[Paper Review] Engineering an Effective Three-spin Hamiltonian in Trapped-ion Systems for Applications in Quantum Simulation

Bárbara Andrade, Zohreh Davoudi+4 more|arXiv (Cornell University)|Aug 2, 2021

Quantum Information and Cryptography137 references41 citations

TL;DR

This paper proposes a protocol to engineer an effective three-spin Hamiltonian in trapped-ion quantum simulators using tailored first- and second-order spin-motion couplings within the Mølmer-Sørensen scheme. By employing a 'mirror' drive protocol, it suppresses unwanted two-spin interactions, enabling high-fidelity three-spin dynamics; numerical simulations confirm >99% fidelity for realistic experimental parameters, demonstrating feasibility for simulating complex quantum systems like U(1) 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.

Motivation & Objective

• To extend the Mølmer-Sørensen scheme to generate effective three-spin interactions in trapped-ion systems.
• To suppress unwanted two-spin interactions while preserving desired three-spin dynamics through a novel 'mirror' drive protocol.
• To validate the scheme via full numerical simulations under realistic experimental parameters.
• To demonstrate the utility of the three-spin interaction for simulating matter-gauge dynamics in U(1) lattice gauge theories.
• To enable scalable simulation of strongly correlated quantum systems governed by multi-spin Hamiltonians.

Proposed method

• Utilizes first- and second-order spin-motion couplings in the Mølmer-Sørensen scheme to generate effective three-spin interactions.
• Employs a 'mirror' drive protocol that applies symmetric laser drives to suppress single- and two-spin terms while preserving three-spin dynamics.
• Applies a high-accuracy rotating-wave approximation to derive analytical expressions for the effective Hamiltonian.
• Performs detailed numerical simulations of the full dynamics, including spin-phonon entanglement and off-resonant effects.
• Maps the three-spin interaction to the quantum link model of U(1) lattice gauge theory for physical relevance.
• Tunes laser intensities, frequencies, and trap parameters to minimize spin-phonon contamination and maximize fidelity.

Experimental results

Research questions

• RQ1 Can a three-spin interaction be engineered in trapped-ion systems using only standard Mølmer-Sørensen-type couplings and tailored drives?
• RQ2 How can unwanted two-spin interactions be effectively suppressed in the presence of three-spin couplings?
• RQ3 What is the achievable fidelity of three-spin dynamics under realistic experimental conditions with finite laser power and trap anharmonicity?
• RQ4 Can the engineered three-spin Hamiltonian simulate nontrivial quantum field theories such as the U(1) quantum link model?
• RQ5 What are the scaling prospects and practical limitations for extending this scheme to larger spin systems?

Key findings

• The proposed mirror drive protocol suppresses single- and two-spin interactions by over 90% compared to the three-spin term, enabling dominant three-spin dynamics.
• Numerical simulations show a three-spin gate fidelity exceeding 99% under realistic experimental parameters, including finite laser power and axial trap frequency.
• The effective three-spin Hamiltonian accurately reproduces the dynamics of the U(1) quantum link model, validating its use for simulating lattice gauge theories.
• The scheme maintains high fidelity even when multiple phonon modes contribute, due to careful tuning of laser detunings and amplitudes.
• The method is scalable in principle, with clear strategies for extending the three-spin interaction to larger trapped-ion chains.
• The approach enables direct analog simulation of complex many-body Hamiltonians, offering a path to quantum advantage in simulating strongly correlated systems.