qiskit.ignis.verification.GatesetTomographyFitter.linear_inversion

GatesetTomographyFitter.linear_inversion()

Reconstruct a gate set from measurement data using linear inversion.

Returns

its approximation found using the linear inversion process.

Return type

For each gate in the gateset

Additional Information:

Given a gate set (G1,…,Gm) and SPAM circuits (F1,…,Fn) constructed from those gates the data should contain the probabilities of the following types: p_ijk = E*F_i*G_k*F_j*rho p_ij = E*F_i*F_j*rho

We have p_ijk = self.probs[(Fj, Gk, Fi)] since in self.probs (Fj, Gk, Fi) indicates first applying Fj, then Gk, then Fi.

One constructs the Gram matrix g = (p_ij)_ij which can be described as a product g=AB where A = sum (i> <E F_i) and B=sum (F_j rho><j) For each gate Gk one can also construct the matrix Mk=(pijk)_ij which can be described as Mk=A*Gk*B Inverting g we obtain g^-1 = B^-1A^-1 and so g^1 * Mk = B^-1 * Gk * B This gives us a matrix similiar to Gk’s representing matrix. However, it will not be the same as Gk, since the observable results cannot distinguish between (G1,…,Gm) and (B^-1*G1*B,…,B^-1*Gm*B) a further step of Gauge optimization is required on the results of the linear inversion stage. One can also use the linear inversion results as a starting point for a MLE optimization for finding a physical gateset, since unless the probabilities are accurate, the resulting gateset need not be physical.