pygsti.baseobjs.basisconstructors.qsim_matrices

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pygsti.baseobjs.basisconstructors.qsim_matrices#

qsim_matrices(matrix_dim)#

Get the elements of the QuantumSim basis with matrix dimension matrix_dim.

These matrices span the space of matrix_dim x matrix_dim density matrices (matrix-dimension matrix_dim, space dimension matrix_dim^2).

The returned matrices are given in the QuantumSim representation of the density matrix space, and are thus kronecker products of the standard representation of the QuantumSim matrices:

  • ‘0’ == [[1, 0],[0,0]]

  • ‘X’ == [[0, 1],[1,0]]

  • ‘Y’ == [[0,-1.j],[1.j,0]]

  • ‘1’ == [[0, 0],[0,1]]

The normalization is such that the resulting basis is orthonormal under the trace inner product:

Tr( dot(Mi,Mj) ) == delta_ij.

In the returned list, the right-most factor of the kronecker product varies the fastest, so, for example, when matrix_dim == 4 the returned list is:

[ 00,0X,0Y,01,X0,XX,XY,X1,Y0,Y0,YX,YY,Y1,10,1X,1Y,11 ].

Parameters:

matrix_dim (int) – Matrix-dimension of the density-matrix space. Must be a power of 2.

Returns:

A list of N numpy arrays each of shape (matrix_dim, matrix_dim), where N == matrix_dim^2, the dimension of the density-matrix space.

Return type:

list

Notes

Matrices are ordered with first qubit being most significant, e.g., for 2 qubits: 00, 0X, 0Y, 01, X0, XX, XY, X1, Y0, … 11

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