Source code for qrisp.qaoa.problems.minSetCover
"""
\********************************************************************************
* 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 QuantumVariable, QuantumBool, x, mcx
from qrisp.algorithms.qaoa.mixers import controlled_RX_mixer_gen
[docs]
def create_min_set_cover_mixer(sets, universe):
r"""
Creates the ``controlled_RX_mixer`` for an instance of the minimum set cover problem following `Hadfield et al. <https://arxiv.org/abs/1709.03489>`_
The belonging ``predicate`` function indicates if a set can be swapped out of the solution.
Parameters
----------
sets : list[set]
A list of sets.
universe : set
The union of all sets.
Returns
-------
function
A Python function receiving a :ref:`QuantumVariable` and real parameter $\beta$.
This function performs the application of the mixer associated to the problem instance.
"""
membership_dict = {element: [i for i, subset in enumerate(sets) if element in subset] for element in universe}
def predicate(qv,i):
anc = QuantumVariable(len(sets[i]))
x(anc)
for anc_index, element in enumerate(sets[i]):
other_sets = [item for item in membership_dict[element] if item != i]
mcx([qv[set_index] for set_index in other_sets],anc[anc_index],ctrl_state="0"*len(other_sets))
qbl = QuantumBool()
mcx(anc,qbl)
return qbl
controlled_RX_mixer=controlled_RX_mixer_gen(predicate)
return controlled_RX_mixer
[docs]
def create_min_set_cover_cl_cost_function(sets, universe):
"""
Creates the classical cost function for an instance of the minimum set cover problem.
Parameters
----------
sets : list[set]
A list of sets.
universe : set
The union of all sets.
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():
indices = [index for index, value in enumerate(state) if value == '1']
solution_sets = [sets[index] for index in indices]
if len(solution_sets)>0 and set.union(*solution_sets)==universe:
cost += len(indices)*prob
else:
cost += len(sets)
return cost
return cl_cost_function
[docs]
def min_set_cover_init_function(qv):
r"""
Prepares the initial state $\ket{1}^{\otimes n}$.
Parameters
----------
qv : :ref:`QuantumVariable`
The quantum argument.
"""
x(qv)
[docs]
def min_set_cover_problem(sets, universe):
"""
Creates a QAOA problem instance with appropriate phase separator, mixer, and
classical cost function.
Parameters
----------
sets : list[set]
A list of sets.
universe : set
The union of all sets.
Returns
-------
:ref:`QAOAProblem`
A QAOA problem instance for MinSetCover for given ``sets`` and ``universe``.
"""
from qrisp.qaoa import QAOAProblem, RZ_mixer
return QAOAProblem(cost_operator=RZ_mixer,
mixer= create_min_set_cover_mixer(sets, universe),
cl_cost_function=create_min_set_cover_cl_cost_function(sets, universe),
init_function=min_set_cover_init_function)
