Experimental observation of symmetry-protected signatures of N-body interactions

Characterizing higher-order interactions in quantum processes with unknown Hamiltonians presents a significant challenge. This challenge arises, in part, because two-body interactions can lead to an arbitrary evolution, resulting in the so-called universality of two-qubit gates for quantum computing. However, recent research has demonstrated that when the unknown Hamiltonian follows a U(1) symmetry, like charge or number conservation, N-body interactions display a distinct and symmetry-protected feature called the N-body phase. This signature cannot be replicated by interactions involving fewer bodies.

In this study, our focus is on exploring the time evolution of quantum systems under U(1)-invariant Hamiltonians. Specifically, we have developed and experimentally demonstrated an efficient technique for detecting N-body interactions, even in the presence of unknown lower-body interactions. This technique involves probing unitary evolution and measuring its determinant within a small subspace that scales linearly with the system's size, making it a practical and efficient approach.\\

This work is supported by the NSF STAQ Program, the DOE QSA Program, the AFOSR MURI on Quantum Dissipation Engineering, and the AFOSR MURI on Certification of Quantum Computers.