Dynamic Hamiltonian engineering of 2D rectangular lattices in a one-dimensional ion chain

TL;DR

This paper presents a hybrid analog-digital method to engineer 2D rectangular lattice interactions in a 1D ion chain, enabling simulation of higher-dimensional quantum spin models with scalable control parameters.

Contribution

The authors introduce a novel Hamiltonian engineering technique using Fourier decomposition and Stark shift pulses to simulate 2D lattices in a 1D ion chain.

Findings

Control parameters scale linearly with ion number

Method enables simulation of 2D spin models in 1D chains

Potential for studying quantum phase transitions and transport

Abstract

Controlling the interaction graph between spins or qubits in a quantum simulator allows user-controlled tailoring of native interactions to achieve a target Hamiltonian. The flexibility of engineering long-ranged phonon-mediated spin-spin interactions in a trapped ion quantum simulator offers such a possibility. Trapped ions, a leading candidate for simulating computationally hard quantum many-body dynamics, are most readily trapped in a linear 1D chain, limiting their utility for readily simulating higher dimensional spin models. In this work, we introduce a hybrid method of analog-digital simulation for simulating 2D spin models and dynamically changing interactions to achieve a new graph using a linear 1D chain. The method relies on time domain Hamiltonian engineering through a successive application of Stark shift gradient pulses, and wherein the pulse sequence can simply be obtained from a Fourier series decomposition of the target Hamiltonian over the space of lattice couplings. We focus on engineering 2D rectangular nearest-neighbor spin lattices, demonstrating that the required control parameters scale linearly with ion number. This hybrid approach offers compelling possibilities for the use of 1D chains in the study of Hamiltonian quenches, dynamical phase transitions, and quantum transport in 2D and 3D. We discuss a possible experimental implementation of this approach using real experimental parameters.