# cirq.givens¶

cirq.givens(angle_rads: Union[float, sympy.core.basic.Basic]) → cirq.ops.phased_iswap_gate.PhasedISwapPowGate[source]

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

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.

Parameters