Demonstration of three- and four-body interactions between trapped-ion spins

Quantum processors use the native interactions between effective spins to simulate Hamiltonians or execute quantum gates. In most processors, the native interactions are pairwise, limiting the efficiency of controlling entanglement between many qubits. The capability of manipulating entanglement generated by higher-order interactions is a key challenge for the simulation of many Hamiltonian models appearing in various fields, including high-energy and nuclear physics, as well as quantum chemistry and error correction applications. Here we experimentally demonstrate control over a class of native interactions between trapped-ion qubits, extending conventional pairwise interactions to a higher order. By exploiting state-dependent squeezing operations, we realize and characterize high-fidelity gates and spin Hamiltonians comprising three- and four-body spin interactions. Our results demonstrate the potential of high-order spin interactions as a toolbox for quantum information applications.