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SPA-QIN Trivia Class

This part of the project documentation focuses on a Trivia object containing basic math constructs facilitating the implementation of quantum operations.

Standalone usage

In your code:

from spa_qin.trivia import Trivia

Class members

You can access Trivia class members:

Pauli matrices:

  • PauliX: \(\sigma_1 = \sigma_x = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}\)
  • PauliY: \(\sigma_2 = \sigma_y = \begin{pmatrix*}[r] 0 & -i \\ -i & 0 \end{pmatrix*}\)
  • PauliZ: \(\sigma_3 = \sigma_z = \begin{pmatrix*}[r] 1 & 0 \\ 0 & -1 \end{pmatrix*}\)

Identity matrices:

  • Identity2: \(\mathbb{I}_2\)
  • Identity4: \(\mathbb{I}_4\)

Class methods:

Kraus operators:

  • Kraus0(d): \(K_0 = \sqrt{1-d}\mathbb{I}_2\)
  • Kraus1(d): \(K_1 = \sqrt{\frac{d}{3}}\sigma_x\)
  • Kraus2(d): \(K_2 = \sqrt{\frac{d}{3}}\sigma_y\)
  • Kraus3(d): \(K_3 = \sqrt{\frac{d}{3}}\sigma_z\)

Example usage:

from spa_qin.trivia import Trivia

print(Trivia.PauliX)

two = 2 * Trivia.Identity2