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The ZX-calculus is a graphical language for reasoning about ZX-diagrams, a type of tensor networks that can represent arbitrary linear maps between qubits. Using the ZX-calculus, we can intuitively reason about quantum theory, and optimise…
Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the…
From Feynman diagrams to tensor networks, diagrammatic representations of computations in quantum mechanics have catalysed progress in physics. These diagrams represent the underlying mathematical operations and aid physical interpretation,…
Categorical Quantum Mechanics, and graphical calculi in particular, has proven to be an intuitive and powerful way to reason about quantum computing. This work continues the exploration of graphical calculi, inside and outside of the…
Graphical calculi are vital tools for representing and reasoning about quantum circuits and processes. Some are not only graphically intuitive but also logically complete. The best known of these is the ZX-calculus, which is an industry…
ZX-calculus is a graphical language for quantum computing which is complete in the sense that calculation in matrices can be done in a purely diagrammatic way. However, all previous universally complete axiomatisations of ZX-calculus have…
The ZX-calculus is a graphical language for suitably represented tensor networks, called ZX-diagrams. Calculations are performed by transforming ZX-diagrams with rewrite rules. The ZX-calculus has found applications in reasoning about…
Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…
We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for…
The Scalable ZX-calculus is a compact graphical language used to reason about linear maps between quantum states. These diagrams have multiple applications, but they frequently have to be constructed in a case-by-case basis. In this work we…
We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing quantum computations…
Quantum computing promises significant speed-ups for certain algorithms but the practical use of current noisy intermediate-scale quantum (NISQ) era computers remains limited by resources constraints (e.g., noise, qubits, gates, and circuit…
This article presents a review of quantum computing research works for Natural Language Processing (NLP). Their goal is to improve the performance of current models, and to provide a better representation of several linguistic phenomena,…
Systematic discovery of optimization paths in quantum circuit simplification remains a challenge. Today, ZX-calculus, a computing model for quantum circuit transformation, is attracting attention for its highly abstract graph-based…
Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations. At the level of fault-tolerant encoding, one likely requirement of this process is the translation into a…
The ZW-calculus is a graphical language capable of representing 2-dimensional quantum systems (qubit) through its diagrams, and manipulating them through its equational theory. We extend the formalism to accommodate finite dimensional…
Classical program analysis techniques, such as abstract interpretation and symbolic execution, are essential for ensuring software correctness, optimizing performance, and enabling compiler optimizations. However, these techniques face…
Quantum computing exploits quantum phenomena such as superposition and entanglement to realize a form of parallelism that is not available to traditional computing. It offers the potential of significant computational speed-ups in quantum…
We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated coloured tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams…
We introduce the language QML, a functional language for quantum computations on finite types. Its design is guided by its categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations,…