Comparative Benchmark of a Quantum Algorithm for the Bin Packing Problem

The Bin Packing Problem (BPP) stands out as a paradigmatic combinatorial optimization problem in logistics. Quantum and hybrid quantum-classical algorithms are expected to show an advantage over their classical counterparts in obtaining approximate solutions for optimization problems. We have recently proposed a hybrid approach to the one dimensional BPP in which a quantum annealing subroutine is employed to sample feasible solutions for single containers. From this reduced search space, a classical optimization subroutine can find the solution to the problem. With the aim of going a step further in the evaluation of our subroutine, in this paper we compare the performance of our procedure with other classical approaches. Concretely we test a random sampling and a random-walk-based heuristic. Employing a benchmark comprising 18 instances, we show that the quantum approach lacks the stagnation behaviour that slows down the classical algorithms. Based on this, we conclude that the quantum strategy can be employed jointly with the random walk to obtain a full sample of feasible solutions in fewer iterations. This work improves our intuition about the benefits of employing the scarce quantum resources to improve the results of a diminishingly efficient classical strategy.Comment: 8 pages, 2 figures, submitted to the IEEE Symposium Series On Computational Intelligence 202

Digital-analog quantum computation with arbitrary two-body Hamiltonians

Digital-analog quantum computing is a computational paradigm which employs an analog Hamiltonian resource together with single-qubit gates to reach universality. Here, we design a new scheme which employs an arbitrary two-body source Hamiltonian, extending the experimental applicability of this computational paradigm to most quantum platforms. We show that the simulation of an arbitrary two-body target Hamiltonian of n qubits requires O(n2) analog blocks with guaranteed positive times, providing a polynomial advantage compared to the previous scheme. Additionally, we propose a classical strategy which combines a Bayesian optimization with a gradient descent method, improving the performance by ∼55% for small systems measured in the Frobenius norm.The Spanish Grants No. PID2019-104002GB-C21, No. PID2019-104002GB-C22, No. PID2022-136228NB-C21, and No. PID2022-136228NB-C22 funded by Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación MCIN/AEI/10.13039/501100011033, FEDER “A Way of Making Europe,” Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía, European Regional Development Fund (ERDF) under Project No. US-1380840, Grant Groups FQM-160 and FQM-177, and the project PAIDI 2020 with Reference No. P20_01247 and No. P20_00617 funded by the Consejería de Economía, Conocimiento, Empresas y Universidad, Junta de Andalucía (Spain).ERDF/MINECO Project No. UNHU-15CE-2848EU FET Open project EPIQUS (899368)HORIZON-CL4-2022-QUANTUM01-SGA Project No. 101113946 OpenSuperQPlus100 of the EU Flagship on Quantum TechnologiesSpanish Ramón y Cajal Grant No. RYC-2020-030503-I, Grant No. PID2021-125823NA-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”“ERDF Invest in your Future,” Basque Government, through Grant No. IT1470-22IKUR Strategy under the collaboration agreement between Ikerbasque Foundation and BCAM on behalf of the Department of Education of the Basque GovernmentUPV/EHU and TECNALIA 2021 PIF contract callMinistry for Digital Transformation and of Civil Service of the Spanish Government through the QUANTUM ENIA project call–Quantum Spain projectThe European Union through the Recovery, Transformation and Resilience Plan–NextGenerationEU within the framework of the “Digital Spain 2026 Agenda

Implementable Hybrid Quantum Ant Colony Optimization Algorithm

We propose a new hybrid quantum algorithm based on the classical Ant Colony Optimization algorithm to produce approximate solutions for NP-hard problems, in particular optimization problems. First, we discuss some previously proposed Quantum Ant Colony Optimization algorithms, and based on them, we develop an improved algorithm that can be truly implemented on near-term quantum computers. Our iterative algorithm codifies only the information about the pheromones and the exploration parameter in the quantum state, while subrogating the calculation of the numerical result to a classical computer. A new guided exploration strategy is used in order to take advantage of the quantum computation power and generate new possible solutions as a superposition of states. This approach is specially useful to solve constrained optimization problems, where we can implement efficiently the exploration of new paths without having to check the correspondence of a path to a solution before the measurement of the state. As an example of a NP-hard problem, we choose to solve the Quadratic Assignment Problem. The benchmarks made by simulating the noiseless quantum circuit and the experiments made on IBM quantum computers show the validity of the algorithm.Comment: 19 pages, 6 figures, submitted to Quantum Machine Intelligenc

Hybrid Quantum-Classical Heuristic for the Bin Packing Problem

Optimization problems is one of the most challenging applications of quantum computers, as well as one of the most relevants. As a consequence, it has attracted huge efforts to obtain a speedup over classical algorithms using quantum resources. Up to now, many problems of different nature have been addressed through the perspective of this revolutionary computation paradigm, but there are still many open questions. In this work, a hybrid classical-quantum approach is presented for dealing with the one-dimensional Bin Packing Problem (1dBPP). The algorithm comprises two modules, each one designed for being executed in different computational ecosystems. First, a quantum subroutine seeks a set of feasible bin configurations of the problem at hand. Secondly, a classical computation subroutine builds complete solutions to the problem from the subsets given by the quantum subroutine. Being a hybrid solver, we have called our method H-BPP. To test our algorithm, we have built 18 different 1dBPP instances as a benchmarking set, in which we analyse the fitness, the number of solutions and the performance of the QC subroutine. Based on these figures of merit we verify that H-BPP is a valid technique to address the 1dBPP.Comment: 10 pages, 2 figures, 3 tables, submitted to the Genetic and Evolutionary Computation Conference 2022 (GECCO 2022