Observation of the Symmetry-Protected Signature of 3-body Interactions

• DOI: 10.48550/arxiv.2408.10475
• Publication Date: 2024-01-01
• Authors: Zhukas, Liudmila A.; Wang, Qingfeng; Katz, Or; Monroe, Christopher; Marvian, Iman
• Keywords: High Energy Physics - Theory; Nuclear Theory (nucl-th); Quantum Physics; Condensed Matter - Strongly Correlated Electrons; Nuclear Theory; Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); FOS: Physical sciences; Mathematical Physics (math-ph); Quantum Physics (quant-ph); Mathematical Physics

Identifying and characterizing multi-body interactions in quantum processes remains a significant challenge. This is partly because 2-body interactions can produce an arbitrary time evolution, a fundamental fact often called the universality of 2-local gates in the context of quantum computing. However, when an unknown Hamiltonian respects a U(1) symmetry such as charge or particle number conservation, N-body interactions exhibit a distinct symmetry-protected signature known as the N-body phase, which fewer-body interactions cannot mimic. We develop and demonstrate an efficient technique for the detection of 3-body interactions despite the presence of unknown 2-body interactions. This technique, which takes advantage of GHZ states for phase estimation, requires probing the unitary evolution and measuring its determinant in a small subspace that scales linearly with the system size, making it an efficient approach.<br/>Comments welcome! 11 pages + 4 pages of Supplementary Material<br/>