ZX-diagrams are a powerful graphical language for the description of quantum processes with applications in fundamental quantum mechanics, quantum circuit optimization, tensor network simulation, and many more. The utility of ZX-diagrams relies on a set of local transformation rules that can be applied to them without changing the underlying quantum process they describe. These rules can be exploited to optimize the structure of ZX-diagrams for a range of applications. However, finding an optimal sequence of transformation rules is generally an open problem. In this work, we bring together ZX-diagrams with reinforcement learning, a machine learning technique designed to discover an optimal sequence of actions in a decision-making problem and show that a trained reinforcement learning agent can significantly outperform other optimization techniques like a greedy strategy or simulated annealing. The use of graph neural networks to encode the policy of the agent enables generalization to diagrams much bigger than seen during the training phase.

The latest work by computer scientists Bob Coecke and Stefano Gogioso, 'Quantum in Pictures', aims to make the quantum world more accessible and inclusive. So, whether you're a high school student or a science enthusiast, the authors are confident that anyone mastering the tools in the book will gain an understanding equivalent to that of a quantum mechanics graduate at university. But what if a complete novice in quantum computing, i.e., this reviewer, could gain a genuine understanding of the field by simply reading this book? Let's test this out, shall we? Full disclosure from the get-go, I have absolutely no prior knowledge or expertise in quantum computing, therefore Coecke and Gogioso's latest research and book is not only worthy of a review but also a lesson for someone who barely scraped a C in GSCE Maths – a learning curve, if you will. For context, 'Quantum in Pictures' is the brainchild of Quantinuum's chief scientist Professor Bob Coecke and Dr Stefano Gogioso of Oxford University. The book introduces a formalism for quantum mechanics based on using'ZX-calculus' (or'ZX'), to describe quantum processes.

ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain unreachable with current ZX techniques. Here we elevate ZX to an analytical perspective by realising differentiation and integration entirely within the framework of ZX-calculus. We explicitly illustrate the new analytic framework of ZX-calculus by applying it in context of quantum machine learning for the analysis of barren plateaus.

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.

Matrices are used everywhere in modern science, like machine learning [11] or quantum computing [12], to name a few. Meanwhile, there is a graphical language called ZX-calculus that could also deal with matrix calculations such as matrix multiplication and tensor product [2, 3]. Then there naturally arises a question: why are people bothering with using diagrams for matrix calculations given that matrix technology has been applied with great successes? There are a few reasons for doing so. First, there is a lot of redundancy in matrix calculations which could be avoided in graphical calculus. For example, to prove the cyclic property of matrices tr(AB) tr(BA), all the elements of the two matrices will be involved, while in graphical language like ZXcalculus, the proof of the cyclic property is almost a tautology [4]. Second, matrix calculations always have all the elements of matrices involved, thus a "global" operation, while in ZX-calculus, the operations are just diagram rewriting where only a part of a diagram is replaced by another sub-diagram according to certain rewriting rule, thus essentially a "local" operation which makes things much easier. Finally, graphical calculus is much more intuitive than matrix calculation, therefore a pattern/structure is more probably to be recognised in a graphical formalism. In fact, as a graphical calculus for matrix calculation, ZX-calculus has achieved plenty of successes in the field of quantum computing and information [1, 5, 7, 13] For research realm beyond quantum, traditional ZX-calculus [2] is inconvenient as "it lacks a way to directly encode the complex numbers" [18].

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.

Many organizations are claiming their stacks in this space [1][2][3][4]. In today's world, the available quantum computers are at very early stages and not capable of handling complex quantum artificial intelligence/machine learning (qAI/qML) tasks [5]. But we still can harness their properties to run some of our quantum AI/ML algorithms more efficiently. In this sense, we can use the "Noisy Intermediate Scale Quantum Systems" (NISQ) [6] to serve the purpose. We can run the less complex quantum subroutines of a big qAI/qML in these kinds of quantum computers and use the results in the main qAI/qML problem-solving pipeline. This way we create a classical-quantum hybrid problem-solving ecosystem in AI/ML space.