Condensed Matter Theory Seminar | June 27, 14:00

Symmetry-adapted quantum algorithms for Hamiltonian simulation of many-body systems

Victor M. Bastidas

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)
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Contact: Matteo Rizzi