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dq.cd_gate

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

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 \(\ket{g}=\ket0\) and \(\ket{e}=\ket1\) are the ground and excited states of the TLS, respectively.

Parameters

  • dim

    Dimension of the oscillator Hilbert space.

  • alpha (array_like of shape (...))

    Displacement amplitude.

Returns

(array 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)
Array([[ 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]], dtype=complex64)
>>> dq.cd_gate(3, [0.1, 0.2]).shape
(2, 6, 6)