We provide conceptual and mathematical foundations for near-term quantum natural
language processing (QNLP), and do so in quantum computer scientist friendly terms. We …

The ZX-calculus is a universal graphical language for qubit quantum computation, meaning
that every linear map between qubits can be expressed in the ZX-calculus. Furthermore, it is …

In existing general-purpose architectures for surface-code-based fault-tolerant quantum
computers, the cost of a quantum computation is determined by the circuit volume, ie, the …

A reconstruction of quantum theory refers to both a mathematical and a conceptual
paradigm that allows one to derive the usual formulation of quantum theory from a set of …

A key challenge in realizing fault-tolerant quantum computers is circuit optimization.
Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T …

We present a smorgasbord of results on the stabiliser ZX-calculus for odd prime-
dimensional qudits (ie qupits). We derive a simplified rule set that closely resembles the …

In this paper, we demonstrate a direct correspondence between phase-free ZX diagrams, a
graphical notation for representing and manipulating a certain class of linear maps on …

We introduce diagrammatic differentiation for tensor calculus by generalising the dual
number construction from rigs to monoidal categories. Applying this to ZX diagrams, we …

This paper develops practical summation techniques in ZXW calculus to reason about
quantum dynamics, such as unitary time evolution. First we give a direct representation of a …

Quantum theory is often regarded as challenging to learn and teach, with advanced
mathematical prerequisites ranging from complex numbers and probability theory to matrix …