calculate_t

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calculate_t#

iqm.qaoa.tree_calculation.generate_basis.calculate_t(v1)#

Given a vector v1, calculate its symmetry sector.

For an input vector v1 of length \(2m\), the symmetry sector \(t\) is the smallest integer, such that removing \(t\) elements from the beginning and the end of v1 makes the array symmetric with respect to flip, i.e., a palindrome. In other words, it’s the smallest integer, such that starting from the middle of v1, the first \(m-t\) elements to the left equal the first \(m-t\) elements to the right. By definition \(t\) lies between 0 and \(m\) (included). Some examples:

Input array

Half of input length \(m\)

Output \(t\)

[-1, 1, 1, 1, 1, 1]

3

1

[-1, 1, -1, -1, -1, 1]

3

2

[-1, 1, -1, -1, 1, -1]

3

0

[-1, 1, -1, 1, 1, 1]

3

3

[-1, 1, 1, 1]

2

1

[-1, 1, 1, 1, 1, 1, 1, 1]

4

1
Parameters:

v1 (ndarray) – The array whose symmetry sector we want to calculate.

Returns:

The symmetry sector of the input array.

Raises:

  • ValueError – If v1 does not have the proper shape (1D array of even length).

  • ValueError – If v1 contains other entries than +1 and -1

Return type:

int64

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