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 Mølmer–Sørensen schemes, leading to effective two-spin Hamiltonians, as well as two-qubit entangling gates. In this work, the Mølmer–Sørensen 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.

Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. II. Single-baryon β -decay in real time

“…[158], the total resource requirements per Trotter step are estimated to be R Z : 264L It is important to note that the addition of H β does not contribute to the quadratic scaling of resources as it is a local operator. Recently, the capability to produce multi-qubit gates natively with similar fidelities to two-qubit gates has also been demonstrated [231][232][233]. This could lead to dramatic reductions in the resources required and, for example, the number of multi-qubit terms in the Hamiltonian scales as Multi-qubit terms : 96L 2 − 68L + 22 .…”

Quantum computing with trapped ions: a beginner’s guide

“…However, recently some promising techniques have been proposed to overcome the limitations of the current approaches [69]. On a partially related note, clever manipulation schemes aimed at coupling systems of N > 2 trapped ions have been presented [74,75]. Apart from scalability challenges, the absolute gate time for trapped ions is longer (∼10 −6 s) than that for superconducting qubits (10 −9 s).…”