TNDistance module

Calculate distances and distributions of logical operator and stabilizer weights for a TensorNetworkCode, see tn_distance and tn_operator_weights.

OperatorWeights(stabilizer_weights,all_operator_weights)

Stores operator weight distribution for stabilizers and all code operators (stabilizers + all logical representatives). Also stores distance. Fields:

stabilizer_weights::Array{Int64,1}
all_operator_weights::Array{Int64,1}
distance::Int64

Note that since julia is 1-indexed stabilizer_weights[j] gives the number of stabilizers of weight j-1.

tn_operator_weights(code::TensorNetworkCode;truncate_to=num_qubits(code)+1)
-> OperatorWeights

Returns OperatorWeights which includes the number of stabilizers of each weight, as well as the number of logical representatives (excluding identity) of each weight, as well as the code distance.

Examples

julia> using TensorNetworkCodes.TNDistance

julia> code = TensorNetworkCode(five_qubit_code());

julia> code = contract(code,code,[[1,1],[3,3]]);

julia> tn_operator_weights(code)
OperatorWeights([1, 0, 0, 0, 9, 0, 6], [1, 0, 9, 24, 99, 72, 51], 2)

tn_distance(code::TensorNetworkCode;truncate_to=num_qubits(code)+1)
-> Int64

Returns the code distance calculated by contracting a tensor network. Returns zero for stabilizer states (codes with no logical qubits).

Examples

julia> using TensorNetworkCodes.TNDistance

julia> code = TensorNetworkCode(steane_code());

julia> code = contract(code,code,[[1,1],[3,3]]); # contract two copies

julia> tn_distance(code) # this code has poor distance!
2

plot_operator_weights(
    weights::OperatorWeights; truncate_to=length(weights.stabilizer_weights)
)

Plots a bar plot (on a log scale) of the number of operators of each weight. This includes all code operators (logicals plus stabilizers) and all stabilizers plotted separately.