Quantum speedup for combinatorial optimization with flat energy landscapes

• URL: http://arxiv.org/abs/2306.13123v2
• Date: Fri, 7 Jul 2023 17:27:02 GMT
• Title: Quantum speedup for combinatorial optimization with flat energy landscapes
• Authors: Madelyn Cain, Sambuddha Chattopadhyay, Jin-Guo Liu, Rhine Samajdar, Hannes Pichler, Mikhail D. Lukin
• Abstract summary: We develop a theoretical framework to analyze the relative performance of the optimized quantum adiabatic algorithm and a broad class of classical Markov chain Monte Carlo algorithms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Designing quantum algorithms with a speedup over their classical analogs is a central challenge in quantum information science. Motivated by recent experimental observations of a superlinear quantum speedup in solving the Maximum Independent Set problem on certain unit-disk graph instances [Ebadi et al., Science 376, 6598 (2022)], we develop a theoretical framework to analyze the relative performance of the optimized quantum adiabatic algorithm and a broad class of classical Markov chain Monte Carlo algorithms. We outline conditions for the quantum adiabatic algorithm to achieve a quadratic speedup on hard problem instances featuring flat low-energy landscapes and provide example instances with either a quantum speedup or slowdown. We then introduce an additional local Hamiltonian with no sign problem to the optimized adiabatic algorithm to achieve a quadratic speedup over a wide class of classical simulated annealing, parallel tempering, and quantum Monte Carlo algorithms in solving these hard problem instances. Finally, we use this framework to analyze the experimental observations.

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