing how they assemble, you understand the meaning of the whole. While this bottom-up principle works seamlessly when writing computer code, it breaks down completely in modern artificial intelligence and quantum mechanics.

In deep learning, combining artificial neurons into a network does not yield an interpretable whole because we do not know the individual meaning of an isolated neuron. Furthermore, information flow in AI does not operate strictly bottom-up; it also runs top-down, where the holistic meaning of the concept (such as identifying a bird) dictates the internal representations of the components rather than the reverse. To address this failure mode, Coecke and his team formulated a framework termed *compositional interpretability for explainable AI (XAI)*, developing a quantum-inspired foundation designed to guarantee transparency and explainability across both classical and quantum architectures.

- **Fregean compositionality:** The classical assumption that meaning is strictly determined bottom-up from constituent parts fails in deep neural networks. - **Top-down semantic flow:** High-level contextual concepts enforce meaning onto individual internal units. - **Explainable AI (XAI):** Quantum-inspired compositional interpretability establishes structural transparency across machine learning pipelines.

---

[16:35](https://www.youtube.com/watch?v=djCZTOUUkcc&t=995s) The Mathematics of Text Structure and Circuit Representations

To formalize meaning beyond single sentences, Coecke developed a framework known as the "mathematics of text structure." In this system, discourse is mapped directly into interacting circuits. For example, a narrative containing sequential interactions—such as "Alex meets Bo," "Bo marries Chris," and "Alex kicks Bo"—is represented as a circuit where entities act as persistent wires (Alex, Bo, Chris) and their verbs represent interacting gates (meets, marries, kicks). When semantic meanings are instantiated as vectors, these representations translate directly into executable quantum circuits.

```mermaid flowchart TD accTitle: Text Structure Circuit Mapping accDescription: Diagram showing entity wires interacting via relational linguistic gates across a multi-sentence discourse.

subgraph Discourse ["Text Input"] S1["'Alex meets Bo'"] S2["'Bo marries Chris'"] S3["'Alex kicks Bo'"] end

subgraph Circuit ["Circuit Representation"] direction LR A["Alex"] --- G1["[Meets]"] --- A2["Alex"] --- G3["[Kicks]"] --- A3["Alex"] B["Bo"] --- G1 --- B2["Bo"] --- G2["[Marries]"] --- B3["Bo"] --- G3 --- B4["Bo"] C["Chris"] --- G2 --- C2["Chris"] end

Discourse --> Circuit ```

This circuit-based model overcomes a major historical limitation of Noam Chomsky’s universal grammar program. While Chomsky sought universal linguistic structures, natural languages exhibit vastly different word orders and type systems. Text circuits, by contrast, are fundamentally language-neutral:

> "It doesn't matter how you explain something. If you want to be a snob and you use long sentences or you want to be simple and understood and use short many short sentences, it's all the same with these circuits. So it's sort of a more condensed model of meaning."

Because these circuits natively mirror quantum processes, mapping them onto quantum hardware delivers an exponential advantage over classical machines for large-scale natural language processing and cognitive modeling.

---

[18:47](https://www.youtube.com/watch?v=djCZTOUUkcc&t=1127s) Scalability, Responsible AI, and Future Directions

In recent experimental benchmarks, Coecke’s team demonstrated practical hybrid execution by training language models classically on laptops and testing them at the absolute computational limits of classical simulation. The underlying circuit structure provides four critical advantages simultaneously: total model interpretability, exponential runtime advantages on quantum processors, broad classical scalability, and high energy efficiency.

Reflecting on the reception of this work, Coecke notes that in 2024 it was recognized as one of the top research achievements in quantum computing. He playfully adds that while he views it equally as a milestone for classical computing, his previous quantum computing employer discouraged promoting that aspect because it sent a "mixed message." At Relational Intelligence, this dual classical-quantum vision is being actively commercialized. For those interested in the deeper philosophical roots of diagrammatic and process-based thinking, Coecke points to his appearance on the *Entangled Things* podcast—where he traces these concepts back to Heraclitus, Gottfried Wilhelm Leibniz, and Erwin Schrödinger—a historical synthesis he is currently expanding into a forthcoming book.

## Notable quotes > [01:27](https://www.youtube.com/watch?v=djCZTOUUkcc&t=87s) I would like to make a confession which may seem [strange]... I do not absolutely believe in Hilbert space no more. — John von Neumann

> [01:27](https://www.youtube.com/watch?v=djCZTOUUkcc&t=87s) the characteristic trait of quantum theory — Erwin Schrödinger

> [08:13](https://www.youtube.com/watch?v=djCZTOUUkcc&t=493s) Hey, Bob, this is grammar. This is grammar. — Jim Lambek

> [08:13](https://www.youtube.com/watch?v=djCZTOUUkcc&t=493s) No, no, Jim. Jim, Jim, this is physics. This is quantum physics. — Bob Coecke

> [16:35](https://www.youtube.com/watch?v=djCZTOUUkcc&t=995s) It doesn't matter how you explain something. If you want to be a snob and you use long sentences or you want to be simple and understood and use short many short sentences, it's all the same with these circuits. So it's sort of a more condensed model of meaning. — Bob Coecke

## Mentioned Ai4, Aleks Kissinger, Bob Coecke, Cambridge University Press, Entangled Things, Erwin Schrödinger, Google, Gottfried Wilhelm Leibniz, Gottlob Frege, Heraclitus, IBM, Jim Lambek, John von Neumann, McGill University, Noam Chomsky, Paul Smolensky, Picturing Quantum Processes, Quantinuum, Quantum in Pictures, Relational Intelligence, Roger Penrose, Stefano Gogioso, The Guardian, University of Oxford, ZX-calculus, lambeq

## Video description Bob Coecke - Founder, CEO, Relational Intelligence

Quantum and natural language share the same structure! Here's the story.

Over some 20 years we have developed a diagrammatic quantum formalism, referred to as quantum picturalism [1, 2]. We showed that this formalism enabled secondary school students to perform exceptionally well on an Oxford University post-grad quantum exam [3]. This quest started when in 1935 John von Neumann denounced `his own’ Hilbert space based quantum formalism. Quantum picturalism on the other hand, is now widespread in quantum technology research.

A remarkable fact is that in its pictorial form, composition of quantum systems shares the same structure as natural language. This resulted in the birth of Quantum NLP [4]. In more recent work, we demonstrated exponential advantage, interpretability, and scalability of Quantum NLP [5]. In fact, interpretability and scalability can also be achieved when adopting a quantum-inspired approach on classical hardware.

The same formalism has also been used the generate the 1st piece of music with a quantum computer [5].

MEDIA REFERENCES:

[1] Bob Coecke and Aleks Kissinger (2017) Picturing Quantum Processes. Cambridge University Press. [2] Bob Coecke and Stefano Gogioso (2022) Quantum in Pictures. Quantinuum. [3] https://www.theguardian.com/science/2023/dec/16/physicist-bob-coecke-its-easier-to-convince-kids-than-adults-about-quantum-mechanics [4] https://www.forbes.com/sites/moorinsights/2021/10/13/cambridge-quantum-makes-quantum-natural-language-processing-a-reality/ [5] https://thequantuminsider.com/2024/09/18/quantinuum-unveils-first-contribution-toward-responsible-ai-uniting-power-of-its-quantum-processors-with-experimental-work-on-integrating-classical-quantum-computing/ [6] https://qspace.fqxi.org/articles/264/quanthovens-fifth

[Source](https://www.youtube.com/watch?v=djCZTOUUkcc)

中文简报

Coecke将语言语法与量子电路相联系以获取AI优势 将自然语言句法直接映射到量子电路中，可提供黑盒深度学习模型无法实现的指数级计算加速与内置可解释性。 Bob Coecke 梳理了量子图像论（quantum picturalism）的演变历程：从 John von Neumann 早期对希尔伯特空间的批判，到中学生比传统形式化方法更快掌握的范畴论可视化图表。他回顾了与语言学家 Jim Lambek 共同取得的关键突破，该突破确立了量子可组合性与语法结构共享完全相同的底层架构。通过将语言向量与图解句法相结合，Coecke 的团队开发了量子自然语言处理（Quantum NLP），使话语能够被表示为与具体语言无关的文本电路。这种受量子启发的组合框架提供了可解释的AI、极高的训练数据效率，以及在量子硬件上可论证的指数级加速与可扩展的经典部署能力。 人工智能与量子计算最深刻的交汇（“量子遇见AI”）之所以存在，是因为量子力学与自然语言处理共享完全相同的底层组合数学。 (0:04) 传统的希尔伯特空间形式化体系于1935年被 John von Neumann 放弃，这为可组合性以及由 Roger Penrose 开创的图形张量网络方法铺平了道路。 (1:27) 量子图像论利用幺半范畴论使量子力学完全可视化，使中学生在量子物理考试中的表现能够超越牛津大学研究生。 (4:25) 像 ZX-演算（ZX-calculus）这样的图解演算在数学上相对于希尔伯特空间量子力学是完备的，并已被 IBM 和 Google 等行业领导者广泛采用。 (4:25) 数学家 Jim Lambek 发现，图解量子隐形传态与语言句法分析中使用的数学语法结构完全相同。 (8:13)

Reading summary

Bob Coecke argues that natural language processing and quantum mechanics share an identical compositional architecture rooted in monoidal category theory, enabling native quantum NLP models that provide interpretability, data efficiency, and potential exponential quantum advantage. Foundations of Quantum Picturalism (1:27) The convergence of quantum physics and artificial intelligence stems from compositional mathematics rather than brute-force computation. Following John von Neumann's 1935 rejection of his own Hilbert space formalism and Erwin Schrödinger's identification of interaction as the defining trait of quantum theory, Roger Penrose introduced graphical tensor network diagrams in 1971. Building on these ideas, Coecke formulated Quantum Picturalism around 2003–2004 using monoidal category theory, translating complex algebraic manipulations across physical interactions into intuitive graphical calculi. This diagrammatic approach was shown to be mathematically complete with respect to traditional Hilbert space quantum mechanics. In educational trials reported by The Guardian, secondary school pupils taught quantum concepts purely through visual diagrams outperformed Oxford University postgraduate students relying on conventional algebraic methods. Diagrammatic tools like ZX-calculus have since been adopted by major quantum computing ecosystems, including IBM and Google, for circuit design and compiler optimization. Bridging Vector Semantics and Linguistic Grammar (8:13) Natural language processing historically struggled to unite statistical word meanings—represented as vectors—with formal grammatical rules. Around 2004–2005, linguist Jim Lambek identified that Coecke's pictorial derivations of quantum teleportation shared the identical mathematical structure of pregroup grammars. Because quantum processes propagate vectors through interactions just as sentences combine word vectors through grammatical constraints, the two fields mapped directly onto the same monoidal category formalism. This structural match gave rise to Quantum Natural Language Processing (QNLP) and a rigorous compositional distributional model of meaning formulated in 2008. In 2016, Coecke and a doctoral student theoretically proved a quantum speedup for executing this model, which led to real hardware demonstrations on processors with as few as six qubits and the open-source software library lambeq. By embedding grammar natively into quantum circuits, QNLP avoids the massive data requirements of purely statistical models. Text Circuits and Explainable AI (14:17) Standard bottom-up Fregean compositionality fails in deep neural networks because individual artificial neurons lack independent meaning and contextual information frequently flows top-down. To resolve this opacity, Coecke developed a compositional framework for explainable AI (XAI) that formalizes text beyond individual sentences into interconnected circuits. Under this mathematics of text structure, narrative entities persist as continuous wires, while verbs and events operate as interacting gates—for example, connecting Alex, Bo, and Chris across sequential relational actions. Unlike Chomskyan universal grammar, which is constrained by surface-level syntactic variations across spoken languages, text circuits operate in a language-neutral format that represents meaning independently of sentence length or word order. Hardware Execution, Scalability, and Industry Strategy (18:47) Recent benchmarks have demonstrated practical hybrid execution, training models on classical laptops while testing their limits through classical simulation. Coecke contends that representing text as quantum-native circuits yields four simultaneous advantages: intrinsic model interpretability, exponential runtime scaling on quantum hardware, classical efficiency, and lower energy usage. Coecke notes that his former employer, Quantinuum, prioritized the quantum narrative, whereas his venture, Relational Intelligence, actively commercializes this circuit architecture across both classical and quantum computing pipelines. While the diagrammatic approach resolves core representational hurdles in both natural language and quantum mechanics, practical empirical advantage currently remains constrained by the maturity of physical quantum hardware, leaving modern implementations reliant on classical simulation and near-term hybrid workflows.

精炼阅读摘要

Relational Intelligence 创始人 Bob Coecke 提出，量子力学与自然语言处理在单子范畴论下共享相同的组合数学结构，通过量子图画主义（Quantum Picturalism）能够构建出兼具强解释性与指数级量子优势的语言模型。 量子图画主义的起源与完备性 (1:27) 量子力学的标准形式最早由 John von Neumann 于 1932 年基于希尔伯特空间建立，但仅三年后他便在信件中对这一纯代数框架表示怀疑。与此同时，Erwin Schrödinger 将系统间的纠缠与组合视为量子理论的本质特征。受 Roger Penrose 早期图张量网络研究的启发，Bob Coecke 自 2003 年起利用单子范畴论创立了量子图画主义，将复杂的张量指标代数转化为严谨的图形演算系统。这套框架在数学上被证明与传统希尔伯特空间完备等价，能够推导标准量子理论的全部内容，如今已被 IBM 和 Google 等行业机构广泛应用于量子编译器优化与电路设计。 语法与量子纠缠的数学同构 (8:13) 2004 年至 2005 年间，Coecke 在麦吉尔大学展示量子隐形传态的图画推导时，语言学家 Jim Lambek 指出该图结构与分析自然语言句法的预群语法完全一致。在现代自然语言处理中，词义被表示为向量空间中的数据，而量子过程中系统传递的实体同样是向量。通过将表征意义的向量与表征句法的图结构结合，研究团队于 2008 年建立了首个严格的组合分布式语义模型，并于 2016 年证明该模型在量子计算硬件上运行可带来加速优势。此后，研究团队开发了开源工具 lambeq，并在 2020 年成功利用仅包含 6 个量子比特的早期含噪物理芯片完成了问答任务测试。 重构组合性与可解释人工智能 (14:17) 自 Gottlob Frege 以来，传统语言学假定整体语义可由各个孤立组成部分自底向上组装而成。然而，深度神经网络在组合神经元时呈现黑盒状态，且高层概念往往自顶向下约束内部表征，使得经典组合性原则彻底失效。为此，Coecke 团队提出了面向可解释人工智能（XAI）的组合可解释性方案，通过量子图张量形式提供透明的因果与语义追踪机制。此外，该体系直接利用语言自身的内在组合结构指导建模，与传统依赖海量无标注语料的统计型大模型相比，能显著降低模型对训练数据规模的依赖。 文本结构数学与跨语言电路映射 (16:35) 为了超越单句限制以处理复杂叙事，Coecke 提出了文本结构数学。在该体系中，跨句篇章被统一转化为交互电路：文本中的实体充当持续存在的导线，动词与谓词则作为连接实体的多体逻辑门。与 Noam Chomsky 追求的形式普遍语法不同，文本电路不受句式长短或语序变动的干扰，表现出对具体语言形式的中立性，从而构成了更紧凑的核心语义表征。因为这种电路形式与量子多体系统在数学上天然对称，将其映射到物理量子硬件时理论上可带来超越经典模拟的指数级加速。 双轨计算架构与工业落地现状 (18:47) 在实验验证中，研究团队实现了经典硬件与量子处理器的混合协同工作：模型可在普通笔记本电脑上完成训练，并在经典模拟的算力极限边缘进行测试验证。Coecke 表示，这一结构同时具备完全的可解释性、高能效比、经典可扩展性以及在量子硬件上的指数加速潜力。尽管该成果在 2024 年被评为量子计算领域的关键研究突破，但 Coecke 指出其商业化重点同样在于推动经典计算系统的效率变革，目前初创公司 Relational Intelligence 正在对底层技术栈进行工业化重构。 该范式为破解黑盒 AI 的解释性困境提供了坚实的范畴论数学基础，但其在超大规模商业应用中的表现仍取决于物理量子硬件的成熟度，以及在经典计算架构上进行超高维张量收缩时面临的工程瓶颈。

Detailed notes — zh

## Background 本视频由 Ai4 频道于 2026 年 8 月 15 日在 YouTube 平台发布，主讲人为 Relational Intelligence 创始人兼 CEO、前牛津大学教授 Bob Coecke。视频简介指出，自然语言与量子系统共享同一套底层数学结构，演讲围绕图示量子力学（Quantum Picturalism）的演进、中学生考试超越牛津研究生的教学突破，以及量子自然语言处理（QNLP）在可解释性、可扩展性与指数级优势上的前沿进展展开。 ## TL;DR Bob Coecke 梳理了从 1935 年冯·诺伊曼反思希尔伯特空间到当代图示量子力学（Quantum Picturalism）的发展脉络，阐明幺半范畴论与拓扑图示记号在数学上严格等价。当该图示体系与兰贝克代数语法交汇时，催生了量子自然语言处理（QNLP）与开源框架 lambeq，使语义向量与语法结构在弦图线路上实现原生融合。针对现代深度学习黑盒与弗雷格式组合性的失效，他提出了基于‘意义量子线路’的文本结构数学与组合可解释性理论，不仅消除了跨语种句法差异，还在真实硬件验证中展现出超越经典计算的指数级量子优势与绿色能效潜力。 ## Atmosphere & style 演讲整体洋溢着学术大师举重若轻的自信与前沿探索的激情，Bob Coecke 以幽默风趣且极具穿透力的叙事将深奥的范畴论与量子物理讲得生动透彻。从黑板前与数学语言学泰斗兰贝克的顿悟对话，到中学生凭图示超越牛津研究生的实验，整场分享充满跨学科碰撞的顿悟感。听众能切身感受到一种颠覆传统符号 AI 与暴力统计大模型的智力震撼，既有严密数理逻辑的优美，又蕴含着开辟全新计算范式的产业野心。 ## Key takeaways - [00:04](https://www.youtube.com/watch?v=djCZTOUUkcc&t=4s) Bob Coecke 将量子与 AI 的交集划分为三种范式：常规加速研发的“AI for Quantum”、受限硬件经验的“Quantum for AI”，以及从底层数学结构统一二者的“Quantum meets AI”。 - [01:27](https://www.youtube.com/watch?v=djCZTOUUkcc&t=87s) 约翰·冯·诺伊曼在 1935 年反思并放弃了希尔伯特空间体系，而埃尔温·薛定谔指出系统的“组合性”（Compositionality）才是量子理论的唯一特征本质。 - [01:27](https://www.youtube.com/watch?v=djCZTOUUkcc&t=87s) 现代数学证明描述系统组合交互的“幺半范畴论”在数学上完全等价于拓扑图示记号，图示成为跨学科通用的严格数学语言。 - [04:25](https://www.youtube.com/watch?v=djCZTOUUkcc&t=265s) 基于图示量子力学的教学实验表明，未接触高等数学的中学生在牛津大学研究生考试题上的整体表现超越了研究生，该图示体系已被 IBM、Google 等工业巨头采纳。 - [08:13](https://www.youtube.com/watch?v=djCZTOUUkcc&t=493s) 语言学家吉姆·兰贝克发现量子隐形传态的图示与语法代数系统同构，揭示了词汇意义组合与量子粒子纠缠相互作用遵循完全相同的数学规律。 - [12:14](https://www.youtube.com/watch?v=djCZTOUUkcc&t=734s) 量子自然语言处理（QNLP）成功将单词的向量语义与语法结构深度融合，研究团队基于开源工具包 lambeq 在 6 比特小规模量子硬件上实现了问答训练。 - [14:17](https://www.youtube.com/watch?v=djCZTOUUkcc&t=857s) 传统的自底向上弗雷格式组合性在深度神经网络黑盒中失效，Bob Coecke 提出了基于量子纠缠灵感的“组合可解释性”理论以赋能可解释 AI（XAI）。 - [16:35](https://www.youtube.com/watch?v=djCZTOUUkcc&t=995s) “文本结构数学”将文本语篇映射为实体导线与交互算符组成的量子线路，超越了传统语法的表层形式，实现了跨语种中立且兼具因果透明性的深层语义表征。 - [18:02](https://www.youtube.com/watch?v=djCZTOUUkcc&t=1082s) 将意义线路映射至量子硬件相较于经典硬件具有指数级量子优势，同时兼具高可解释性、可扩展性以及极高的计算能效，推动了初创公司 Relational Intelligence 的产业落地。 ## Detailed walkthrough ### [00:04](https://www.youtube.com/watch?v=djCZTOUUkcc&t=4s) 量子与人工智能的三种交集路径 Bob Coecke 开场介绍了自己的背景：他目前担任初创公司 Relational Intelligence 的 CEO，此前曾在牛津大学担任正教授长达 20 年，并曾在量子计算公司 Quantinuum 担任过约 5 年的首席科学家。关于受邀探讨的“量子与 AI”这一主题，他首先厘清了两者的三种不同结合方式：第一种是“AI 用于量子”（AI for Quantum），即在量子计算研发中使用常规 AI 加速算法设计，他笑称这完全是“显而易见的无需思考之举”（no-brainer）；第二种是“量子用于 AI”（Quantum for AI），尽管他对量子赋能 AI 的潜力深信不疑，但由于 AI 是一门重度依赖实验经验的学科，在当前量子硬件尚未成熟到能提供坚实经验证据的阶段，这一路线推进起来仍颇为棘手；第三种则是他本次演讲的核心——“量子遇见 AI”（Quantum meets AI），在他看来这才是真正的变革所在。 ```mermaid flowchart TD accTitle: AI 与量子的三种结合范式 subgraph S1["范式划分"] A["AI for Quantum<br/>用 AI 加速量子算法研发（显而易见）"] B["Quantum for AI<br/>用量子硬件跑 AI（受限于当前硬件）"] C["Quantum meets AI<br/>底层数学与结构统一（本次核心）"] end ``` ### [01:27](https://www.youtube.com/watch?v=djCZTOUUkcc&t=87s) 量子语言的演变：从希尔伯特空间到图示范式 现代量子力学语言的奠基人是计算机体系结构之父约翰·冯·诺伊曼（John von Neumann）。冯·诺伊曼在 1932 年出版的专著中建立了基于希尔伯特空间（Hilbert space）的量子数学体系，然而令人震惊的是，仅仅三年后的 1935 年，他便在一封信中公开反思：“我想做一个坦白，这可能显得有些奇怪……我绝对不再相信希尔伯特空间了。”随后，埃尔温·薛定谔（Erwin Schrödinger）在 1935 年指出，当两个物理系统发生相互作用时，所产生的特性并非量子力学的特征之一，而是“唯一的特征特征”（the characteristic trait of quantum theory）。在计算机科学中，这一概念被称为“组合性”（Compositionality），然而物理学界却长期忽视了这种系统组合的本质结构。 与此同时，牛津大学数学家罗杰·彭罗斯（Roger Penrose）早在本科学习广义相对论期间，就发现绘制图示比传统的张量符号更具洞察力且更便于计算。尽管彭罗斯在 1971 年的一篇论文附录中正式发表了张量图示记号（Penrose graphical notation），但当时几乎无人关注，更未被当作严肃的数学语言对待。现代数学已经严格证明，用于研究“组合性”的数学工具正是“幺半范畴论”（Monoidal Category Theory），而它在数学上完全等价于图示化表达（Drawing pictures）。不论是物理学、AI、烹饪还是人类关系，“图示”都是表达组合结构最准确的通用语言。 - **冯·诺伊曼的反思**：1932 年提出希尔伯特空间表述，1935 年宣告放弃，促使学界寻找更底层的量子语言。 - **薛定谔的组合洞见**：系统的组合交互是量子理论区别于经典物理的核心本质。 - **图示与范畴论的等价性**：幺半范畴论的严格代数结构与拓扑图示记号在数学上被证明完全等价。 ### [04:25](https://www.youtube.com/watch?v=djCZTOUUkcc&t=265s) 图示量子力学：从牛津研究生到中学生超越测试 从 2003 至 2004 年起，Bob 致力于将整套量子力学彻底“图示化”。2017 年，他与 Aleks Kissinger 合著出版了《Picturing Quantum Processes》，该书随后成为牛津大学研究生院讲授量子计算的标准教材，实现了一门完全基于图示推理的完整量子计算课程。随后，他又与 Stefano Gogioso 出版了普及著作《Quantum in Pictures》，在书的封底写道：“想学量子力学吗？觉得自己的数学基础不够？没关系，这本书里的图示是一种新型数学，它将带你领略整个量子世界。”这彻底颠覆了以往被数学家戏称为“纯粹抽象废话”（abstract nonsense）的范畴论印象，将其转变为直观易懂的图示教学工具。 为了验证图示化语言的威力，研究团队进行了一场受英国《卫报》（The Guardian）报道的对照实验：他们向高中生教授这套图示方法，结果这些此前没有高等数学背景的中学生在牛津大学的研究生量子考试题中，整体表现竟然超越了牛津大学的研究生。目前这套教学方法已在全球推广，包括在加纳等非洲国家普及量子教育。在理论层面上，他们严格证明了图示量子力学与传统的希尔伯特空间量子力学等价——任何能在希尔伯特空间证明的定理，都能在图示中推导。如今，IBM、Google 等量子科技巨头均已广泛采纳这套图示语言作为量子技术研究的基础工具。 ```mermaid flowchart LR accTitle: 量子力学形式化演进路线 subgraph Formalisms["理论演进"] HS["希尔伯特空间<br/>(1932 冯·诺伊曼)"] -->|"符号繁琐/忽视组合性"| MCT["幺半范畴论"] MCT -->|"严格等价转化为图示"| QP["量子图示学<br/>(Quantum Picturalism)"] end subgraph Applications["应用落地"] QP --> EDU["基础教育<br/>(中学生成绩超越牛津研究生)"] QP --> IND["工业应用<br/>(IBM、Google 采用)"] end ``` ### [08:13](https://www.youtube.com/watch?v=djCZTOUUkcc&t=493s) 当量子隐形传态遇见语法：量子自然语言处理的诞生 图示量子理论与人工智能的交汇始于 2004 至 2005 年间 Bob 在麦吉尔大学（McGill University）范畴论研讨会上的一次演讲。数学语言学之父吉姆·兰贝克（Jim Lambek）在场听讲。兰贝克早在 1950 年代便与乔姆斯基（Noam Chomsky）同期提出了用于判定句子结构合法性的代数语法系统。当兰贝克看到 Bob 在黑板上用图示画出的量子隐形传态（Quantum Teleportation）过程时，突然脱口而出：“嘿，Bob，这就是语法（This is grammar）！”Bob 当时反驳道：“不，吉姆，这是物理，这是量子物理！”兰贝克却坚持：“不，这就是语法。” 两人随即深入探讨并推导了背后的数学结构，结果证明在幺半范畴论框架下，二者在数学本质上完全同一：人类语言中词汇相互作用并组合成语义的过程、人类大脑中概念相互结合的认知过程，与量子系统中粒子相互作用与纠缠的组合结构遵循完全相同的数学规律。这一跨学科洞见促使他们在 2008 年发表了首篇组合分布式语义模型论文（DisCoCat 模型奠基之作），并最终在 2020 年正式开创了量子自然语言处理（QNLP, Quantum Natural Language Processing）领域。令人惊叹的是，研究团队在仅有 6 个量子比特的微型量子计算机上成功运行了 QNLP 模型并完成了问答训练——之所以能在极小算力下成功，正是因为模型内嵌了语言天然的组合结构，从而大幅削减了传统暴力统计 AI 对海量训练数据的病态依赖。 - **语言与量子的数学同构**：词汇组合产生句意的拓扑路径与量子力学中态的演化与测量路径完全对应。 - **数据效率突破**：利用天然组合结构进行建模，使得在 6 比特小规模量子硬件上训练自然语言处理模型成为现实。 - **新范式确立**：摆脱了旧式符号 AI（GOFAI）的局限，建立了全新的量子组合语义计算框架。 ### [12:14](https://www.youtube.com/watch?v=djCZTOUUkcc&t=734s) 量子图式与语言学的结合：QNLP 与 lambeq 的诞生 在探讨语言的计算模型时，学界早期曾出现过如保罗·斯莫伦斯基（Paul Smolensky）提出的张量积表示等尝试，但这些早期方案存在许多缺陷与不良特性。当时自然语言处理领域面临的核心困境在于：一方面，人们通过现代机器学习方法将单词的含义理解为高维向量（即词嵌入）；另一方面，语言学家长期深耕并建立了一套严密的句法结构理论。然而，如何在一个统一的形式化体系中将“单词的向量语义”与“语言的语法结构”完美结合，一直是悬而未决的难题。 当吉姆·兰贝克（Jim Lambek）指出鲍勃·库克（Bob Coecke）所构建的图式量子形式化理论（Diagrammatic Quantum Formalism）在本质上与语言结构完全相通时，破解这一难题的钥匙终于浮现。在量子力学体系中，沿着图式流动的基本单元正是向量；而语言模型中承载语义的也是向量。库克坦言，自己当时对人工智能和自然语言处理一无所知，但敏锐地意识到图式量子力学正是解答该问题的终极工具。随后，库克团队发表了关于如何在自然语言中组合意义与语法的开创性论文。到了 2016 年，库克与其博士生进一步证实，若将该模型部署在量子计算机上运行，能够展现出实际的量子加速优势（在当时初步实现了二次量子优势），并在量子计算机上成功实现了首个问答（Question Answering）实验。 为了让学界和开发者广泛应用这一范式，团队开源了量子自然语言处理软件工具包 `lambeq`。库克身穿印有其新创立公司 Relational Intelligence 标识的 T 恤，风趣地提到团队正在对整套软件架构进行大幅度的重构与升级，预计数月内将推出性能更为出色的新版本。 ```mermaid flowchart LR accTitle: QNLP 形式化融合架构 subgraph Language["语言与语义"] A["词汇语义 (向量表示)"] B["语法结构 (兰贝克范畴语法)"] end subgraph Quantum["图式量子形式化"] C["图式量子线路 (弦图/范畴论)"] D["量子态/向量流动"] end subgraph Execution["计算实现"] E["QNLP 框架 (lambeq)"] F["量子硬件加速运行"] end A --> C B --> C D --> C C --> E E --> F ``` --- ### [14:17](https://www.youtube.com/watch?v=djCZTOUUkcc&t=857s) 重新定义组合性：从弗雷格原则到可解释 AI 的反向流动 组合性（Compositionality）是现代信息技术的基石，从底层计算机体系结构到智能手机的正常运转，都依赖于将基础模块组合为复杂系统的原则。在传统语言学与逻辑学中，组合性通常归功于戈特洛布·弗雷格（Gottlob Frege）提出的“弗雷格原则”：如果已知各个组成部分的意义，并且知道它们是如何拼接组合的，就能推导出整体的意义。这种自底向上（Bottom-up）的逻辑完美契合传统程序编写与计算机科学，但在现代人工智能（尤其是深度神经网络）以及量子系统中却彻底失效。 以人工神经网络为例，弗雷格式的组合性遇到了显而易见的挑战：即便将大量神经元连接在一起，由于单个神经元的物理参数与权重本身不具备孤立的语义，我们无法通过单个神经元的“意义”推导整体网络输出的意义。更重要的是，现代 AI 中的语义流动是双向的，甚至是由整体自顶向下（Top-down）决定的——例如在图像识别中，是“鸟”这一宏观整体概念决定了底层神经元特征的激活与解释，而非相反。 针对这一理论鸿沟，库克在最新论文中提出了面向可解释人工智能（XAI）的“组合可解释性”（Compositional Interpretability）全新框架。该理论彻底摆脱了传统的单向拼装假设，完全从量子系统的纠缠与整体性中汲取灵感，为打开神经网络黑盒、实现严密的因果解释提供了全新的数学基础。 --- ### [16:35](https://www.youtube.com/watch?v=djCZTOUUkcc&t=995s) 文本结构的数学：超越语言表层的“意义量子线路” 为了打破传统语法的局限，库克提出了名为“文本结构数学”（Mathematics of Text Structure）的形式化框架。在该模型中，多句话组成的语篇（例如“Alex meets Bo”、“Bo marries Chris”、“Alex kicks Bo”）被直接抽象为包含实体与交互的线路图。在此类线路中，交互的主体（如 Alex、Bo、Chris）充当流动的线路导线，而动词及事件（如 meets、marries、kicks）则是作用于这些导线上的交互算符或逻辑门。当各个实体的语义以向量形式注入时，这套图式在数学上完全等价于一个标准的量子线路。 ```mermaid flowchart TD accTitle: 文本到量子线路的映射 subgraph Text["文本交互序列"] T1["Alex meets Bo"] T2["Bo marries Chris"] T3["Alex kicks Bo"] end subgraph Circuit["意义量子线路结构"] W["实体导线: Alex / Bo / Chris"] G["交互门: Meets / Marries / Kicks"] W --- G end subgraph Advantage["核心特性"] Adv1["跨语种中立性 (Language-Neutral)"] Adv2["结构化与因果可解释性"] end Text --> Circuit Circuit --> Advantage ``` 这一方法解决了诺姆·乔姆斯基（Noam Chomsky）普适语法（Universal Grammar）未能解决的跨语言差异问题。乔姆斯基试图寻找人类语言统一的代数类型系统，但不同语种在语序、屈折变化和语法表层形态上千差万别。相比之下，文本意义线路完全独立于具体语种的句法表象： - 无论表达者是喜欢使用结构冗长复杂的复合句，还是倾向于使用短促简洁的单句，其底层生成的意义线路拓扑完全一致。 - 它直接锚定思维与概念本身的因果拓扑，形成了一种高度浓缩、跨语言通用的深层语义表征。 --- ### [18:02](https://www.youtube.com/watch?v=djCZTOUUkcc&t=1082s) 指数级量子优势、能效与 Relational Intelligence 的愿景 当这些意义线路被映射至量子计算硬件时，系统相较于经典机器展现出了真正的**指数级量子优势**（Exponential Advantage）。尽管该模型目前也可以在经典硬件上模拟运行，但随着语篇规模与语义复杂度的增加，经典计算不可避免地面临维度灾难。这种由量子理论启发而生的全新 NLP 与认知计算范式，最终必须完全依托量子计算机来实现规模化爆发。 在实验验证中，研究团队采取了一种突破性的混合部署策略：模型参数在普通的经典笔记本电脑上进行高效训练，而推理与结构验证则直接推演至经典硬件的模拟极限，并在真实的量子处理器上运行。这一图式结构同时带来了四大关键价值： 1. **强可解释性**：所有语义交互与逻辑推理路径在图式线路中完全透明可视化。 2. **指数级计算加速**：利用量子叠加与纠缠原生支持多实体复合推理。 3. **极高可扩展性**：支持大规模文本图谱的高效表征。 4. **绿色与能效友好**：相比传统超大规模语言模型极高的算力消耗与碳排放，该方案在物理底层极度节能。 库克在总结时提到，该研究在 2024 年被评为量子计算领域的第二大科研成就。他幽默地调侃道，这实质上也是经典计算领域的重大突破，但由于此前身处量子计算公司（Quantinuum），为了避免品牌传播中的“信息混淆”，公司曾禁止他过多宣扬其在经典计算层面的价值。如今，作为新创立公司 Relational Intelligence 的负责人，他正全面推进这一技术的产业化落地。此外，库克还在播客《Entangled Things》中深入探讨了赫拉克利特（Heraclitus）、莱布尼茨（Leibniz）以及薛定谔（Schrödinger）等先哲思想对该体系的哲学渊源，并正着手将其撰写成书。 ## Notable quotes > [01:27](https://www.youtube.com/watch?v=djCZTOUUkcc&t=87s) 我想做一个坦白，这可能显得有些奇怪……我绝对不再相信希尔伯特空间了。 — John von Neumann > [01:27](https://www.youtube.com/watch?v=djCZTOUUkcc&t=87s) 唯一的特征特征 — Erwin Schrödinger > [04:25](https://www.youtube.com/watch?v=djCZTOUUkcc&t=265s) 想学量子力学吗？觉得自己的数学基础不够？没关系，这本书里的图示是一种新型数学，它将带你领略整个量子世界。 — Bob Coecke & Stefano Gogioso > [08:13](https://www.youtube.com/watch?v=djCZTOUUkcc&t=493s) 嘿，Bob，这就是语法！ — Jim Lambek > [08:13](https://www.youtube.com/watch?v=djCZTOUUkcc&t=493s) 不，吉姆，这是物理，这是量子物理！ — Bob Coecke > [08:13](https://www.youtube.com/watch?v=djCZTOUUkcc&t=493s) 不，这就是语法。 — Jim Lambek > [08:13](https://www.youtube.com/watch?v=djCZTOUUkcc&t=493s) This is grammar — Jim Lambek > [00:04](https://www.youtube.com/watch?v=djCZTOUUkcc&t=4s) Quantum meets AI — Bob Coecke ## Mentioned Bob Coecke, Relational Intelligence, Quantinuum, John von Neumann, Erwin Schrödinger, Roger Penrose, Aleks Kissinger, Stefano Gogioso, Jim Lambek, Noam Chomsky, Paul Smolensky, Gottlob Frege, Heraclitus, Gottfried Wilhelm Leibniz, Picturing Quantum Processes, Quantum in Pictures, lambeq, Entangled Things, The Guardian, IBM, Google, Oxford University, McGill University ## Video description Bob Coecke - Founder, CEO, Relational Intelligence Quantum and natural language share the same structure! Here's the story. Over some 20 years we have developed a diagrammatic quantum formalism, referred to as quantum picturalism [1, 2]. We showed that this formalism enabled secondary school students to perform exceptionally well on an Oxford University post-grad quantum exam [3]. This quest started when in 1935 John von Neumann denounced `his own’ Hilbert space based quantum formalism. Quantum picturalism on the other hand, is now widespread in quantum technology research. A remarkable fact is that in its pictorial form, composition of quantum systems shares the same structure as natural language. This resulted in the birth of Quantum NLP [4]. In more recent work, we demonstrated exponential advantage, interpretability, and scalability of Quantum NLP [5]. In fact, interpretability and scalability can also be achieved when adopting a quantum-inspired approach on classical hardware. The same formalism has also been used the generate the 1st piece of music with a quantum computer [5]. MEDIA REFERENCES: [1] Bob Coecke and Aleks Kissinger (2017) Picturing Quantum Processes. Cambridge University Press. [2] Bob Coecke and Stefano Gogioso (2022) Quantum in Pictures. Quantinuum. [3] https://www.theguardian.com/science/2023/dec/16/physicist-bob-coecke-its-easier-to-convince-kids-than-adults-about-quantum-mechanics [4] https://www.forbes.com/sites/moorinsights/2021/10/13/cambridge-quantum-makes-quantum-natural-language-processing-a-reality/ [5] https://thequantuminsider.com/2024/09/18/quantinuum-unveils-first-contribution-toward-responsible-ai-uniting-power-of-its-quantum-processors-with-experimental-work-on-integrating-classical-quantum-computing/ [6] https://qspace.fqxi.org/articles/264/quanthovens-fifth [Source](https://www.youtube.com/watch?v=djCZTOUUkcc)

Source quotes

[1:27] John von Neumann: 我想做一个坦白，这可能显得有些奇怪……我绝对不再相信希尔伯特空间了。 [1:27] Erwin Schrödinger: 唯一的特征特征 [4:25] Bob Coecke & Stefano Gogioso: 想学量子力学吗？觉得自己的数学基础不够？没关系，这本书里的图示是一种新型数学，它将带你领略整个量子世界。 [8:13] Jim Lambek: 嘿，Bob，这就是语法！ [8:13] Bob Coecke: 不，吉姆，这是物理，这是量子物理！ [8:13] Jim Lambek: 不，这就是语法。 [8:13] Jim Lambek: This is grammar [0:04] Bob Coecke: Quantum meets AI

Source quotes

[1:27] John von Neumann: I would like to make a confession which may seem [strange]... I do not absolutely believe in Hilbert space no more. [1:27] Erwin Schrödinger: the characteristic trait of quantum theory [8:13] Jim Lambek: Hey, Bob, this is grammar. This is grammar. [8:13] Bob Coecke: No, no, Jim. Jim, Jim, this is physics. This is quantum physics. [16:35] Bob Coecke: It doesn't matter how you explain something. If you want to be a snob and you use long sentences or you want to be simple and understood and use short many short sentences, it's all the same with these circuits. So it's sort of a more condensed model of meaning.

Original transcript

[0:04] So hello everybody. So I'm Bob. Uh at the  moment I'm like CEOing for a new company [0:09] called relation intelligence. Before I was  like 20 years a professor at Oxford and uh [0:13] I was also chief scientist at Continum which is  a quantum computing company for like uh 5 years [0:19] and then I've got some other stuff. Uh okay.  So ju just because this is I was invited here [0:26] to tell something about AI and quantum. So I'll  just first clarify what that can mean. This can [0:32] mean many different things. So one thing is AI for  quantum which is b blantly a no-brainer. It means [0:38] like whatever you're going to do in your quantum  computing research you use some AI maybe to speed [0:42] up your algorithms or whatever. It's a no-brainer.  Then you can try to do quantum for AI. Uh [0:50] at the moment it's a bit tricky because the  machines aren't really there to support the [0:56] uh the the empirical evidence that this actually  is going to give a lot of advantage. I mean I I've [1:03] got all my belief that is real that is but it's  it's not we basically need the machines because [1:09] AI is an is an empirical practice. So you really  need the machines. Uh there's a third thing which [1:15] is called which I call quantum meets AI and  that's what I'm going to talk about and uh [1:21] uh of course for me that's the real deal.  So I'll try to explain what is all about. [1:27] So this starts all with the language of quantum.  So the language of quantum is due to this guy [1:33] John Vanoyand you obviously all know because the  father of computer architecture and all of that. [1:38] Uh but he's also the father of the quantum  mechanical language formalism we use today. [1:43] and uh one which which he published in a  book in 1932 and then remarkably in 1935 he [1:51] wrote something which he says I would like to make  confession which may seem more I do not absolutely [1:56] believe in Hilbert space no more. So Hilbert space  is the language people have everybody used for [2:00] quantum. So Voy was the father and he denounced it  literally 3 years after he publicized it. Lots of [2:06] stuff went on people finding for new languages.  Okay, this is Arin Sherninger. Uh you may know [2:12] from a cat or from an equation and something  Arwin Sherninger said is okay I can't see like [2:18] the entirely the bottom but it doesn't matter  when two systems enter into temporal physical [2:22] interaction I would not call that one but rather  the characteristic trait of quantum theory. So, [2:29] so we now go into the topic of compositionality.  Basically what Shinger is saying here is [2:33] that if you bring two things together be classical  or quantum that's actually the characteristic [2:40] distinction between classical and quantum in  computer science we call this compositionality [2:46] in physics nobody really cared about that for a  very long time uh wrongly. So this Roger Penrose [2:55] he lives in Oxford like myself uh in a mass  department where I still teach. Uh and uh [3:01] at some point when he was an undergraduate student  he publicized stuff like this when he was studying [3:06] relat publicized he basically started drawing  these pictures when he had to study relative [3:12] relativity theory he thought that his pictures  were actually much more insightful and useful for [3:17] calculations than the usual tensor symbols which  you see there. So he introduced that it was only [3:24] published much later in 1971 in the appendix of a  paper but it was never taken seriously or I mean [3:30] nobody even knew about it. So there was no even  an issue of taking it seriously as as a language [3:35] or as a mathematical com content for anything. Now  this changed this changed uh and I'll explain you [3:42] why. Now just to summarize wanted the new quantum  language said quantum is about composing stuff. [3:49] Pandro uses pictures instead of symbols. The  result two last things are exactly the same thing [3:54] like the right language to focus on  compositionality be in physics be in AI [4:00] be in cooking be in like relationships be in  whatever are pictures and this is a mathematical [4:06] statement which has mean well be formally proved  now I'm not going to go into that you can ask me [4:11] about that but this is just a mathematical fact  the mathematics to focus on composition is called [4:17] monoidal category theory of category theory has  proven to be equivalent to drawing pictures. [4:25] So, okay. So, what did I do? So, I started  trying to turn quantum mechanics into [4:30] pictures. Uh started in 2003 2004. Uh this  is this is a book which we published in [4:36] 2017 and which has been the course of quantum  computing at Oxford University since 2013ish. [4:44] So, it's a full-blown course on quantum computing  but entirely thought in terms of pictures. Uh, [4:50] of course you see it's a thick book. It's a  it's an Oxford University postgraduate course. [4:54] Now there's another book, this one which  is more recent, quantum in pictures and [5:01] it does something different. You can read it on  the back. Hello there. Want to learn some quantum? [5:07] Maybe you think you don't know enough maths?  Well, that's not a problem. The picture in this [5:10] book are a new kind of maths that will  teach you all about the quantum world. [5:15] So basically what's happening here is that  quantum mechanics which is usually seen as [5:22] very complicated and very difficult to understand  mathematically uh and we start to use something [5:27] which is moral category theory which according to  many mathematicians is complete abstract nonsense. [5:33] We start to use that and because it turns into  picture as a way to teach quantum to kids. [5:39] So we effectively have been doing that now. So  I mean here is this garden article you see uh [5:44] this was about the experiment we did. So we  showed basically kids that quantum mechanics [5:51] can can be understood and we did an experiment and  these kits I mean I can't go in details these kids [5:56] outperformed Oxford University postgraduate  students using this diagrammatic formalism. [6:01] Uh I mean you can look in this paper  wait a bit so you can take a picture. [6:09] You can also just look up the Guardian article  which explains everything. So basically this [6:13] formalism I just showed you. I mean I just talked  about is now something we're actually teaching to [6:18] kids and kids can now. We teach this around the  world. We teach this in Ghana. We teach this in [6:23] in many countries now. So this is like a story  about making quantum inclusive not just inclusive [6:30] uh effectively. This may be a weird weird sort of  slide. You see an equation between John Vonoyman [6:38] and this book. Basically what this slide is  saying is that we proved that whatever you can [6:45] derive or prove in Hilbert space quantum mechanics  you can also derive using the pictures we use [6:52] to describe quantum mechanics.  Uh I mean give me a second. [6:57] I updated my slides yesterday with some pictures  but they unfortunately are not included. So, [7:04] so, but it's okay. They were supposed  to be here, but they're not here. [7:08] So, I'll show you. So, this is the book. I've got  a few copies, and if you're very interested and [7:12] you're going to use it, you can get one. And  uh I don't know whether you can see it, but [7:21] there's lots. I mean, I'm going to leave it  here or we you can I can give it to somebody [7:25] and you can sort of pass it along. Huh. And  then you can see that's what I'm going to do. [7:32] just pass it along to whoever is  interested. Yeah, I'll take another copy [7:37] to make it a little bit more efficient. So, just  to summarize, we we we made we did a course at [7:42] some point teaching quantum using this book and  videos and stuff like that to high school students [7:50] and they basically outperformed Oxford University  postgraduate students using this new language. [7:55] Now, this is an AI conference. Why I'm  even talking about that? Well, I mean [7:59] one thing is now this this language is widespread  in quantum technology. IBM is using it. Google is [8:04] using it. It's really as Vonoyman asked a new  language for quantum which does the job. Okay. [8:13] Okay. Now I've got AI on the slides. How did  we end up here? So in 2004 or something in 2005 [8:24] I was giving a talk at McGill University in  the category theory seminar and there was [8:30] a person there called Jim Lombbeck who's the  who's the father of mathematical linguistics. [8:35] So what the stuff he did was you probably know  Chsky stuff stuff he did very very early on [8:41] like in 56 was to come up with algebraic systems  which tell you when a sentence is wellformed [8:49] which is a it's an obvious question we do  this naturally humans but how do you do [8:53] how do you mathematize sort of how we  form grammar well when when Jim Lumbik [8:59] saw my description of quantum teleportation  which you see on top that's a description [9:04] of quantum Don't tell him teleportation in  pictures. He told me, "Hey, Bob, this is grammar. [9:11] This is grammar." He didn't. I said,  "No, no, Jim. Jim, Jim, this is physics. [9:17] This is quantum physics." So, no, no, no,  Bob. This is grammar. Okay. So, we sat down, [9:24] we looked into the mathematics of both things.  And when you go to the right sort of mathematics [9:30] which as I said before is manual category theory  they are indeed exactly the same. So the structure [9:38] the structure of uh the way meaning composes  the way meaning interacts with each other the [9:47] way words interact with each other in senses the  way concepts interact with each other in our head. [9:53] If you I mean I worked together with  like cognitive scientists about this. [9:58] It basically forms the same compositional  structure as we find in quantum mechanics. [10:03] It's the same thing. It's the same thing. I mean  this this this like I said goes back to 2004 2005 [10:09] when nobody was interested in this  stuff to be honest. Uh okay. So [10:17] many many years forward this observation that on  the one hand the structure of language and the [10:25] structure of meaning and cognition more generally  and on the other hand the structure of quantum [10:33] share are basically the same enabled us in  2020 to do quantum natural language processing [10:40] on a small quantum computer and I emphasize  small quantum like six cubits. So we trained it, [10:48] we asked it some questions and it turned out to  work out uh which which was quite quite surprising [10:56] even to ourselves. Now why was this the case?  Well, because if you use compositional structure [11:05] represented in the phenomenon,  which in this case is language, [11:11] then you're much cheaper in the amount  of data you need. It's as simple as that. [11:18] I'll say a bit more about compositional structure  later. What I mean, I don't mean compositional [11:22] structure in the old-fashioned good oldfashioned  AI sort of way. I mean it in a different sense. [11:29] But I I'll go a little bit into that later  because I got quite a bit of time left to do so. [11:36] Uh but so yes, so we so we rel we launched the  field of quantum natural language processing. [11:42] At the time it was just like a big surprise that  this was even possible on small quantum computers [11:48] given the amount of data AI  usually needs, of course. [11:56] So I mean if you're interested in reading some  papers from that from then and earlier. So [12:02] the first theory paper came out in 2008 where  basically what we produced was a a compositional [12:09] model of meaning. I mean there there was not  not something like that at all. I mean there [12:14] was something by Smolansky which which had a lot  of bad features. So basically the idea was like [12:20] okay we understand the meaning of words. They're  vectors in the way people do this now in in [12:26] machine learning. We understand the structure of  language. Linguists have been working long about [12:31] that. How do we combine the two in one formalism?  Now because of because of this observation [12:39] that when I was talking quantum and lumb told me  wait this is a structure of language. I said okay [12:46] that's very easy we can solve this problem. We  just take this diagrammatic quantum formalism [12:51] because this diagrammatic quantum formalism as  lic says has the structure of language built in [12:56] what flows in quantum mechanical system it's  vectors. So in quantum mechanics you represent [13:02] things by vector just like people do now in  NLP and large language models and all of that. [13:10] Uh so I I mean I I didn't know anything about AI  NLP anything but I just realized that if that's [13:19] the question well the answer is probably our new  quantum formalism. It turned out to be true. So, [13:26] so in this paper we proposed this this new  formalism on how to compose meaning and language [13:31] in a in natural language. We in 2016 with a PhD  student of mine we actually figured out that if [13:39] you do this on a quantum computer you get quantum  advantage you'll get at this point this is about [13:46] quadratic quantum advantage nothing more at this  stage uh we like this is the paper representing [13:52] our first experiment that we do question answering  on quantum computers and then we also produced uh [14:00] like a software package lumb where everybody can  use I must say that with my new company like which [14:05] you can see on my t-shirt relation intelligence  we're going to redo all the software much better [14:10] uh so maybe should wait a few months for  an update to all of that okay so now what [14:17] is compositionality compositional of course is  the principle that on the pins functionality of [14:22] all current information technology I mean  there wouldn't be anything I mean nothing [14:28] would work you wouldn't have a mobile phone if  you wouldn't have compositionality the use uh [14:34] formulation within linguistics is attributed  to Frager although it's it's a more complicated [14:38] story. I mean I wrote a paper about that uh and  and in particular in this paper I emphasize that [14:45] quantum needs a new notion of compositionality  other than so the compositionality in linguistics [14:51] is stated as four as follows. Usually if you know  the if you know the if you know the structure [14:57] and you know the meanings of parts if you  know the meanings of parts and you know [15:03] if you know what the parts are let's put  it like that if you know what the parts are [15:06] and you know how they are put together then  you know the whole that's composity and uh [15:12] I mean it makes perfect sense that's that's how  people write programs this this how computer [15:17] science works of course but it doesn't really  work for modern AI and it doesn't really work for [15:23] uh quantum meter. I mean because because now  here is like a stupid counter example. It's [15:29] very old. This slide is way outdated. But  I mean if you put some neurons together, [15:34] the meaning of the neurons doesn't give you the  meaning of the whole because we don't know the [15:37] meaning of the neurons. It's as simple as that.  So so we we need we need something new in AI too. [15:42] And another problem in AI uh is that things  don't just go bottom up, they also go top down. [15:50] The meaning of the whole determines the meaning of  the parts. Especially here the meaning of the bird [15:55] determines the meaning of the of the  neutrons not the other way around. [15:59] So you need a sort of new notion which as I said  uh we also wrote a paper most recently about like [16:07] uh comp what we called in compositional  interpretability for explainable AI. [16:12] I'm actually still I'm writing a new paper now  which I think this one is better than this one. [16:16] So but you have a look it's a very big one.  It's about interpretability. All inspired by so [16:23] it's all inspired by quantum stuff. All what  I'm talking about about AI is like very quantum [16:27] inspired in the to the extent that there is  this correspondence between quantum and and so [16:35] a few years ago I came up with a new formalism  for meaning. I called this the mathematics of [16:40] text structure. It works like this. So you  got a few sentences here. Alex meets bow. [16:45] Boom. Where is Chris? Alex kicks bow.  And we just represent this as circuits. [16:52] So you see the three agents Alex, Bo, Chris, you  see the three interaction meets, Mary's cakes. And [16:57] this is just circuit. And uh we can think of  the and if if if if your meanings are vectors, [17:03] this pretty much is a quantum circuit.  This pretty much is a quantum circuit. [17:10] Now one one one thing which Chomsky  didn't achieve because Chomsky was very uh [17:19] he was looking for universality in language and  he said we come up with these new grammar things [17:24] which are universal and it was not true because  the algebra was universal the type system was not [17:29] in in different languages we put words in  different order and stuff like that these circuits [17:35] which I'm talking about now they're neutral to  language so this is compos opposite of structure [17:40] which is neutral to language. So it's much closer  to the way we think which is much closer to our [17:45] meaning. It it doesn't matter how you explain  something. If you want to be a snob and you [17:50] use long sentences or you want to be simple and  understood and use short many short sentences, [17:56] it's all the same with these circuits. So it's  sort of a more condensed uh model of meaning. [18:02] Uh and basically we've put this on a quantum  computer because it's quantum session [18:07] and we know that this stuff on a quantum  computer gives exponential advantage [18:14] to classical machines. It doesn't mean  that you can't put it on classical machines [18:17] but at some point you're going to get in  trouble of course. So this is why I think that [18:23] this is all quantum inspired but at some point  we'll have to go full on quantum with this kind [18:29] kind of approach to natural language processing  and cognition. Not going to go into technical [18:33] details if you want. I mean if you want to take a  picture of the paper you can read it and you can [18:39] basically look for the the claims and  stuff yourself. All right. Okay. Yeah. [18:47] uh and uh I think the most important thing we  did was when we put this on a quantum computer [18:55] we trained classically on laptops and then we  tested on on the limit of what's classically [19:01] possible with any kind of classical hardware and  the structure which we use like in these circuits [19:08] basically made that possible the fact that you can  so this structure serves a lot it makes the the AI [19:15] interpretable it makes exponentially advances a  quantum computer. It makes it scalable, makes it [19:22] nice for nature, efficient, and all of that. So, I  think I'm about out of my time now. What else do I [19:29] have to say? I mean, you can read a lot about this  in this blog post if you want to take a picture. [19:35] We were we were in in 2004, I think we were  this this work was chosen as the second biggest [19:40] research achievement in the field of quantum  computing. Although for me, it's also a result [19:44] in the field of classical computing. But because I  was working in a quantum computing company, I was [19:48] not allowed to say that because this was a mixed  message and uh they didn't want me to say that. [19:54] Anyway, so this is where I'm working now.  It's called relational intelligence and uh [20:00] the sort of stuff I just was talking about that's  what we are doing. And uh if you want to hear more [20:07] about the philosophy behind of this, yesterday  a podcast came out which called entangle things. [20:12] entangle things where I talk about like aracitus  and linenets and shreddering and the whole [20:19] historical philosophy behind this work which I'm  writing a book about if I find time. Thank you.