We initiate the development of a new language and theory for quantum music, to which we refer as Quantum Concept Music (QCM). This new music formalism is based on Categorical Quantum Mechanics (CQM), and more specifically, its diagrammatic incarnation Quantum Picturalism (QPict), which is heavily based on ZX-calculus. In fact, it is naturally inherited from CQM/QPict. At its heart is the explicit notational representation of relations that exist within and between the key concepts of music composition, performance, and automation. QCM also enables one to directly translate quantum phenomena into music compositions in a both intuitively obvious, rigorous and mechanical manner. Following this pattern, we propose a score for musicians interacting like a Bell-pair under measurement, and outline examples of how it could be live performed. While most of the Western classical music notation has heavily relied on linear representation of music - which does not always adequately capture the nature of music - our approach is distinct by highlighting the fundamental relational dimension of music. In addition, this quantum-based technique not only influences the music at the profound level of composition, but also has a direct impact on a live performance, and also provides a new template for automating music, e.g.~in the context of AI-generation. All together, we initiate the creation of new music formalism that is powerful and efficient in capturing the interactive nature of music, both in terms of internal and external interactions, and goes beyond the boundaries of Western classical music notation, which allows to use it in many different genres and directions.

The fast-growing field of Quantum Natural Language Processing (QNLP: Widdows et al., 2024), in which the current article is situated, seeks to explain how information is processed in human language, using the mathematical framework of quantum theory. In QNLP, machine learning models are quantum circuits, which capture the meaning of sentences or other pieces of linguistic information. These models reflect an inherently compositional approach, in contrast to state-of-the-art machine learning models, such as deep neural networks, which renders them more interpretable (Coecke et al., 2020). The contributions of the current article are formulated in terms of diagrams in the Categorical Compositional Distributional (DisCoCat) framework (Coecke et al., 2010), in which word meanings are represented by tensors of various ranks. A noun, for example, is represented by a vector, whereas an intransitive verb is modelled as a matrix, and a transitive verb is represented by a rank-three tensor. The interaction of the meaning of these words, which results in the meaning of a sentence, is guided by the pregroup grammar. This combination of grammar and mathematical methods from tensor calculus allows the DisCoCat model to account for both the distributional and the compositional aspect of language. This connection is formally established via the mathematical framework of Category Theory . 1

Quantum Natural Language Processing (QNLP) deals with the design and implementation of NLP models intended to be run on quantum hardware. In this paper, we present results on the first NLP experiments conducted on Noisy Intermediate-Scale Quantum (NISQ) computers for datasets of size greater than 100 sentences. Exploiting the formal similarity of the compositional model of meaning by Coecke, Sadrzadeh, and Clark (2010) with quantum theory, we create representations for sentences that have a natural mapping to quantum circuits. We use these representations to implement and successfully train NLP models that solve simple sentence classification tasks on quantum hardware. We conduct quantum simulations that compare the syntax-sensitive model of Coecke et al. with two baselines that use less or no syntax; specifically, we implement the quantum analogues of a "bag-of-words" model, where syntax is not taken into account at all, and of a word-sequence model, where only word order is respected. We demonstrate that all models converge smoothly both in simulations and when run on quantum hardware, and that the results are the expected ones based on the nature of the tasks and the datasets used. Another important goal of this paper is to describe in a way accessible to AI and NLP researchers the main principles, process and challenges of experiments on quantum hardware. Our aim in doing this is to take the first small steps in this unexplored research territory and pave the way for practical Quantum Natural Language Processing.

Natural language processing (NLP) is at the forefront of great advances in contemporary AI, and it is arguably one of the most challenging areas of the field. At the same time, in the area of Quantum Computing (QC), with the steady growth of quantum hardware and notable improvements towards implementations of quantum algorithms, we are approaching an era when quantum computers perform tasks that cannot be done on classical computers with a reasonable amount of resources. This provides a new range of opportunities for AI, and for NLP specifically. In this work, we work with the Categorical Distributional Compositional (DisCoCat) model of natural language meaning, whose underlying mathematical underpinnings make it amenable to quantum instantiations. Earlier work on fault-tolerant quantum algorithms has already demonstrated potential quantum advantage for NLP, notably employing DisCoCat. In this work, we focus on the capabilities of noisy intermediate-scale quantum (NISQ) hardware and perform the first implementation of an NLP task on a NISQ processor, using the DisCoCat framework. Sentences are instantiated as parameterised quantum circuits; word-meanings are embedded in quantum states using parameterised quantum-circuits and the sentence's grammatical structure faithfully manifests as a pattern of entangling operations which compose the word-circuits into a sentence-circuit. The circuits' parameters are trained using a classical optimiser in a supervised NLP task of binary classification. Our novel QNLP model shows concrete promise for scalability as the quality of the quantum hardware improves in the near future and solidifies a novel branch of experimental research at the intersection of QC and AI.

The purpose of this work is to contribute toward the larger goal of creating a Quantum Natural Language Processing (QNLP) translator program. This work contributes original diagrammatic representations of the Japanese language based on prior work that accomplished on the English language based on category theory. The germane differences between the English and Japanese languages are emphasized to help address English language bias in the current body of research. Additionally, topological principles of these diagrams and many potential avenues for further research are proposed. Why is this endeavor important? Hundreds of languages have developed over the course of millennia coinciding with the evolution of human interaction across time and geographic location. These languages are foundational to human survival, experience, flourishing, and living the good life. They are also, however, the strongest barrier between people groups. Over the last several decades, advancements in Natural Language Processing (NLP) have made it easier to bridge the gap between individuals who do not share a common language or culture. Tools like Google Translate and DeepL make it easier than ever before to share our experiences with people globally. Nevertheless, these tools are still inadequate as they fail to convey our ideas across the language barrier fluently, leaving people feeling anxious and embarrassed. This is particularly true of languages born out of substantially different cultures, such as English and Japanese. Quantum computers offer the best chance to achieve translation fluency in that they are better suited to simulating the natural world and natural phenomenon such as natural speech. Keywords: category theory, DisCoCat, DisCoCirc, Japanese grammar, English grammar, translation, topology, Quantum Natural Language Processing, Natural Language Processing

DisCoCirc is a newly proposed framework for representing the grammar and semantics of texts using compositional, generative circuits. While it constitutes a development of the Categorical Distributional Compositional (DisCoCat) framework, it exposes radically new features. In particular, [14] suggested that DisCoCirc goes some way toward eliminating grammatical differences between languages. In this paper we provide a sketch that this is indeed the case for restricted fragments of English and Urdu. We first develop DisCoCirc for a fragment of Urdu, as it was done for English in [14]. There is a simple translation from English grammar to Urdu grammar, and vice versa. We then show that differences in grammatical structure between English and Urdu - primarily relating to the ordering of words and phrases - vanish when passing to DisCoCirc circuits.

There are different meanings of the term "compositionality" within science: what one researcher would call compositional, is not at all compositional for another researcher. The most established conception is usually attributed to Frege, and is characterised by a bottom-up flow of meanings: the meaning of the whole can be derived from the meanings of the parts, and how these parts are structured together. Inspired by work on compositionality in quantum theory, and categorical quantum mechanics in particular, we propose the notions of Schrodinger, Whitehead, and complete compositionality. Accounting for recent important developments in quantum technology and artificial intelligence, these do not have the bottom-up meaning flow as part of their definitions. Schrodinger compositionality accommodates quantum theory, and also meaning-as-context. Complete compositionality further strengthens Schrodinger compositionality in order to single out theories like ZX-calculus, that are complete with regard to the intended model. All together, our new notions aim to capture the fact that compositionality is at its best when it is `real', `non-trivial', and even more when it also is `complete'. At this point we only put forward the intuitive and/or restricted formal definitions, and leave a fully comprehensive definition to future collaborative work.

This paper concerns the intersection of natural language and the physical space around us in which we live, that we observe and/or imagine things within. Many important features of language have spatial connotations, for example, many prepositions (like in, next to, after, on, etc.) are fundamentally spatial. Space is also a key factor of the meanings of many words/phrases/sentences/text, and space is a, if not the key, context for referencing (e.g. pointing) and embodiment. We propose a mechanism for how space and linguistic structure can be made to interact in a matching compositional fashion. Examples include Cartesian space, subway stations, chesspieces on a chess-board, and Penrose's staircase. The starting point for our construction is the DisCoCat model of compositional natural language meaning, which we relax to accommodate physical space. We address the issue of having multiple agents/objects in a space, including the case that each agent has different capabilities with respect to that space, e.g., the specific moves each chesspiece can make, or the different velocities one may be able to reach. Once our model is in place, we show how inferences drawing from the structure of physical space can be made. We also how how linguistic model of space can interact with other such models related to our senses and/or embodiment, such as the conceptual spaces of colour, taste and smell, resulting in a rich compositional model of meaning that is close to human experience and embodiment in the world.

We cast aspects of consciousness in axiomatic mathematical terms, using the graphical calculus of general process theories (a.k.a symmetric monoidal categories and Frobenius algebras therein). This calculus exploits the ontological neutrality of process theories. A toy example using the axiomatic calculus is given to show the power of this approach, recovering other aspects of conscious experience, such as external and internal subjective distinction, privacy or unreadability of personal subjective experience, and phenomenal unity, one of the main issues for scientific studies of consciousness. In fact, these features naturally arise from the compositional nature of axiomatic calculus.

Scientific studies of consciousness rely on objects whose existence is independent of any consciousness. This theoretical-assumption leads to the "hard problem" of consciousness. We avoid this problem by assuming consciousness to be fundamental, and the main feature of consciousness is characterized as being other-dependent. We set up a framework which naturally subsumes the other-dependent feature by defining a compact closed category where morphisms represent conscious processes. These morphisms are a composition of a set of generators, each being specified by their relations with other generators, and therefore other-dependent. The framework is general enough, i.e. parameters in the morphisms take values in arbitrary commutative semi-rings, from which any finitely dimensional system can be dealt with. Our proposal fits well into a compositional model of consciousness and is an important step forward that addresses both the hard problem of consciousness and the combination problem of (proto)-panpsychism.