I am a theoretical computer science/mathematician trying to learn more physics. I am interested in finding abstract mathematical models of systems/networks: particularly in the domains of quantum and classical mechanics. I understand things best in terms of pictures. Usually such pictures are formalized using monoidal categories, which are a ubiquitous structure in the field of category theory.
I recently defended my PhD in computer science at the University of Oxford. I am currently employed by the Université de Lorraine in France.
Here is a copy of my CV, updated March 2024.
I have recently thinking about string diagrams for classical mechanics and geometric quantization. I recently have become interested in diagramatic approaches quantum dynamics, and the categorical semantics for generating functions. I am also interested in diagrammatic approaches to quantum error correction, and recently quantum convolutional codes. I am also interested in diagrammatic and categorical formulations of infinite dimensional quantum mechanics and photonics.
I have fallen in love with bimodules and profunctors, and I am interested in their applications in theoretical computer science and linear logic.
I have lots of ideas so please feel free to contact me if anything here interests me. I will try to find projects to students looking for a purpose as I was.
You can also find me a the ZX-calculus seminar, and the category theory zulip channel.
firstnamedotlastname(at)univ-lorraine.fr
Université de Lorraine
CNRS, Inria, LORIA
F 54000 Nancy
France
Recent activities
- 06-2024
- I gave two talks (combined together) "Graphical Symplectic Algebra" and "Complete equational theories for classical and quantum Gaussian relations" at ACT 2024 in Oxford.
- 06-2024
- I gave a talk "A phase-space approach to rewriting infinite-dimensional quantum circuits," at LHC Days 2024 in Nantes.
- 05-2024
- I gave a talk "A ZX-calculus for continous-variable Gaussian quantum circuits," at the QUACS group in Saclay.
- 04-2024
- My PhD thesis "A diagrammatic approach to networks of spans and relations," was published in the Oxford University Research Archive.
- 03-2024
- I was invited to give an online talk about, "Graphical Calculi for Phase-Space Representations in Quantum Mechanics," by Dr. Branislav Jurco at the Prague Mathematical Physics Seminar at Charles University.
- We put our paper "Complete equational theories for classical and quantum Gaussian relations" on the arxiv.
- 01-2024
- We put our paper "Graphical symplectic algebra" on the arxiv.
- 12-2023
- I gave an invited talk at the seminar for geometric methods in mathematics at the Technische Universität Dresden.
- 10-2023
- I successfully defended my PhD in Computer Science in the Quantum Group at the University of Oxford.
- 09-2023
- I started a postdoc at the MOCQUA group in the Université de Lorraine.
Diagrams
- Complete equational theories for classical and quantum Gaussian relations R I Booth, T Carette, C Comfort
CV teleportation:
Equations for vacuum state:
Representation of Gaussian states:
Map of Gaussian relations:
- Graphical Symplectic Algebra R I Booth, T Carette, C Comfort
Scalable spiders:
Normal form:
- Sheet diagrams for bimonoidal categories C Comfort, A Delpeuch, J Hedges
Normalization:
- A Graphical Calculus for Lagrangian Relations C Comfort, A Kissinger
- The ZX&-calculus: A complete graphical calculus for classical circuits using spiders C Comfort
- Coend optics for quantum combs C Comfort, J Hefford
- Dagger linear logic for categorical quantum mechanics JRB Cockett, C Comfort, P Srinivasan
- The category TOF JRB Cockett, C Comfort
- The category CNOT JRB Cockett, C Comfort, P Srinivasan
