PIRSA:24020098 Scientific Series Quantum Information

DOI10.48660/24020098

Series: Perimeter Institute Quantum Discussions

Zhou, L. (2024). Quantum Advantages in Energy Minimization - VIRTUAL ONLY. Perimeter Institute. https://pirsa.org/24020098

Zhou, Leo. Quantum Advantages in Energy Minimization - VIRTUAL ONLY. Perimeter Institute, Feb. 28, 2024, https://pirsa.org/24020098 

@misc{ pirsa_PIRSA:24020098,
  doi = {10.48660/24020098},
  url = {https://pirsa.org/24020098},
  author = {Zhou, Leo},
  keywords = {Quantum Information},
  language = {en},
  title = {Quantum Advantages in Energy Minimization - VIRTUAL ONLY},
  publisher = {Perimeter Institute},
  year = {2024},
  month = {feb},
  note = {PIRSA:24020098 see, \url{https://pirsa.org}}
}

Abstract

Minimizing the energy of a many-body system is a fundamental problem in many fields. Although we hope a quantum computer can help us solve this problem better than classical computers, we have a very limited understanding of where a quantum advantage may be found. In this talk, I will present some recent theoretical advances that shed light on quantum advantages in this domain. First, I describe rigorous analyses of the Quantum Approximate Optimization Algorithm applied to minimizing energies of classical spin glasses. For certain families of spin glasses, we find the QAOA has a quantum advantage over the best known classical algorithms. Second, we study the problem of finding a local minimum of the energy of quantum systems. While local minima are much easier to find than ground states, we show that finding a local minimum under thermal perturbations is computationally hard for classical computers, but easy for quantum computers.

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