Condensed Matter Theory Seminar | June 27, 14:00
Symmetry-adapted quantum algorithms for Hamiltonian simulation of many-body systems
From ancient times, symmetries have played an important role in our culture and even in our perception of beauty. In modern physics, symmetries are not only a guiding principle to build physical theories, but they serve as a fundamental tool to predict new particles and to unify the fundamental forces in nature [1,2]. In the context of quantum simulation, symmetries can be exploited to simplify a problem and to make the simulation more efficient [3,4]. In previous works, however, human efforts are used to exploit symmetries.
In this talk, I will discuss how to encode the symmetries in a quantum routine that effectively decompose the system into symmetric subspaces and allows their coherent evolution. At the end of the quantum algorithm, a measurement probabilistically projects the system into a desired subspace. We show applications of our approach to quantum simulation of condensed matter systems and electronic structure in chemistry. I will discuss the application of the algorithm to simulation of the Hofstadter model.
[1] A. J. Buras, J. Ellis, M. K. Gaillard, and D. V. Nanopoulos, Aspects of the grand unification of strong, weak and electromagnetic interactions, Nucl. Phys. B 135, 66 (1978).
[2] S. Weinberg, Conceptual foundations of the unified theory of weak and electromagnetic interactions, Rev. Mod. Phys. 52, 515 (1980).
[3] S. M. Goodlett, N. L. Kitzmiller, J. M. Turney, and H. F. Schaefer, Molsym: A python package for handling symmetry in molecular quantum chemistry, J. Chem. Phys. 161, 024107 (2024).
[4] P. Kratzer and J. Neugebauer, The basics of electronic structure theory for periodic systems, Front. Chem. (Lausanne, Switz.) 7, 106 (2019).
[5] V. M. Bastidas, N. Fitzpatrick, K. J. Joven, Z. M. Rossi , S. Islam, T. Van Voorhis , I. L. Chuang, and Y. Liu, Phys. Rev. A 111, 052433 (2025).
NTT Basic Research Laboratories (Japan)
0.03
Contact: Matteo Rizzi