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dq.cd_gate 

cd_gate(dim: int, alpha: ArrayLike) -> QArray

Returns a conditional displacement gate.

The conditional displacement (CD) gate displaces an oscillator conditioned on the state of a coupled two-level system (TLS) state. It is defined by $$ \mathrm{CD}(\alpha) = D(\alpha/2)\ket{g}\bra{g} + D(-\alpha/2)\ket{e}\bra{e}, $$ where \(\ket{g}\) (defined by dq.ground()) and \(\ket{e}\) (defined by dq.excited()) are the ground and excited states of the TLS.

Parameters

  • dim –

    Dimension of the oscillator Hilbert space.

  • alpha (array-like of shape (...)) –

    Displacement amplitude.

Returns

(qarray of shape (..., n, n)) CD gate operator (acting on the oscillator + TLS system of dimension n = 2 x dim).

Examples 

>>> dq.cd_gate(2, 0.1)
QArray: shape=(4, 4), dims=(2, 2), dtype=complex64, layout=dense
[[ 0.999+0.j  0.   +0.j  0.05 +0.j  0.   +0.j]
 [ 0.   +0.j  0.999+0.j  0.   +0.j -0.05 +0.j]
 [-0.05 +0.j  0.   +0.j  0.999+0.j  0.   +0.j]
 [ 0.   +0.j  0.05 +0.j  0.   +0.j  0.999+0.j]]
>>> dq.cd_gate(3, [0.1, 0.2]).shape
(2, 6, 6)