scaling.jl

DepolarisingPlanarScaling

Scaling data for an experimental design for the syndrome extraction circuit of a surface code with depolarising Pauli noise.

Fields

• dist_range::Vector{Int}: Code distances.
• merit_scaling::Vector{Merit}: Merit of the design for a range of code distances.
• G_fit::Function: Gate number fit.
• G_params::Vector{Int}: Gate number fit parameters; $a + bd + cd^2$.
• N_fit::Function: Gate eigenvalue number fit.
• N_params::Vector{Int}: Gate eigenvalue number fit parameters; $a + bd + cd^2$.
• trace_fit::Function: Trace of the gate eigenvalue estimator covariance matrix fit.
• trace_params::Vector{Float64}: Trace of the gate eigenvalue estimator covariance matrix fit parameters; $a + bd + cd^2$.
• trace_sq_fit::Function: Trace of the gate eigenvalue estimator covariance matrix squared fit.
• trace_sq_params::Vector{Float64}: Trace of the gate eigenvalue estimator covariance matrix squared fit parameters; $a + bd + cd^2$.
• expectation_fit::Function: Normalised RMS error expectation fit.
• variance_fit::Function: Normalised RMS error variance fit.
• circuit_param::AbstractCircuitParameters: Code parameters.
• noise_param::DepolarisingParameters: Depolarising noise parameters.
• tuple_set::Vector{Vector{Int}}: Set of tuples which arrange the circuit layers.
• tuple_set_data::TupleSetData: TupleSetData object that generates the tuple set.
• shot_weights::Vector{Float64}: Shot weights for each tuple in the set, which add to 1.
• ls_type::Symbol: Type of least squares estimator for which the merits were calculated.
• calculation_times::Matrix{Float64}: Time taken to generate the design and calculate the merit, respectively, for each distance.
• overall_time::Float64: The overall time taken to calculate the merit scaling data for depolarising noise.

LognormalPlanarScaling

Scaling data for an experimental design for the syndrome extraction circuit of a surface code with log-normal random Pauli noise.

Fields

• dist_range::Vector{Int}: Code distances.
• N_fit::Function: Gate eigenvalue number fit.
• N_params::Vector{Int}: Gate eigenvalue number fit parameters; $a + bd + cd^2$.
• expectation_scaling::Vector{Vector{Float64}}: Expected normalised RMS error for a range of code distances.
• expectation_fit::Function: Mean expected normalised RMS error fit.
• variance_scaling::Vector{Vector{Float64}}: Normalised RMS error variance for a range of code distances.
• variance_fit::Function: Mean normalised RMS error variance fit.
• eigenvalues_scaling::Vector{Vector{Vector{Float64}}}: Eigenvalues of the gate log-eigenvalue estimator covariance matrix for a range of code distances.
• circuit_param::AbstractCircuitParameters: Code parameters.
• noise_param::LognormalParameters: Log-normal random noise parameters.
• seeds::Vector{UInt64}: Seeds for the log-normal noise parameters.
• tuple_set::Vector{Vector{Int}}: Set of tuples which arrange the circuit layers.
• tuple_set_data::TupleSetData: TupleSetData object that generates the tuple set.
• shot_weights::Vector{Float64}: Shot weights for each tuple in the set, which add to 1.
• ls_type::Symbol: Type of least squares estimator for which the merits were calculated.
• calculation_times::Matrix{Float64}: The time taken to generate the design and calculate the figures of merit for random instances of log-normal Pauli noise, and for depolarising Pauli noise, respectively.
• overall_time::Float64: The overall time taken to calculate the merit scaling for log-normal random noise.

calc_depolarising_planar_scaling(d::Design, dist_max::Int; kwargs...)
calc_depolarising_planar_scaling(d::Design, dist_range::Vector{Int}; kwargs...)

Returns the scaling data as a DepolarisingPlanarScaling object for the figure of merit of the design d for the syndrome extraction circuit of a surface code with depolarising Pauli noise, as a function of the distance of the code.

Arguments

• d::Design: Design for which the merit scaling is calculated.
• dist_max::Int: Maximum code distance for which the merit scaling is calculated.
• dist_range::Vector{Int}: Vode distances for which the merit scaling is calculated.

Keyword arguments

• ls_type::Symbol = :none: Type of least squares estimator used to calculate the merit scaling, which defaults to the least squares estimator type of the design, or if that is not specified, :wls.
• diagnostics::Bool = true: Whether to print diagnostic information.
• save_data::Bool = false: Whether to save the merit scaling data.

calc_lognormal_planar_scaling(d::Design, dist_max::Int; kwargs...)
calc_lognormal_planar_scaling(d::Design, dist_range::Vector{Int}; kwargs...)

Returns the scaling data as a LognormalPlanarScaling object for the figure of merit of the design d for the syndrome extraction circuit of a surface code with log-normal random Pauli noise, as a function of the distance of the code.

Arguments

• d::Design: Design for which the merit scaling is calculated.
• dist_max::Int: Maximum code distance for which the merit scaling is calculated.
• dist_range::Vector{Int}: Code distances for which the merit scaling is calculated.

Keyword arguments

• ls_type::Symbol = :none: Type of least squares estimator used to calculate the merit scaling, which defaults to the least squares estimator type of the design, or if that is not specified, :wls.
• precision::Float64 = 1e-3: Precision to which the figure of merit is estimated, corresponding to the target standard error of the mean.
• max_repetitions::Int = 10000: Maximum number of random instances of log-normal Pauli noise over which the figure of merit is calculated.
• min_repetitions::Int = 100: Minimum number of random instances of log-normal Pauli noise over which the figure of merit is calculated.
• print_repetitions::Int = 100: Number of random instances of log-normal Pauli noise between printing diagnostics.
• seed::Union{UInt64, Nothing} = nothing: Seeds used to generate instances of log-normal Pauli noise.
• diagnostics::Bool = true: Whether to print diagnostic information.
• save_data::Bool = false: Whether to save the merit scaling data.