Quantum computing with diagrams: the ZX-calculus for quantum circuit simulation

Alejandro Villoria

Leiden University

The way we describe the operations we perform on a quantum computer can have a significant impact on how we understand the quantum states we generate and what we can do with them. From quantum circuits, tensor networks, and the ZX-calculus, the landscape is varied and offers multiple alternatives that one should carefully choose depending on the task at hand. In this talk we will explore the ZX-calculus, a graphical language that can be used to represent quantum operations and states as diagrams, and consists of two main parts. First, a small set of simple graphical generators that can be composed to represent complicated quantum operations. Second, a set of rewrite rules that allows us to modify our diagrams into equivalent diagrams that could have a more desirable structure. We will study the properties of the ZX-calculus, how it can be used to intuitively reason about quantum mechanics, and how its rewrite system effectively works as a tool for quantum circuit simulation and compilation.