dq.eye

eye(*dims: int, layout: Layout | None = None) -> QArray

Returns the identity operator.

If multiple dimensions are provided $\mathtt{dims}=(n_1,\dots,n_N)$, it returns the identity operator of the composite Hilbert space of dimension $n=\prod n_k$: $$I_n = I_{n_1}\otimes\dots\otimes I_{n_N}.$$

Parameters

• *dims –

  Hilbert space dimension of each subsystem.

• layout –

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

Returns

(qarray of shape (n, n)) Identity operator, with n = prod(dims).

Examples

Single-mode $I_4$:

>>> dq.eye(4)
QArray: shape=(4, 4), dims=(4,), dtype=complex64, layout=dia, ndiags=1
[[1.+0.j   ⋅      ⋅      ⋅   ]
 [  ⋅    1.+0.j   ⋅      ⋅   ]
 [  ⋅      ⋅    1.+0.j   ⋅   ]
 [  ⋅      ⋅      ⋅    1.+0.j]]

Multi-mode $I_2 \otimes I_3$:

>>> dq.eye(2, 3)
QArray: shape=(6, 6), dims=(2, 3), dtype=complex64, layout=dia, ndiags=1
[[1.+0.j   ⋅      ⋅      ⋅      ⋅      ⋅   ]
 [  ⋅    1.+0.j   ⋅      ⋅      ⋅      ⋅   ]
 [  ⋅      ⋅    1.+0.j   ⋅      ⋅      ⋅   ]
 [  ⋅      ⋅      ⋅    1.+0.j   ⋅      ⋅   ]
 [  ⋅      ⋅      ⋅      ⋅    1.+0.j   ⋅   ]
 [  ⋅      ⋅      ⋅      ⋅      ⋅    1.+0.j]]

See also

• dq.eye_like(): returns the identity operator in the Hilbert space of the input.