Source code for qutip.core.expect

__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` 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 # 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(, # 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