186 citations · 332 across the 13 of their papers we have counts for
11 papers · 1 filter
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…
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…
Decoding Across the Quantum LDPC Code Landscape
Joschka Roffe, David R. White, Simon Burton +1
We show that belief propagation combined with ordered statistics post-processing is a general decoder for quantum low density parity check codes constructed from the hypergraph pro…
Optimal local unitary encoding circuits for the surface code
Oscar Higgott, Matthew Wilson, James Hefford +4
The surface code is a leading candidate quantum error correcting code, owing to its high threshold, and compatibility with existing experimental architectures. Bravyi et al. (2006)…
Spectra of Gauge Code Hamiltonians
Simon Burton
We study the spectral gap of frustrated spin (qubit) Hamiltonians constructed from quantum subsystem (gauge) codes. Such a Hamiltonian can be block diagonalized, with blocks labell…
A Short Guide to Anyons and Modular Functors
Simon Burton
To the working physicist, anyon theory is meant to describe certain quasi-particle excitations occurring in two dimensional topologically ordered systems. A typical calculation usi…
Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code
Simon Burton, Courtney G. Brell, Steven T. Flammia
Classically simulating the dynamics of anyonic excitations in two-dimensional quantum systems is likely intractable in general because such dynamics are sufficient to implement uni…
Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems
Courtney G. Brell, Simon Burton, Guillaume Dauphinais +2
We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-tim…