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Primitive quantum gates for an SU(3) discrete subgroup: Σ(36×3)

Published:2024-08-23 Issue:3 Volume:110 Page:
ISSN:2470-0010
Container-title:Physical Review D
language:en
Short-container-title:Phys. Rev. D

Author:

Gustafson Erik J.¹²³⁴⁵^ORCID,Ji Yao⁶^ORCID,Lamm Henry¹²^ORCID,Murairi Edison M.⁷^ORCID,Perez Sebastian Osorio²,Zhu Shuchen⁸^ORCID

Affiliation:

1. Superconducting and Quantum Materials System Center (SQMS)

2. Fermi National Accelerator Laboratory

3. Quantum Artificial Intelligence Laboratory (QuAIL)

4. NASA Ames Research Center

5. USRA Research Institute for Advanced Computer Science (RIACS)

6. Technische Universität München

7. The George Washington University

8. Georgetown University

Abstract

We construct the primitive gate set for the digital quantum simulation of the 108-element Σ(36×3) group. This is the first time a non-Abelian crystal-like subgroup of SU(3) has been constructed for quantum simulation. The gauge link registers and necessary primitives—the inversion gate, the group multiplication gate, the trace gate, and the Σ(36×3) Fourier transform—are presented for both an eight-qubit encoding and a heterogeneous three-qutrit plus two-qubit register. For the latter, a specialized compiler was developed for decomposing arbitrary unitaries onto this architecture.

Published by the American Physical Society

2024

Funder

U.S. Department of Energy

Office of Science

National Aeronautics and Space Administration

Deutsche Forschungsgemeinschaft

Nuclear Physics

National Science Foundation

Institute for Pure and Applied Mathematics, University of California, Los Angeles

Fermilab

National Quantum Information Science Research Centers