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A benchmark for quantum optimization: the traveling salesman

Richard H. Warren

We present compelling reasons for symmetric traveling salesman problems (TSPs) to be the benchmark for quantum computing of combinatorial optimization problems for all types of quantum hardware. There are seven reasons for endorsing these TSPs to be the benchmark and no shortcomings.

Quantum Information and ComputationApr 27, 20218 citations

Some combinatorial problems in quantum computation

Shanzhen Gao

Journal of Guizhou Education InstituteJan 1, 20030 citations

Explicit Solution Equation for Every Combinatorial Problem via Tensor Networks: MeLoCoToN

Alejandro Mata Ali

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 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.

arXiv:2502.05981Feb 9, 20250 citations

Some Combinatorial Problems in Quantum Computation

Xu Xu

河南广播电视大学学报Jan 1, 20050 citations

Some Results from the Combinatorial Approach to Quantum Logic

Richard J. Greechie

Springer eBooksJan 1, 197614 citations

Multiobjective Optimization in a Quantum Adiabatic Computer

Benjamı́n Barán, Marcos Villagra

In this work we propose what we consider the first quantum algorithm for multiobjective combinatorial optimization, at least to the best of our knowledge. The proposed algorithm is based on the adiabatic algorithm of Farhi et al. and it is constructed by mapping a multiobjective combinatorial optimization problem into a Hamiltonian using a convex combination among objectives. We present mathematical properties of the eigenspectrum of the associated Hamiltonian and prove that the quantum adiabatic algorithm can find Pareto-optimal solutions provided certain convex combinations of objectives are used and the underlying multiobjective problem meets certain restrictions.In this work we propose what we consider the first quantum algorithm for multiobjective combinatorial optimization, at least to the best of our knowledge. The proposed algorithm is based on the adiabatic algorithm of Farhi et al. and it is constructed by mapping a multiobjective combinatorial optimization problem into a Hamiltonian using a convex combination among objectives. We present mathematical properties of the eigenspectrum of the associated Hamiltonian and prove that the quantum adiabatic algorithm can find Pareto-optimal solutions provided certain convex combinations of objectives are used and the underlying multiobjective problem meets certain restrictions.

arXiv:1605.03152Electronic Notes in Theoretical Computer ScienceDec 1, 20169 citations

Seven combinatorial equations in quantum computation

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Seven combinatorial equations in quantum computation

Abstract

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