def generate_variable(name, hermitian=False, commutative=False):
"""Generates a commutative or noncommutative variable
:param name: The symbolic name of the variable.
:type name: str.
:param hermitian: Optional parameter to request Hermitian variables .
:type hermitian: bool.
:param commutative: Optional parameter to request commutative variables.
Commutative variables are Hermitian by default.
:type commutative: bool.
:returns: :class:`sympy.physics.quantum.operator.Operator` or
:class:`sympy.physics.quantum.operator.HermitianOperator`
variable
:Example:
>>> generate_variable("c", commutative=True)
c
"""
if hermitian or commutative:
variable = HermitianOperator(name)
else:
variable = Operator(name)
variable.is_commutative = commutative
return variable
def test_hermitian():
H = HermitianOperator('H')
assert isinstance(H, HermitianOperator)
assert isinstance(H, Operator)
assert Dagger(H) == H
assert H.inv() != H
assert H.is_commutative is False
assert Dagger(H).is_commutative is False
def non_commutative_sympify(expr_string, status, boolean):
if "^" in expr_string:
expr_string = expr_string.replace("^", "**")
if "Ad" in expr_string:
expr_string = expr_string.replace("Ad", "Dagger")
fixed_string = ""
if 'Dagger' in expr_string:
fixed_string = expr_string.replace("Dagger", "sin")
else:
fixed_string = expr_string
temp_evaluated_expr = parse_expr(fixed_string, evaluate=False)
if status == '0':
status1 = False
elif status == '1':
status1 = True
new_locals = {
sym.name: Symbol(sym.name, commutative=status1)
for sym in temp_evaluated_expr.atoms(Symbol)
}
#new_locals = {}
#for sym in temp_evaluated_expr.atoms(Symbol):
# new_locals.update({sym.name:Operator(sym.name)})
#{'C': C, 'E': E, 'I': I, 'N': N, 'O': O, 'Q': Q, 'S': S}
new_locals.update({'U': UnitaryOperator('U')})
new_locals.update({'c': Symbol('c', commutative=True)})
new_locals.update({'r': Symbol('r', commutative=True)})
new_locals.update({'t': Symbol('t', commutative=True)})
new_locals.update({'W': UnitaryOperator('W')})
new_locals.update({'V': UnitaryOperator('V')})
new_locals.update({'u': UnitaryOperator('u')})
new_locals.update({'w': UnitaryOperator('w')})
new_locals.update({'v': UnitaryOperator('v')})
new_locals.update({'H': HermitianOperator('H')})
new_locals.update({'A': HermitianOperator('A')})
new_locals.update({'T': HermitianOperator('T')})
new_locals.update({'C': Operator('C')})
new_locals.update({'Dagger': Dagger})
return sympify(expr_string, locals=new_locals, evaluate=boolean)
def generate_variables(n_vars, hermitian=False, commutative=False, name='x'):
"""Generates a number of commutative or noncommutative variables
:param n_vars: The number of variables.
:type n_vars: int.
:returns: list of :class:`sympy.physics.quantum.operator.Operator` or
:class:`sympy.physics.quantum.operator.HermitianOperator`
variables
"""
variables = []
for i in range(n_vars):
if hermitian or commutative:
variables.append(HermitianOperator('%s%s' % (name, i)))
else:
variables.append(Operator('%s%s' % (name, i)))
variables[i].is_commutative = commutative
return variables
def test_sympy__physics__quantum__operator__HermitianOperator():
from sympy.physics.quantum.operator import HermitianOperator
assert _test_args(HermitianOperator('H'))
# -*- coding: utf-8 -*-
"""
This script replicates the results of gloptipolydemo.m, which is packaged with
Gloptipoly3.
Created on Thu May 15 11:16:58 2014
@author: wittek
"""
from sympy.physics.quantum.operator import HermitianOperator
from ncpol2sdpa import SdpRelaxation, write_to_sdpa
# Get commutative variables
x1 = HermitianOperator("x1")
x1.is_commutative = True
x2 = HermitianOperator("x2")
x2.is_commutative = True
g0 = 4 * x1 ** 2 + x1 * x2 - 4 * x2 ** 2 - \
2.1 * x1 ** 4 + 4 * x2 ** 4 + x1 ** 6 / 3
# Obtain SDP relaxation
sdpRelaxation = SdpRelaxation([x1, x2])
sdpRelaxation.get_relaxation(3, objective=g0)
write_to_sdpa(sdpRelaxation, 'gloptipoly_demo.dat-s')
