Variational Quantum Multi-Objective Optimization
- URL: http://arxiv.org/abs/2312.14151v2
- Date: Thu, 8 Feb 2024 16:10:29 GMT
- Title: Variational Quantum Multi-Objective Optimization
- Authors: Linus Ekstrom and Hao Wang and Sebastian Schmitt
- Abstract summary: We present a variational quantum multiple-objective optimization (QMOO) algorithm.
At the core of the algorithm is a variational quantum circuit (VQC) tuned to produce a quantum state.
We show the effectiveness of the proposed algorithm on several benchmark problems with up to five objectives.
- Score: 6.04831065589027
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Solving combinatorial optimization problems using variational quantum
algorithms to be executed on near-term quantum devices has gained a lot of
attraction in recent years. Currently, most works have focused on
single-objective problems. In contrast, many real-world problems need to
consider multiple conflicting objectives simultaneously, which is not well
studied using variation quantum algorithms. In multi-objective optimization,
one seeks the optimal trade-offs among conflicting objectives - the well-known
Pareto set/front. We present a variational quantum multiple-objective
optimization (QMOO) algorithm, which allows us to solve multi-objective
optimization problems using NISQ computers. At the core of the algorithm is a
variational quantum circuit (VQC) tuned to produce a quantum state which is a
superposition of Pareto-optimal solutions, solving the original multi-objective
optimization problem. The VQC achieves this by incorporating all cost
Hamiltonians representing the classical objective functions. We retrieve a set
of solutions from the quantum state prepared by the VQC, and utilize the
widely-applied hypervolume indicator to determine the quality of it as
approximation to the Pareto-front. The variational parameters of the VQC are
tuning by maximizing the hypervolume indicator. As many realistic problems are
integer optimization problems we formulate the whole scheme for qudit quantum
systems. We show the effectiveness of the proposed algorithm on several
benchmark problems with up to five objectives.
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