dq.fdestroy

Returns a fermionic annihilation operator, or a tuple of annihilation operators for a multi-mode system.

If n=1, it returns the single-mode annihilation operator \(a = \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}\). If n>1, it returns a tuple with n operators \((a_1,\dots,a_n)\) acting on the composite Hilbert space of dimension \(2^n\). To satisfy the anti-commutation relations \(\{a_j, a_k^\dag\} = \delta_{jk}\) and \(\{a_j, a_k\} = 0\), they are constructed with the Jordan-Wigner transformation: $$ a_k = \sigma_z^{\otimes (k-1)} \otimes a \otimes I_2^{\otimes (n-k)}. $$

Parameters:

• n –

  Number of fermionic modes.

• layout –

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

Returns:

• (qarray or tuple of qarrays, each of shape (2^n, 2^n)) –

  Annihilation operator(s).

Examples:

Single-mode \(a\):

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

Multi-mode \(a_1 = a \otimes I_2\) and \(a_2 = \sigma_z \otimes a\):

>>> a1, a2 = dq.fdestroy(2)
>>> a1
QArray: shape=(4, 4), dims=(2, 2), dtype=complex64, layout=dia, ndiags=1
[[  ⋅      ⋅    1.+0.j   ⋅   ]
 [  ⋅      ⋅      ⋅    1.+0.j]
 [  ⋅      ⋅      ⋅      ⋅   ]
 [  ⋅      ⋅      ⋅      ⋅   ]]
>>> a2
QArray: shape=(4, 4), dims=(2, 2), dtype=complex64, layout=dia, ndiags=1
[[   ⋅     1.+0.j    ⋅       ⋅   ]
 [   ⋅       ⋅       ⋅       ⋅   ]
 [   ⋅       ⋅       ⋅    -1.+0.j]
 [   ⋅       ⋅       ⋅       ⋅   ]]