1. Variational Amplitude Amplification for Solving QUBO Problems.
- Author
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Koch, Daniel, Cutugno, Massimiliano, Patel, Saahil, Wessing, Laura, and Alsing, Paul M.
- Subjects
COST functions ,PROBLEM solving ,QUANTUM computing ,QUBITS ,COMBINATORIAL optimization ,HOPFIELD networks - Abstract
We investigate the use of amplitude amplification on the gate-based model of quantum computing as a means for solving combinatorial optimization problems. This study focuses primarily on quadratic unconstrained binary optimization (QUBO) problems, which are well-suited for qubit superposition states. Specifically, we demonstrate circuit designs which encode QUBOs as 'cost oracle' operations U C , which distribute phases across the basis states proportional to a cost function. We then show that when U C is combined with the standard Grover diffusion operator U s , one can achieve high probabilities of measurement for states corresponding to optimal and near optimal solutions while still only requiring O( π 4 2 N / M ) iterations. In order to achieve these probabilities, a single scalar parameter p s is required, which we show can be found through a variational quantum–classical hybrid approach and can be used for heuristic solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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