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- #!/usr/bin/python
- # -*- coding: utf-8 -*-
-
- """
- Generates and enumerates the 24 elements of the local Clifford group
- Following the prescription of Anders (thesis pg. 26):
- > Table 2.1: The 24 elements of the local Clifford group. The row index (here called the “sign symbol”) shows how the operator
- > U permutes the Pauli operators σ = X, Y, Z under the conjugation σ = ±UσU† . The column index (the “permutation
- > symbol”) indicates the sign obtained under the conjugation: For operators U in the I column it is the sign of the permutation
- > (indicated on the left). For elements in the X, Y and Z columns, it is this sign only if the conjugated Pauli operator is the one
- > indicated by the column header and the opposite sign otherwise.
- """
-
- from numpy import *
-
- i = matrix(eye(2, dtype=complex))
- px = matrix([[0, 1], [1, 0]], dtype=complex)
- py = matrix([[0, -1j], [1j, 0]], dtype=complex)
- pz = matrix([[1, 0], [0, -1]], dtype=complex)
- h = matrix([[1, 1], [1, -1]], dtype=complex) / sqrt(2)
- p = matrix([[1, 0], [0, 1j]], dtype=complex)
-
- permutations = (i, h, p, h*p, h*p*h, h*p*h*p)
- signs = (i, px, py, pz)
- unitaries = [p*s for p in permutations for s in signs]
-
-
- # TODO:
- # - check that we re-generate the table
- # - do conjugation
- # - do times table
- # - write tests
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