{
    "info": {
        "author": "Joseph T. Iosue",
        "author_email": "joe.iosue@yahoo.com",
        "bugtrack_url": null,
        "classifiers": [
            "License :: OSI Approved :: Apache Software License",
            "Operating System :: OS Independent",
            "Programming Language :: Python :: 3"
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        "description": "========\nQUBOVert\n========\n*master branch*\n\n.. image:: https://travis-ci.com/jiosue/QUBOVert.svg?branch=master\n    :target: https://travis-ci.com/jiosue/QUBOVert\n    :alt: Travis-CI\n.. image:: https://readthedocs.org/projects/qubovert/badge/?version=latest\n    :target: https://qubovert.readthedocs.io/en/latest/?badge=latest\n    :alt: Documentation Status\n.. image:: https://codecov.io/gh/jiosue/QUBOVert/branch/master/graph/badge.svg\n    :target: https://codecov.io/gh/jiosue/QUBOVert\n    :alt: Code Coverage\n.. image:: https://img.shields.io/lgtm/grade/python/g/jiosue/QUBOVert.svg?logo=lgtm&logoWidth=18\n    :target: https://lgtm.com/projects/g/jiosue/QUBOVert/context:python\n    :alt: Code Quality\n\n*dev branch*\n\n.. image:: https://travis-ci.com/jiosue/QUBOVert.svg?branch=dev\n    :target: https://travis-ci.com/jiosue/QUBOVert\n    :alt: Travis-CI\n.. image:: https://readthedocs.org/projects/qubovert/badge/?version=dev\n    :target: https://qubovert.readthedocs.io/en/latest/?badge=dev\n    :alt: Documentation Status\n.. image:: https://codecov.io/gh/jiosue/QUBOVert/branch/dev/graph/badge.svg\n    :target: https://codecov.io/gh/jiosue/QUBOVert\n    :alt: Code Coverage\n\n*pypi distribution*\n\n.. image:: https://badge.fury.io/py/qubovert.svg\n    :target: https://badge.fury.io/py/qubovert\n    :alt: pypi dist\n.. image:: https://pepy.tech/badge/qubovert\n    :target: https://pepy.tech/project/qubovert\n    :alt: pypi dist downloads\n\n\nPlease see the `Repository <https://github.com/jiosue/QUBOVert>`_ and `Docs <https://qubovert.readthedocs.io>`_. For examples/tutorials, see the `notebooks <https://github.com/jiosue/QUBOVert/tree/master/notebook_examples>`_.\n\n\nInstallation\n------------\n`For the stable release`.\n\n.. code:: shell\n\n  pip install qubovert\n\n\nTo install from source:\n\n.. code:: shell\n\n  git clone https://github.com/jiosue/qubovert.git\n  cd qubovert\n  pip install -e .\n\n\nThen you can use it in Python **versions 3.6 and above** with\n\n.. code:: python\n\n    import qubovert\n\n    # get info\n    help(qubovert)\n\n    # see the main functionality\n    print(qubovert.__all__)\n\n    # see the utilities defined\n    help(qubovert.utils)\n    print(qubovert.utils.__all__)\n\n    # see the satisfiability library\n    help(qubovert.sat)\n    print(qubovert.sat.__all__)\n\n    # see all the probles defined\n    print(qubovert.problems.__all__)\n\n    # to see specifically the np problems:\n    help(qubovert.problems.np)\n    print(qubovert.problems.np.__all__)\n\n    # to see specifically the benchmarking problems:\n    help(qubovert.problems.benchmarking)\n    print(qubovert.problems.benchmarking.__all__)\n\n    # etc ...\n\n\nManaging QUBO, Ising, PUBO, HIsing, HOBO, and HOIO formulations\n---------------------------------------------------------------\n\nSee ``qubovert.__all__``.\n\n- QUBO: Quadratic Unconstrained Binary Optimization\n- Ising: quadratic unconstrained spin-1/2 Hamiltonian\n- PUBO: Polynomial Unconstrained Binary Optimization\n- HIsing: Higher order unconstrained spin-1/2 Hamiltonian\n- HOBO: Higher Order Binary Optimization\n- HOIO: Higher Order Ising Optimization\n\nSee the docstrings for ``qubovert.HOBO``, ``qubovert.HOIO``, ``qubovert.QUBO``, ``qubovert.Ising``, ``qubovert.PUBO``, and ``qubovert.HIsing``.\n\nSee the following HOBO examples (much of the same functionality can be used with HOIO problems).\n\n.. code:: python\n\n    from qubovert import HOBO\n\n    H = HOBO()\n    H.add_constraint_eq_zero({('a', 1): 2, (1, 2): -1, (): -1})\n    print(H)\n    # {('a', 1, 2): -4, (1, 2): 3, (): 1}\n    H -= 1\n    print(H)\n    # {('a', 1, 2): -4, (1, 2): 3}\n\n\n.. code:: python\n\n    from qubovert import binary_var\n\n    x0, x1, x2 = binary_var(\"x0\"), binary_var(\"x1\"), binary_var(\"x2\")\n    H = x0 + 2 * x1 * x2 - 3 + x2\n    print(H)\n    # {('x0',): 1, ('x1', 'x2'): 2, (): -3, ('x2',): 1}\n\n\nNote that for large problems, it is slower to use the `binary_var` functionality. For example, consider the following where creating `H0` is much faster than creating `H1`!\n\n.. code:: python\n\n    from qubovert import binary_var, HOBO\n\n    H0 = HOBO()\n    for i in range(1000):\n        H0[(i,)] += 1\n\n    xs = [binary_var(i) for i in range(1000)]\n    H1 = sum(xs)\n\n\nHere we show how to solve problems with the bruteforce solver, and how to convert problems to QUBO and Ising form. You can use any QUBO/Ising solver you'd like to solve!\n\n.. code:: python\n\n    H = HOBO()\n\n    # minimize -x_0 - x_1 - x_2\n    for i in (0, 1, 2):\n        H[(i,)] -= 1\n\n    # subject to constraints\n    H.add_constraint_eq_zero(  # enforce that x_0 x_1 - x_2 == 0\n        {(0, 1): 1, (2,): -1}\n    ).add_constraint_lt_zero(  # enforce that x_1 x_2 + x_0 < 1\n        {(1, 2): 1, (0,): 1, (): -1}\n    )\n    print(H)\n    # {(1,): -2, (2,): -1, (0, 1): 2, (1, 2): 2, (0, 1, 2): 2}\n\n    print(H.solve_bruteforce(all_solutions=True))\n    # [{0: 0, 1: 1, 2: 0}]\n\n    Q = H.to_qubo()\n    solutions = [H.convert_solution(sol)\n                 for sol in Q.solve_bruteforce(all_solutions=True)]\n    print(solutions)\n    # [{0: 0, 1: 1, 2: 0}]  # matches the HOBO solution!\n\n    L = H.to_ising()\n    solutions = [H.convert_solution(sol)\n                 for sol in L.solve_bruteforce(all_solutions=True)]\n    print(solutions)\n    # [{0: 0, 1: 1, 2: 0}]  # matches the HOBO solution!\n\n\nHere we show how to add various boolean constraints to models.\n\n.. code:: python\n\n    H = HOBO()\n    # make it favorable to AND variables a and b, and variables b and c\n    H.add_constraint_AND('a', 'b').add_constraint_AND('b', 'c')\n\n    # make it favorable to OR variables b and c\n    H.add_constraint_OR('b', 'c')\n\n    # make it favorable to (a AND b) OR (c AND d) OR e\n    H.add_constraint_OR(['a', 'b'], ['c', 'd'], 'e')\n\n    # enforce that 'b' = NOR('a', 'c', 'd')\n    H.add_constraint_eq_NOR('b', 'a', 'c', 'd')\n\n    print(H)\n    # {(): 5, ('c',): -2, ('c', 'a', 'b', 'd'): 1, ('a', 'e', 'b'): 1,\n    #  ('c', 'e', 'd'): 1, ('e',): -1, ('a',): -1, ('c', 'a'): 1,\n    #  ('a', 'd'): 1, ('c', 'b'): 2, ('d',): -1, ('b', 'd'): 2}\n    Q = H.to_qubo()\n    print(Q)\n    # {(): 5, (2,): -2, (5,): 12, (0, 1): 4, (0, 5): -8, (1, 5): -8,\n    #  (6,): 12, (2, 3): 4, (2, 6): -8, (3, 6): -8, (5, 6): 1, (4, 5): 1,\n    #  (4, 6): 1, (4,): -1, (0,): -1, (0, 2): 1, (0, 3): 1, (1, 2): 2,\n    #  (3,): -1, (1, 3): 2}\n    obj_value, sol = qubo_solver(Q)\n    print(sol)\n    # {0: 0, 1: 0, 2: 1, 3: 0, 4: 1, 5: 0, 6: 0}\n    solution = H.convert_solution(sol)\n    print(solution)\n    # {'a': 0, 'b': 0, 'c': 1, 'd': 0, 'e': 1}\n\n\nSee the following PUBO example.\n\n.. code:: python\n\n    from qubovert import PUBO\n    from any_module import qubo_solver\n    # or you can use my bruteforce solver...\n    # from qubovert.utils import solve_qubo_bruteforce as qubo_solver\n\n    pubo = PUBO()\n    pubo[('a', 'b', 'c', 'd')] -= 3\n    pubo[('a', 'b', 'c')] += 1\n    pubo[('c', 'd')] -= 2\n    pubo[('a',)] += 1\n    pubo -= 3  # equivalent to pubo[()] -= 3\n    pubo **= 4\n    pubo *= 2\n\n    Q = pubo.to_qubo()\n    obj, sol = qubo_solver(Q)\n    solution = pubo.convert_solution(sol)\n    print((obj, solution))\n    # (2, {'a': 1, 'b': 1, 'c': 1, 'd': 0})\n\n\nSymbols can also be used, for example:\n\n.. code:: python\n\n    from qubovert import HOIO\n    from sympy import Symbol\n\n    a, b = Symbol('a'), Symbol('b')\n\n    # enforce that z_0 + z_1 == 0 with penalty a\n    H = HOIO().add_constraint_eq_zero({(0,): 1, (1,): 1}, lam=a)\n    print(H)\n    # {(): 2*a, (0, 1): 2*a}\n    H[(0, 1)] += b\n    print(H)\n    # {(): 2*a, (0, 1): 2*a + b}\n    H_subs = H.subs({a: 2})\n    print(H_subs)\n    # {(): 4, (0, 1): 4 + b}\n\n    H_subs = H.subs({a: 2, b: 3})\n    print(H_subs)\n    # {(): 4, (0, 1): 7}\n\nPlease note that ``H.mapping`` is not necessarily equal to ``H.subs(...).mapping``. Thus, when using the ``HOBO.convert_solution`` function, make sure that you use the correct ``HOBO`` instance!\n\nThe convension used is that ``()`` elements of every dictionary corresponds to offsets. Note that some QUBO solvers accept QUBOs where each key is a two element tuple (since for a QUBO ``{(0, 0): 1}`` is the same as ``{(0,): 1}``). To get this standard form from our ``QUBOMatrix`` object, just access the property ``Q``. Similar for the ``IsingMatrix``. For example:\n\n.. code:: python\n\n    from qubovert.utils import QUBOMatrix\n    Q = QUBOMatrix()\n    Q += 3\n    Q[(0,)] -= 1\n    Q[(0, 1)] += 2\n    Q[(1, 1)] -= 3\n    print(Q)\n    # {(): 3, (0,): -1, (0, 1): 2, (1,): -3}\n    print(Q.Q)\n    # {(0, 0): -1, (0, 1): 2, (1, 1): -3}\n    print(Q.offset)\n    # 3\n\n.. code:: python\n\n    from qubovert.utils import IsingMatrix\n    L = IsingMatrix()\n    L += 3\n    L[(0, 1, 1)] -= 1\n    L[(0, 1)] += 2\n    L[(1, 1)] -= 3\n    print(L)\n    # {(0,): -1, (0, 1): 2}\n    print(L.h)\n    # {0: -1}\n    print(L.J)\n    # {(0, 1): 2}\n    print(L.offset)\n    # 0\n\n\nCommon binary optimization utilities (the ``utils`` library)\n------------------------------------------------------------\n\nSee ``qubovert.utils.__all__``.\n\nWe implement various utility functions, including\n\n- ``solve_pubo_bruteforce``,\n- ``solve_hising_bruteforce``,\n- ``pubo_value``,\n- ``hising_value``,\n- ``pubo_to_hising``,\n- ``hising_to_pubo``,\n- ``subgraph``,\n\nand more.\n\n\nConverting SAT problems (the ``sat`` library)\n---------------------------------------------\n\nSee ``qubovert.sat.__all__``.\n\nConsider the following 3-SAT example.\n\n.. code:: python\n\n    from qubovert.sat import AND, NOT, OR\n    from anywhere import qubo_solver\n\n    C = AND(OR(0, 1, 2), OR(NOT(0), 2, NOT(3)), OR(NOT(1), NOT(2), 3))\n\n    # C is 1 for a satisfying assignment, else 0\n    # So minimizing P will solve it.\n    P = -C\n\n    # P is a PUBO\n    Q = P.to_qubo()\n    solution = qubo_solver(Q)\n\n    print(solution)  # {0: 0, 1: 0, 2: 0, 3: 1, 4: 0, 5: 0, 6: 0}\n    converted_sol = P.convert_solution(solution)\n    print(converted_sol) # {0: 0, 3: 0, 1: 0, 2: 1}\n\n    print(C.value(converted_sol))  # will print 1 because it satisfies C\n\n\nConvert common problems to QUBO form (the ``problems`` library)\n---------------------------------------------------------------\n\nSee ``qubovert.problems.__all__``.\n\nSo far we have just implemented some of the formulations from [Lucas]_. The goal of QUBOVert is to become a large collection of problems mapped to QUBO and Ising forms in order to aid the recent increase in study of these problems due to quantum optimization algorithms. Use Python's ``help`` function! I have very descriptive doc strings on all the functions and classes.\n\n\nSee the following Set Cover example. All other problems can be used in a similar way.\n\n.. code:: python\n\n    from qubovert.problems import SetCover\n    from any_module import qubo_solver\n    # or you can use my bruteforce solver...\n    # from qubovert.utils import solve_qubo_bruteforce as qubo_solver\n\n    U = {\"a\", \"b\", \"c\", \"d\"}\n    V = [{\"a\", \"b\"}, {\"a\", \"c\"}, {\"c\", \"d\"}]\n\n    problem = SetCover(U, V)\n    Q = problem.to_qubo()\n\n    obj, sol = qubo_solver(Q)\n\n    solution = problem.convert_solution(sol)\n\n    print(solution)\n    # {0, 2}\n    print(problem.is_solution_valid(solution))\n    # will print True, since V[0] + V[2] covers all of U\n    print(obj == len(solution))\n    # will print True\n\nTo use the Ising formulation instead:\n\n.. code:: python\n\n    from qubovert.problems import SetCover\n    from any_module import ising_solver\n    # or you can use my bruteforce solver...\n    # from qubovert.utils import solve_ising_bruteforce as ising_solver\n\n    U = {\"a\", \"b\", \"c\", \"d\"}\n    V = [{\"a\", \"b\"}, {\"a\", \"c\"}, {\"c\", \"d\"}]\n\n    problem = SetCover(U, V)\n    L = problem.to_ising()\n\n    obj, sol = ising_solver(L)\n\n    solution = problem.convert_solution(sol)\n\n    print(solution)\n    # {0, 2}\n    print(problem.is_solution_valid(solution))\n    # will print True, since V[0] + V[2] covers all of U\n    print(obj == len(solution))\n    # will print True\n\n\nTo see problem specifics, run\n\n.. code:: python\n\n    help(qubovert.problems.SetCover)\n    help(qubovert.problems.VertexCover)\n    # etc\n\nI have very descriptive doc strings that should explain everything you need to know to use each problem class.\n\n\nReferences\n----------\n\n.. 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