Channel Conversions

choi2liou

Takes a superoperator in choi matrix form and returns the liouville superoperator (computational basis)

takes the choi matrix and returns the kraus operators. This stays the same, save that we need to take into account dimensional factors. Note slight negative eigenvalue (rounding can cause problems). Here I round to 15 digits.

takes the Chi matrix (Choi matrix in Pauli basis) and return the liouville superoperator, computaitonal basis

Takes a choi matrix and returns the Chi Matrix Note the basis here has changed from marcusps version, The rightmost paulis are varying the quickest.

Takes a chi matrix and returns the choi Matrix Note the basis here has changed from marcusps version, Note we normalise (divide by dsq). Some conventions differ.

Takes a vector of kraus operators and returns the choi matrix

Takes a vector of kraus operators (matrices) and converts them to a liouville superoperator (computational basis)

liou2choi

Take a liouville superoperator (computational basis) and return the choi matrix

takes a liouville superoperator (computational basis) and returns the Chi matrix (basically the choi matrix in Pauli basis)

Takes a liouville superoperator (computational basis) and returns a vector of the equivalen Krawu vectors

Converts a liouville superoperator in the computaional basis to one in the pauli basis. Order of Paulis is I,X,Y and Z.

Converts a liouville superoperator in the Pauli basis to one in the computational basis. Order of Paulis is I,X,Y and Z.

function makeSuper(u)

Takes an operator and turns into a superoperator. Pauli basis.

pass in a density matrix, gives you the super vector that corresponds to it

istp(m;tol)

Returns whether is trace perserving.. Assumes input is in liouville basis (not pauli-liouville - use pauliliou2liou)

iscp(m;tol)

Returns whether is completely positivel. Assumes input is in liouville basis (not pauli-liouville - use pauliliou2liou) Converts to choi and checks the eigenvalues. – tweaked to increase eps slightly was getting a trivial false !cp right on the boundary.

ischannel(m;tol)

Returns whether is the liouville superoperator is trace perserving and completely positive. Assumes input is in liouville basis (not pauli-liouville - use pauliliou2liou)

unital(m;tol)

Returns whether is the liouville superoperator is unital. Assumes input is in liouville basis (not pauli-liouville - use pauliliou2liou)

observeBasis(basis,Λ)

Arguments

• basis: Array{Float64,1} A list of the Paulis basis you want to oberve in. e.g. [1,2,1,3] would be four qubits representing [X,Y,X,Z]
• Λ: Array{Float64,2}: The superoperator of the noise. Assumed appropriately sized (4^n x 4^n) , where n is the number of basis provided.

Returns

The 2^n probability distribution (of up/down measurements) that would be seen if you put those Paulis through the channel and tried to measure in the same basis.

observeBasis(basis,Λ)

Arguments

• basis: Array{Float64,1} A list of the Paulis basis you want to oberve in. e.g. [1,2,1,3] would be four qubits representing [X,Y,X,Z]
• Λ: Array{Float64,1}: In this case we assume a Pauli channel and the noise is represented as a vector of the Pauli eigenvalues (4^n) long.

Returns

The 2^n probability distribution (of up/down measurements) that would be seen if you put those Paulis through the channel and tried to measure in the same basis.

Helper function for labeling graphs, pass in the qubits get the string of Is and Zs e.g. with two you get ["00","01","10","11"]

measure(s,measureNoise, allZs)

Helper function in open-systems.jl Pass in the state, the noise (as a superOperator) and the measurements - use allZs to generate) returns the mapped function (x->x'measureNoises,allZs)

Helper function (chart axis) return all the ups and downs for a certain number of qubits as a list of strings

returns an array of the 'measurement' operators that extract each of the z measurements e.g. for two qubits will return the II, IZ, ZI and ZZ measurements