arXiv subjects

Beatriz García Markaida

Publications and source records attributed to Beatriz García Markaida.

4 recordsLinked to original sources

arXiv2026

Task Scheduling Optimization with Direct Constraints from a Tensor Network Perspective

This work presents a novel method for task optimization in industrial plants using quantum-inspired tensor network technology. This method obtains the best possible combination of tasks on a set of machines with directed constraints while minimizing the total execution cost. With this method, an exact and explicit solution of the problem is provided. This algorithm constructs a tensor network representation of the tensor which provides the solution of the problem. This method is improved in order to reduce the computational complexity of the solution computation, using problem preprocessing, new techniques of condensation of logical constraints, optimization of the value determination technique with previously calculated results, reuse of intermediate computations, and iterative relations for constraints. Three algorithms for computation are presented: the main algorithm, the iterative algorithm which adds only the minimal amount of necessary constraints, and the genetic algorithm which combines the iterative algorithm with basic genetic algorithms. Finally, a simple version of both algorithms was implemented, and their performance was tested, all publicly available.

quant-ph↗

arXiv2023

QUBO Resolution of the Job Reassignment Problem

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.

quant-ph↗

arXiv2023

Quantum hobbit routing: Annealer implementation of generalized Travelling Salesperson Problem

In this paper, we present an implementation of a Job Selection Problem (JSP) -- a generalization of the well-known Travelling Salesperson Problem (TSP) -- of $N=9$ jobs on its Quadratic Unconstrained Binary Optimization (QUBO) form, using $\mathcal{O}(N)$ qubits on DWave's Advantage$\_$system4.1 quantum annealing device. The best known quantum algorithm for TSP to date uses $\mathcal{O}(N^2)$ qubits. A solution is found using the quantum method. However, since hardware is not yet able to compensate the increase in search-space size, no present overall advantage is achieved when comparing the quantum results with either exhaustive or equiprobably sampled classical solutions of the problem.

quant-ph↗

arXiv2023

Qubit Number Optimization for Restriction Terms of QUBO Hamiltonians

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.

quant-ph↗