A quantum inspired method and apparatus for integer optimization problems

Integer optimization problems are ubiquitous in various fields. From computer science to operation research or engineering, many problems can be formulated or casted as an instance of an integer optimization problem. An integer optimization problem involves finding the optimal solution of a given objective function subject to a set of constraints. The objective function is a function that we want to maximize or minimize, and the constraints are the conditions that the solution must satisfy. The solution to an integer optimization problem is a set of integer values that satisfy the constraints and optimize the objective function.Examples of applications of integer optimization problems include: in computer science, the knapsack problem, the traveling salesman problem, or the job scheduling problem; in operation research, the transportation problem, the assignment problem, or the network flow problem; in engineering, the optimal design of a system, the optimal allocation of resourcer, or the optimal control of a system.The present disclosure relates to methods, devices and systems for quantum-inspired integer optimization, which do no showcase the limitations of known quantum inspired algorithms listed above.According to this disclosure, a qudit is defined as a quantum system with a finite number of levels, where the levels are binary or greater. Examples of these include, but are not limited to, qubits or qutrits. The methods disclosed herein are based on the use of qudits to represent the integer variables of an integer optimization problem. In some preferred embodiments, such qudits are represented using spherical coordinates, which allow for a natural respresetnation of the integer variables. Other representations of the quedits, in accordance with some other embodiments, include, but are not limited to, the Cartesian representation, the Bloch sphere representation, the Wigner representation, or the Fock representation.