Source code for qrisp.qaoa.problems.maxIndepSet
"""
\********************************************************************************
* Copyright (c) 2024 the Qrisp authors
*
* This program and the accompanying materials are made available under the
* terms of the Eclipse Public License 2.0 which is available at
* http://www.eclipse.org/legal/epl-2.0.
*
* This Source Code may also be made available under the following Secondary
* Licenses when the conditions for such availability set forth in the Eclipse
* Public License, v. 2.0 are satisfied: GNU General Public License, version 2
* with the GNU Classpath Exception which is
* available at https://www.gnu.org/software/classpath/license.html.
*
* SPDX-License-Identifier: EPL-2.0 OR GPL-2.0 WITH Classpath-exception-2.0
********************************************************************************/
"""
from qrisp import QuantumBool, x, mcx
from qrisp.algorithms.qaoa.mixers import controlled_RX_mixer_gen
import itertools
[docs]
def create_max_indep_set_mixer(G):
r"""
Creates the ``controlled_RX_mixer`` for an instance of the maximal independet set problem for a given graph $G$ following `Hadfield et al. <https://arxiv.org/abs/1709.03489>`_
The belonging ``predicate`` function indicates if a set can be swapped into the solution.
Parameters
----------
G : nx.Graph
The graph for the problem instance.
Returns
-------
function
A Python function receiving a ``QuantumVariable`` and real parameter $\beta$.
This function performs the application of the mixer associated to the graph $G$.
"""
neighbors_dict = {node: list(G.adj[node]) for node in G.nodes()}
def predicate(qv,i):
qbl = QuantumBool()
if len(neighbors_dict[i])==0:
x(qbl)
else:
mcx([qv[j] for j in neighbors_dict[i]],qbl,ctrl_state='0'*len(neighbors_dict[i]))
return qbl
controlled_RX_mixer=controlled_RX_mixer_gen(predicate)
return controlled_RX_mixer
[docs]
def create_max_indep_set_cl_cost_function(G):
"""
Creates the classical cost function for an instance of the maximal independet set problem for a given graph $G$.
Parameters
----------
G : nx.Graph
The Graph for the problem instance.
Returns
-------
cl_cost_function : function
The classical cost function for the problem instance, which takes a dictionary of measurement results as input.
"""
def cl_cost_function(res_dic):
cost = 0
for state, prob in res_dic.items():
temp = True
indices = [index for index, value in enumerate(state) if value == '1']
combinations = list(itertools.combinations(indices, 2))
for combination in combinations:
if combination in G.edges():
temp = False
break
if temp:
cost += -len(indices)*prob
return cost
return cl_cost_function
[docs]
def max_indep_set_init_function(qv):
r"""
Prepares the initial state $\ket{0}^{\otimes n}$.
Parameters
----------
qv : :ref:`QuantumVariable`
The quantum argument.
"""
pass
[docs]
def max_indep_set_problem(G):
"""
Creates a QAOA problem instance with appropriate phase separator, mixer, and
classical cost function.
Parameters
----------
G : nx.Graph
The graph for the problem instance.
Returns
-------
:ref:`QAOAProblem`
A QAOA problem instance for MaxIndepSet for a given graph ``G``.
"""
from qrisp.qaoa import QAOAProblem, RZ_mixer
return QAOAProblem(cost_operator=RZ_mixer,
mixer=create_max_indep_set_mixer(G),
cl_cost_function=create_max_indep_set_cl_cost_function(G),
init_function=max_indep_set_init_function)
