Quantum computers and simulators rely on the controllable generation of quantum entanglement between their elementary constituents, such as qubits or effective spins. Such entanglement allows the efficient exploration of a large state space, which can speed up the computation of certain problems or the simulation of the dynamics or phases of model physical systems. The generation of entanglement relies on the native interactions between subsets of spins, which in most quantum platforms is pairwise. However, higher-order interactions are often featured in Hamiltonian models in nuclear and high-energy physics and spin systems, as well as quantum circuits and algorithms in quantum chemistry, error correction codes and other applications. Sequential or parallel application of universal one- and two-body gate sets can, in principle, generate any unitary mapping in Hilbert space that is equivalent to evolution under high-order interactions. Yet, such constructions carry a large overhead in the number of Trotterization steps or entangling operations, thereby limiting the practical performance of such an approach in the presence of decoherence and noise. We have recently demonstrated a new class of native higher-order interactions between qubits in a trapped-ion quantum processor. This class relies on a state-dependent squeezing optical drive, which is a simple extension over the conventional state-dependent displacement used for Mølmer–Sørensen (MS) pairwise gates.

Three Body Interaction Gate, realizing the Fully entangling quantum operation U=exp(-iπσx(1)σx(2)σx(3)/4) via native sequences of spin-dependent squeezing and displacement. Top: measured limited tomography of the population in the X basis for 8 different input states showing good match to theory (frame). Bottom: Parity fringe measurement which characterize the coherence of the two different 3-qubit GHZ states formed by the gate. See Nature Physics 19, 1452-1458 (2023) for details.

Phase-space trajectory of four body interaction gate.  Sequence of spin-dependent displacement and squeezing operation parallel transport the phonon wavepacket in motional phase space, accumulating phase that depends on the many body state. See PRX Quantum 4, 030311 (2023).) for details.

We have demonstrated high fidelity three- and four-body interaction gates, and showed concrete avenues how this scheme works for N-body gate with N scaling with the number of qubits. This technique opens the door in realizing a new class of gates.

Selected Publications

• “Demonstration of three- and four-body interactions between trapped-ion spins“. Katz, Feng, Risinger, Monroe, Cetina.                         Nature Physics 19, 1452-1458 (2023).
• “Programmable N-body Interactions between Trapped Ions“. Katz, Cetina, Monroe. PRX Quantum 4, 030311 (2023).
• “N-body Interactions between Trapped Ion Qubits via Spin-Dependent Squeezing“. Katz, Cetina, Monroe. Phys. Rev. Lett. 129, 063603 (2022).