186 citations · 332 across the 13 of their papers we have counts for
13 papers
Meromorphic Quantum Computing
Simon Burton, Hussain Anwar
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…
Categorified Path Calculus
Simon Burton
Path calculus, or graphical linear algebra, is a string diagram calculus for the category of matrices over a base ring. It is the usual string diagram calculus for a symmetric mono…
CSS code surgery as a universal construction
Alexander Cowtan, Simon Burton
We define code maps between Calderbank-Shor-Steane (CSS) codes using maps between chain complexes, and describe code surgery between such codes using a specific colimit in the cate…
Fold-Transversal Clifford Gates for Quantum Codes
Nikolas P. Breuckmann, Simon Burton
We generalize the concept of folding from surface codes to CSS codes by considering certain dualities within them. In particular, this gives a general method to implement logical o…
Entropy, Derivation Operators and Huffman Trees
Simon Burton
We build a theory of binary trees on finite multisets that categorifies, or operationalizes, the entropy of a finite probability distribution. Multisets operationalize probabilitie…
Limitations on transversal gates for hypergraph product codes
Simon Burton, Dan Browne
We analyze the structure of the logical operators from a class of quantum codes that generalizes the surface codes. These are the hypergraph product codes, restricted to the vertic…