Engineering an Effective Three-spin Hamiltonian in Trapped-ion Systems for Applications in Quantum Simulation

TL;DR

This paper extends the Molmer-Sorensen scheme in trapped-ion systems to engineer three-spin interactions, enabling more complex quantum simulations such as lattice gauge theories and condensed-matter models.

Contribution

The authors develop a method to induce and control three-spin interactions in trapped-ion systems, expanding the capabilities of quantum simulators beyond two-spin Hamiltonians.

Findings

Analytical expressions for three-spin effective evolution.

Numerical simulations confirm scheme feasibility.

Potential for simulating complex quantum models like lattice gauge theories.

Abstract

Trapped-ion quantum simulators, in analog and digital modes, are considered a primary candidate to achieve quantum advantage in quantum simulation and quantum computation. The underlying controlled ion-laser interactions induce all-to-all two-spin interactions via the collective modes of motion through Cirac-Zoller or Molmer-Sorensen schemes, leading to effective two-spin Hamiltonians, as well as two-qubit entangling gates. In this work, the Molmer-Sorensen scheme is extended to induce three-spin interactions via tailored first- and second-order spin-motion couplings. The scheme enables engineering single-, two-, and three-spin interactions, and can be tuned via an enhanced protocol to simulate purely three-spin dynamics. Analytical results for the effective evolution are presented, along with detailed numerical simulations of the full dynamics to support the accuracy and feasibility of the proposed scheme for near-term applications. With a focus on quantum simulation, the advantage of a direct analog implementation of three-spin dynamics is demonstrated via the example of matter-gauge interactions in the U(1) lattice gauge theory within the quantum link model. The mapping of degrees of freedom and strategies for scaling the three-spin scheme to larger systems, are detailed, along with a discussion of the expected outcome of the simulation of the quantum link model given realistic fidelities in the upcoming experiments. The applications of the three-spin scheme go beyond the lattice gauge theory example studied here and include studies of static and dynamical phase diagrams of strongly interacting condensed-matter systems modeled by two- and three-spin Hamiltonians.