Discrete quadratic model QUBO solution landscapes

• URL: http://arxiv.org/abs/2305.00568v3
• Date: Thu, 15 Feb 2024 03:10:31 GMT
• Title: Discrete quadratic model QUBO solution landscapes
• Authors: Tristan Zaborniak, Ulrike Stege
• Abstract summary: We investigate the effects of choice of encoding and penalty strength on the structure of QUBO DQM solution landscapes. This research focuses specifically on one-hot and domain-wall encodings.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many computational problems involve optimization over discrete variables with quadratic interactions. Known as discrete quadratic models (DQMs), these problems in general are NP-hard. Accordingly, there is increasing interest in encoding DQMs as quadratic unconstrained binary optimization (QUBO) models to allow their solution by quantum and quantum-inspired hardware with architectures and solution methods designed specifically for such problem types. However, converting DQMs to QUBO models often introduces invalid solutions to the solution space of the QUBO models. These solutions must be penalized by introducing appropriate constraints to the QUBO objective function that are weighted by a tunable penalty parameter to ensure that the global optimum is valid. However, selecting the strength of this parameter is non-trivial, given its influence on solution landscape structure. Here, we investigate the effects of choice of encoding and penalty strength on the structure of QUBO DQM solution landscapes and their optimization, focusing specifically on one-hot and domain-wall encodings.

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