A Universal Quantum Algorithm for Weighted Maximum Cut and Ising Problems

• URL: http://arxiv.org/abs/2306.06539v2
• Date: Thu, 15 Jun 2023 11:20:46 GMT
• Title: A Universal Quantum Algorithm for Weighted Maximum Cut and Ising Problems
• Authors: Natacha Kuete Meli, Florian Mannel, Jan Lellmann
• Abstract summary: We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted maximum cut or the Ising Hamiltonian. Measuring the expectation of this operator on a variational quantum state yields the variational energy of the quantum system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted maximum cut or the Ising Hamiltonian. Measuring the expectation of this operator on a variational quantum state yields the variational energy of the quantum system. The system is enforced to evolve towards the ground state of the problem Hamiltonian by optimizing a set of angles using normalized gradient descent. Experimentally, our algorithm outperforms the state-of-the-art quantum approximate optimization algorithm on random fully connected graphs and challenges D-Wave quantum annealers by producing good approximate solutions. Source code and data files are publicly available.

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