cirq.givens

View source on GitHub

Returns gate with matrix exp(-i angle_rads (Y⊗X - X⊗Y) / 2).

cirq.givens(
    angle_rads: cirq.TParamVal
) -> cirq.PhasedISwapPowGate

In numerical linear algebra Givens rotation is any linear transformation with matrix equal to the identity except for a 2x2 orthogonal submatrix [[cos(a), -sin(a)], [sin(a), cos(a)]] which performs a 2D rotation on a subspace spanned by two basis vectors. In quantum computational chemistry the term is used to refer to the two-qubit gate defined as

givens(a) ≡ exp(-i a (Y⊗X - X⊗Y) / 2)

with the matrix

[[1, 0, 0, 0],
 [0, c, -s, 0],
 [0, s, c, 0],
 [0, 0, 0, 1]]

where

c = cos(a),
s = sin(a).

The matrix is a Givens rotation in the numerical linear algebra sense acting on the subspace spanned by the |01⟩ and |10⟩ states.

The gate is also equivalent to the ISWAP conjugated by T^-1 ⊗ T.