Homological Measurements

Homological measurement constructs the mapping-cone code associated with measuring logical operators of a CSS stabilizer code. The supplied logical operators are validated against the code before the new code is returned.

CodingTheory.Cheeger_constant — Method
Cheeger_constant(
    S::AbstractSubsystemCodeCSS,
    L::Union{Nemo.FqMatrix, Nemo.fpMatrix, Hecke.SMat, SparseArrays.SparseMatrixCSC}
) -> Float64

Return the Cheeger constant of the incidence graph induced by the pure X or Z logical operator L and the opposite-type stabilizers of S.

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CodingTheory.Cheeger_constant — Method
Cheeger_constant(M::Array{T<:Integer, 2}) -> Float64

Return the Cheeger constant of the matrix M assuming M is a vertex-edge incidence matrix.

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CodingTheory.homological_measurement — Method
homological_measurement(
    S::AbstractStabilizerCodeCSS,
    L::Union{Nemo.FqMatrix, Nemo.fpMatrix, Hecke.SMat, SparseArrays.SparseMatrixCSC};
    style,
    r,
    max_iters,
    cellulate,
    improve_cycles,
    remove_and_improve_cycles,
    log_checking,
    rng
) -> Any

Return the (mapping) cone code associated with measuring the logical(s) L of the CSS stabilizer code S.

Keyword arguments

All parameters are aligned with their respective papers.

  • style - :Xanadu, :IBM, or :Cohen
  • max_iters - used for :Xanadu and :IBM
  • r - used for :Cohen
  • improve_cycles - used for IBM
  • remove_and_improve_cycles - used for IBM, supersedes previous parameter
  • log_checking - set to false to intentionally use an L that isn't a logical
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