dq.quadrature

quadrature(
    dim: int, phi: float, *, layout: Layout | None = None, hbar: float = 0.5
) -> QArray

Returns the quadrature operator of phase angle \(\phi\).

It is defined by \(x_\phi = \sqrt{\hbar/2}\,(e^{i\phi} a^\dag + e^{-i\phi} a)\), where \(a\) and \(a^\dag\) are the annihilation and creation operators respectively.

Parameters:

• dim –

  Dimension of the Hilbert space.

• phi –

  Phase angle.

• layout –

  Matrix layout (dq.dense, dq.dia or None).

• hbar –

  Value of \(\hbar\) in the commutation relation \([\hat{x}, \hat{p}] = i\hbar\). Common choices are 0.5 (default), 1.0, and 2.0.

Returns:

• (qarray of shape (dim, dim)) –

  Quadrature operator.

Examples:

>>> dq.quadrature(3, 0.0)
QArray: shape=(3, 3), dims=(3,), dtype=complex64, layout=dia, ndiags=2
[[    ⋅     0.5  +0.j     ⋅    ]
 [0.5  +0.j     ⋅     0.707+0.j]
 [    ⋅     0.707+0.j     ⋅    ]]
>>> dq.quadrature(3, jnp.pi / 2)
QArray: shape=(3, 3), dims=(3,), dtype=complex64, layout=dia, ndiags=2
[[   ⋅       -0.-0.5j      ⋅      ]
 [-0.+0.5j      ⋅       -0.-0.707j]
 [   ⋅       -0.+0.707j    ⋅      ]]