pygsti.tools.symplectic.symplectic_form

symplectic_form(n, convention='standard')

Creates the symplectic form for the number of qubits specified.

There are two variants, of the sympletic form over the finite field of the integers modulo 2, used in pyGSTi. These corresponding to the ‘standard’ and ‘directsum’ conventions. In the case of ‘standard’, the symplectic form is the 2n x 2n matrix of ((0,1),(1,0)), where ‘1’ and ‘0’ are the identity and all-zeros matrices of size n x n. The ‘standard’ symplectic form is probably the most commonly used, and it is the definition used throughout most of the code, including the Clifford compilers. In the case of ‘directsum’, the symplectic form is the direct sum of n 2x2 bit-flip matrices. This is only used in pyGSTi for sampling from the symplectic group.

Parameters:

• n (int) – The number of qubits the symplectic form should be constructed for. That is, the function creates a 2n x 2n matrix that is a sympletic form

• convention (str, optional) – Can be either ‘standard’ or ‘directsum’, which correspond to two different definitions for the symplectic form.

Returns:

The specified symplectic form.

Return type:

numpy array