dq.expect

expect(O: QArrayLike, x: QArrayLike) -> Array

Returns the expectation value of an operator or list of operators on a ket, bra or density matrix.

The expectation value $\braket{O}$ of an operator $O$ is computed

• as $\braket{O}=\braket{\psi|O|\psi}$ if x is a ket $\ket\psi$ or bra $\bra\psi$,
• as $\braket{O}=\tr{O\rho}$ if x is a density matrix $\rho$.

Warning

The returned array is complex-valued. If the operator $O$ corresponds to a physical observable, it is Hermitian: $O^\dag=O$, and the expectation value is real. One can then keep only the real values of the returned array using dq.expect(O, x).real.

Parameters

• O (qarray-like of shape (nO?, n, n)) –

  Arbitrary operator or list of nO operators.

• x (qarray-like of shape (..., n, 1) or (..., 1, n) or (..., n, n)) –

  Ket, bra or density matrix.

Returns

(array of shape (nO?, ...)) Complex-valued expectation value.

Examples

>>> O = dq.number(16)
>>> psi = dq.coherent(16, 2.0)
>>> dq.expect(O, psi)
Array(4.+0.j, dtype=complex64)
>>> psis = [dq.fock(16, i) for i in range(5)]
>>> dq.expect(O, psis).shape
(5,)
>>> Os = [dq.position(16), dq.momentum(16)]
>>> dq.expect(Os, psis).shape
(2, 5)