arXiv subjects
Publications and source records attributed to Alejandro Mata Ali.
In this paper we present a QUBO formulation for the Takuzu game (or Binairo), for the most recent LinkedIn game, Tango, and for its generalizations. We optimize the number of variables needed to solve the combinatorial problem, making it suitable to be solved by quantum devices with fewer resources.
In this paper we show that every combinatorial problem has an exact explicit equation that returns its solution. We present a method to obtain an equation that solves exactly any combinatorial problem, both inversion, constraint satisfaction and optimization, by obtaining its equivalent tensor network. This formulation only requires a basic knowledge of classical logical operators, at a first year level of any computer science degree. These equations are not necessarily computable in a reasonable time, nor do they allow to surpass the state of the art in computational complexity, but they allow to have a new perspective for the mathematical analysis of these problems. These equations computation can be approximated by different methods such as Matrix Product State compression. We also present the equations for numerous combinatorial problems. This work proves that, if there is a physical system capable of contracting in polynomial time the tensor networks presented, every NP-Hard problem can be solved in polynomial time.
In this paper we present a study of the applicability and feasibility of quantum-inspired algorithms and techniques in tensor networks for industrial environments and contexts, with a compilation of the available literature and an analysis of the use cases that may be affected by such methods. In addition, we explore the limitations of such techniques in order to determine their potential scalability.
We present a subproblemation scheme for heuristical solving of the JSP (Job Reassignment Problem). The cost function of the JSP is described via a QUBO hamiltonian to allow implementation in both gate-based and annealing quantum computers. For a job pool of $K$ jobs, $\mathcal{O}(K^2)$ binary variables -- qubits -- are needed to solve the full problem, for a runtime of $\mathcal{O}(2^{K^2})$. With the presented heuristics, the average variable number of each of the $D$ subproblems to solve is $\mathcal{O}(K^2/2D)$, and the expected total runtime $\mathcal{O}(D2^{K^2/2D})$, achieving an exponential speedup.
In usual restriction terms of the Quadratic Unconstrained Binary Optimization (QUBO) hamiltonians, a integer number of logical qubits R, called the Integer Restriction Coefficient (IRC), are forced to stay active. In this paper we gather the well-known methods of implementing these restrictions, as well as some novel methods that show to be more efficient in some frequently implemented cases. Moreover, it is mathematically allowed to ask for fractional values of $R$. For these Fractionary Restriction Coefficients (FRC) we show how they can reduce the number of qubits needed to implement the restriction hamiltonian even further. Lastly, we characterize the response of DWave's Advantage$\_$system4.1 Quantum Annealer (QA) when faced with the implementation of FRCs, and offer a summary guide of the presented methods and the situations each of them is to be used.