Sparse Pauli-Lindblad noise model

The SPLNoiseModel type represents a sparse Pauli-Lindblad (SPL) noise model: a collection of one- and two-body Pauli-string Lindblad generators, each with its own coefficient, acting on a specific set of qbits. This is the noise model described for example in [1].

Constructing a noise model

A model can be built directly from a dictionary mapping PauliStrings (from PauliStringTensors.jl) to their coefficients, together with the list of qbit indices the strings refer to:

julia> using PauliStringTensors, QuantumCircuitSimulator

julia> params = Dict("XI" => 0.01, "ZI" => 0.02, "XX" => 0.005);

julia> model = SPLNoiseModel(params, 1:2);

Only Pauli strings of order 1 or 2 (on adjacent positions) are allowed. The second argument can be omitted, in which case the qbit range is assumed to be 1:N, with N the length of the Pauli strings. A model can also be loaded from a JSON file mapping Pauli strings to coefficients, such as

model = SPLNoiseModel("noise_parameters.json")

Noise layers

Given the ITensor site indices of a circuit (necessarily with the "vQubit" site type), noiselayer builds the MPO representation of one layer of the noise channel described by an SPL model:

julia> using ITensorMPS

julia> sites = siteinds("vQubit", 4);

julia> noise_mpo = noiselayer(sites, model);

An optional maxbonddim keyword argument truncates the resulting MPO to a maximum bond dimension. The MPO(sites, model::SPLNoiseModel) constructor is an alias for the same operation.

Finally, inversenoiselayer builds the MPO for the inverse of the noise channel (useful for error mitigation), using the same interface as noiselayer.