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Unconstrained Binary Models of the Travelling Salesman Problem Variants for Quantum Optimization
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TLDR
In this paper, the authors provide a detailed analysis of the Travelling Salesman Problem with Time Windows (TSPTW) in the context of solving it on a quantum computer and introduce quadratic unconstrained binary optimization and higher order binary optimization formulations of this problem.Abstract:
Quantum computing is offering a novel perspective for solving combinatorial optimization problems. To fully explore the possibilities offered by quantum computers, the problems need to be formulated as unconstrained binary models, taking into account limitation and advantages of quantum devices. In this work, we provide a detailed analysis of the Travelling Salesman Problem with Time Windows (TSPTW) in the context of solving it on a quantum computer. We introduce quadratic unconstrained binary optimization and higher order binary optimization formulations of this problem. We demonstrate the advantages of edge-based and node-based formulations of the TSPTW problem. Additionally, we investigate the experimental realization of the presented methods on a quantum annealing device. The provided results pave the path for utilizing quantum computer for a variety of real-world task which can be cast in the form of Travelling Salesman Problem with Time Windows problem.read more
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Error mitigation for variational quantum algorithms through mid-circuit measurements
TL;DR: In this paper , a postselection scheme for one-hot, binary, gray, and domain-wall encoding was proposed. But it is not suitable for the currently available hardware, where measuring and resetting are possible, but classical conditional operators are not.
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Quadratic and higher-order unconstrained binary optimization of railway rescheduling for quantum computing
TL;DR: In this article , the authors introduce QUBO and HOBO representations for rescheduling problems of railway traffic management and demonstrate the proof of concept implementation on the D-Wave Quantum Processing Unit and D-wave hybrid solver.
Posted Content
Error mitigation for variational quantum algorithms through mid-circuit measurements
Ludmila A. S. Botelho,Adam Glos,Akash Kundu,Jarosław Adam Miszczak,Özlem Salehi,Zoltán Zimborás +5 more
TL;DR: In this article, a post-selection scheme for one-hot, binary, gray, and domain-wall encodings is proposed, which works by compressing the full Hilbert space to a smaller subspace, allowing projecting to the desired subspace without using any ancilla qubits.
Journal ArticleDOI
An Integer Linear Programming Model for Partially Ordered Sets
TL;DR: Robert Dilworth’s Decomposition theorem is formulated by ILPM and proves its correctness using the paradigm of strong duality in linear programming.
References
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Optimization by Simulated Annealing
TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Journal ArticleDOI
A variational eigenvalue solver on a photonic quantum processor
Alberto Peruzzo,Jarrod R. McClean,Peter Shadbolt,Man-Hong Yung,Xiao-Qi Zhou,Peter J. Love,Alán Aspuru-Guzik,Jeremy L. O'Brien +7 more
TL;DR: The proposed approach drastically reduces the coherence time requirements and combines this method with a new approach to state preparation based on ansätze and classical optimization, enhancing the potential of quantum resources available today and in the near future.
Journal ArticleDOI
Quantum Computing in the NISQ era and beyond
TL;DR: Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future, and the 100-qubit quantum computer will not change the world right away - but it should be regarded as a significant step toward the more powerful quantum technologies of the future.
Posted Content
A Quantum Approximate Optimization Algorithm
TL;DR: A quantum algorithm that produces approximate solutions for combinatorial optimization problems that depends on a positive integer p and the quality of the approximation improves as p is increased, and is studied as applied to MaxCut on regular graphs.
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The Traveling Salesman Problem: A Computational Study
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