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

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.

24 pages, 9 figures, 3 tables

References in corpus (27)

• Chiral effective field theory and nuclear forces
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Observation of a prethermal discrete time crystal
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• Trapped ion quantum computation with transverse phonon modes
• Optical Abelian Lattice Gauge Theories
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Cold atom simulation of interacting relativistic quantum field theories
• Robust two-qubit gates in a linear ion crystal using a frequency-modulated driving force
• SU(2) hadrons on a quantum computer
• Ion trap quantum gates with amplitude-modulated laser beams
• Experimental Realization of a Quantum Integer-Spin Chain with Controllable Interactions
• SU(2) lattice gauge theory on a quantum annealer
• Phase-modulated decoupling and error suppression in qubit-oscillator systems
• Simulation of Collective Neutrino Oscillations on a Quantum Computer
• Single-particle digitization strategy for quantum computation of a ${\varphi }^4$ scalar field theory
• Competing many-body interactions in systems of trapped ions
• Long-range multi-body interactions and three-body anti-blockade in a trapped Rydberg ion chain
• Boson-mediated quantum spin simulators in transverse fields: XY model and spin-boson entanglement
• Chiral entanglement in triangular lattice models
• Native three-body interaction in superconducting circuits
• Quantum Simulation of Field Theories Without State Preparation
• Fate of Lattice Gauge Theories Under Decoherence
• Reliability of lattice gauge theories in the thermodynamic limit
• Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach
• Cold atoms meet lattice gauge theory