Source code for qutip.expect

# This file is part of QuTiP: Quantum Toolbox in Python.
#
#    Copyright (c) 2011 and later, Paul D. Nation and Robert J. Johansson.
#    All rights reserved.
#
#    Redistribution and use in source and binary forms, with or without
#    modification, are permitted provided that the following conditions are
#    met:
#
#    1. Redistributions of source code must retain the above copyright notice,
#       this list of conditions and the following disclaimer.
#
#    2. Redistributions in binary form must reproduce the above copyright
#       notice, this list of conditions and the following disclaimer in the
#       documentation and/or other materials provided with the distribution.
#
#    3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names
#       of its contributors may be used to endorse or promote products derived
#       from this software without specific prior written permission.
#
#    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
#    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
#    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
#    PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
#    HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
#    SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
#    LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
#    DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
#    THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
#    (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
#    OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
###############################################################################

__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_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 cy_expect_psi(oper.data, state.full(squeeze=True), 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