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We axiomatise the dagger category of complex Hilbert spaces and bounded linear maps, using exclusively purely categorical conditions. Our axioms are chosen with the aim of an easy interpretability: two of them describe the composition of…
Central to near-term quantum machine learning is the use of hybrid quantum-classical algorithms. This paper develops a formal framework for describing these algorithms in terms of string diagrams: a key step towards integrating these hybrid…
While the ZX and ZW calculi have been effective as graphical reasoning tools for finite-dimensional quantum computation, the possibilities for continuous-variable quantum computation (CVQC) in infinite-dimensional Hilbert space are only…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
Quantum information brings together theories of physics and computer science. This synthesis challenges the basic intuitions of both fields. In this thesis, we show that adopting a unified and general language for process theories advances…
Quantum mechanical systems whose symmetry is given by $\mathbb{Z}_2^3$-graded version of superconformal algebra are introduced. This is done by finding a realization of a $\mathbb{Z}_2^3$-graded Lie superalgebra in terms of a standard Lie…
Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space. This feature map provides opportunities to incorporate quantum advantages into machine learning algorithms…
The ZX-calculus was introduced as a graphical language able to represent specific quantum primitives in an intuitive way. The recent completeness results have shown the theoretical possibility of a purely graphical description of quantum…
In this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum…
The quantum theory can be formulated in the language of positive functionals on Weyl or Clifford algebra ($L$-functionals). It is shown that this language gives simple understanding of diagrams of Keldysh formalism (that coincide in our…
ZX-calculus is graphical language for quantum computing which usually focuses on qubits. In this paper, we generalise qubit ZX-calculus to qudit ZX-calculus in any finite dimension by introducing suitable generators, especially a carefully…
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…
Many insights into the quantum world can be found by studying it from amongst more general operational theories of physics. In this thesis, we develop an approach to the study of such theories purely in terms of the behaviour of their…
Quantum operations are the most widely used tool in the theory of quantum information processing, representing elementary transformations of quantum states that are composed to form complex quantum circuits. The class of quantum…
We consider the kinematic axioms of quantum mechanics projectively. Instead of normalized (pure) states up to global phase, states become one-dimensional subspaces of vector spaces. This process of projectivization is functorial and lax…
This Master thesis examines issues of interoperability and integration between the Classic Information Science (CIS) and Quantum Information Science (QIS). It provides a short introduction to the Extensible Markup Language (XML) and…
In this paper, we extend diagrammatic reasoning in monoidal categories with algebraic operations and equations. We achieve this by considering monoidal categories that are enriched in the category of Eilenberg-Moore algebras for a monad.…
We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical languages for both affinely constrained classical mechanical…
We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including…
We extend the graphical calculus developed in the first part of this paper to the parametrising spaces of quantum vertex operators. This involves a graphical implementation of the dynamical twist functor, which is a strict monoidal functor…