__all__ = ['expect', 'variance']
import numpy as np
from .qobj import Qobj
from . import data as _data
[docs]def expect(oper, state):
"""
Calculate the expectation value for operator(s) and state(s). The
expectation of state ``k`` on operator ``A`` is defined as
``k.dag() @ A @ k``, and for density matrix ``R`` on operator ``A`` it is
``trace(A @ R)``.
Parameters
----------
oper : qobj/array-like
A single or a `list` of operators for expectation value.
state : qobj/array-like
A single or a `list` of quantum states or density matrices.
Returns
-------
expt : float/complex/array-like
Expectation value. ``real`` if ``oper`` is Hermitian, ``complex``
otherwise. A (nested) array of expectaction values if ``state`` or
``oper`` are arrays.
Examples
--------
>>> expect(num(4), basis(4, 3)) == 3 # doctest: +NORMALIZE_WHITESPACE
True
"""
if isinstance(state, Qobj) and isinstance(oper, Qobj):
return _single_qobj_expect(oper, state)
elif isinstance(oper, (list, np.ndarray)):
if isinstance(state, Qobj):
dtype = np.complex128
if all(op.isherm for op in oper) and (state.isket or state.isherm):
dtype = np.float64
return np.array([_single_qobj_expect(op, state) for op in oper],
dtype=dtype)
return [expect(op, state) for op in oper]
elif isinstance(state, (list, np.ndarray)):
dtype = np.complex128
if oper.isherm and all(op.isherm or op.isket for op in state):
dtype = np.float64
return np.array([_single_qobj_expect(oper, x) for x in state],
dtype=dtype)
raise TypeError('Arguments must be quantum objects')
def _single_qobj_expect(oper, state):
"""
Private function used by expect to calculate expectation values of Qobjs.
"""
if not oper.isoper or not (state.isket or state.isoper):
raise TypeError('invalid operand types')
if oper.dims[1] != state.dims[0]:
msg = (
"incompatible dimensions "
+ str(oper.dims[1]) + " and " + str(state.dims[0])
)
raise ValueError(msg)
out = _data.expect(oper.data, state.data)
# This ensures that expect can return something that is not a number such
# as a `tensorflow.Tensor` in qutip-tensorflow.
return out.real if (oper.isherm
and (state.isket or state.isherm)
and hasattr(out, "real")
) else out
[docs]def variance(oper, state):
"""
Variance of an operator for the given state vector or density matrix.
Parameters
----------
oper : qobj
Operator for expectation value.
state : qobj/list
A single or ``list`` of quantum states or density matrices..
Returns
-------
var : float
Variance of operator 'oper' for given state.
"""
return expect(oper**2, state) - expect(oper, state)**2