A Comparative Study On Solving Optimization Problems With Exponentially Fewer Qubits

• URL: http://arxiv.org/abs/2210.11823v1
• Date: Fri, 21 Oct 2022 08:54:12 GMT
• Title: A Comparative Study On Solving Optimization Problems With Exponentially Fewer Qubits
• Authors: David Winderl, Nicola Franco, Jeanette Miriam Lorenz
• Abstract summary: We evaluate and improve an algorithm based on Variational Quantum Eigensolver (VQE) We highlight the numerical instabilities generated by encoding the problem into the variational ansatz. We propose a classical optimization procedure to find the ground-state of the ansatz in less iterations with a better objective.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Variational Quantum optimization algorithms, such as the Variational Quantum Eigensolver (VQE) or the Quantum Approximate Optimization Algorithm (QAOA), are among the most studied quantum algorithms. In our work, we evaluate and improve an algorithm based on VQE, which uses exponentially fewer qubits compared to the QAOA. We highlight the numerical instabilities generated by encoding the problem into the variational ansatz and propose a classical optimization procedure to find the ground-state of the ansatz in less iterations with a better or similar objective. Furthermore, we compare classical optimizers for this variational ansatz on quadratic unconstrained binary optimization and graph partitioning problems.

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