# Source code for qutip.expect

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__all__ = ['expect', 'variance']

import numpy as np
import scipy.sparse as sp

from qutip.qobj import Qobj, isoper
from qutip.eseries import eseries
from qutip.cy.spmatfuncs import (cy_expect_rho_vec, cy_expect_psi, cy_spmm_tr,
expect_csr_ket)

expect_rho_vec = cy_expect_rho_vec
expect_psi = cy_expect_psi

[docs]def expect(oper, state):
'''Calculates the expectation value for operator(s) and state(s).

Parameters
----------
oper : qobj/array-like
A single or a list or 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 of state or operator
are arrays.

Examples
--------
>>> expect(num(4), basis(4, 3))
3

'''
if isinstance(state, Qobj) and isinstance(oper, Qobj):
return _single_qobj_expect(oper, state)

elif isinstance(oper, Qobj) and isinstance(state, eseries):
return _single_eseries_expect(oper, state)

elif isinstance(oper, (list, np.ndarray)):
if isinstance(state, Qobj):
if (all([op.isherm for op in oper]) and
(state.isket or state.isherm)):
return np.array([_single_qobj_expect(o, state) for o in oper])
else:
return np.array([_single_qobj_expect(o, state) for o in oper],
dtype=complex)
else:
return [expect(o, state) for o in oper]

elif isinstance(state, (list, np.ndarray)):
if oper.isherm and all([(op.isherm or op.type == 'ket')
for op in state]):
return np.array([_single_qobj_expect(oper, x) for x in state])
else:
return np.array([_single_qobj_expect(oper, x) for x in state],
dtype=complex)
else:
raise TypeError('Arguments must be quantum objects or eseries')

def _single_qobj_expect(oper, state):
"""
Private function used by expect to calculate expectation values of Qobjs.
"""
if isoper(oper):
if oper.dims[1] != state.dims[0]:
raise Exception('Operator and state do not have same tensor ' +
'structure: %s and %s' %
(oper.dims[1], state.dims[0]))

if state.type == 'oper':
# calculates expectation value via TR(op*rho)
return cy_spmm_tr(oper.data, state.data,
oper.isherm and state.isherm)

elif state.type == 'ket':
# calculates expectation value via <psi|op|psi>
return expect_csr_ket(oper.data, state.data,
oper.isherm)
else:
raise TypeError('Invalid operand types')

def _single_eseries_expect(oper, state):
"""
Private function used by expect to calculate expectation values for
eseries.
"""

out = eseries()

if isoper(state.ampl[0]):
out.rates = state.rates
out.ampl = np.array([expect(oper, a) for a in state.ampl])

else:
out.rates = np.array([])
out.ampl = np.array([])

for m in range(len(state.rates)):
op_m = state.ampl[m].data.conj().T * oper.data

for n in range(len(state.rates)):
a = op_m * state.ampl[n].data

if isinstance(a, sp.spmatrix):
a = a.todense()

out.rates = np.append(out.rates, state.rates[n] -
state.rates[m])
out.ampl = np.append(out.ampl, a)

return 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