Qubits on programmable geometries with a trapped-ion quantum processor

TL;DR

This paper demonstrates the engineering of high-dimensional quantum spin models using a linear ion chain, enabling exploration of complex quantum phenomena and potential applications in quantum computation.

Contribution

It introduces a method to realize high-dimensional Ising, XY, and Heisenberg models on a 1D ion chain, expanding the capabilities of analog quantum simulation.

Findings

Successfully implemented high-dimensional Ising interactions with up to 8 qubits.

Extended the method to non-commuting circuits for XY and Heisenberg models.

Demonstrated tunable symmetries and Floquet periodic drives in quantum simulations.

Abstract

Geometry and dimensionality have played crucial roles in our understanding of the fundamental laws of nature, with examples ranging from curved space-time in general relativity to modern theories of quantum gravity. In quantum many-body systems, the entanglement structure can change if the constituents are connected differently, leading to altered bounds for correlation growth and difficulties for classical computers to simulate large systems. While a universal quantum computer can perform digital simulations, an analog-digital hybrid quantum processor offers advantages such as parallelism. Here, we engineer a class of high-dimensional Ising interactions using a linear one-dimensional (1D) ion chain with up to 8 qubits through stroboscopic sequences of commuting Hamiltonians. %with a thorough understanding of the error sources and deviation from the target Hamiltonian. In addition, we extend this method to non-commuting circuits and demonstrate the quantum XY and Heisenberg models using Floquet periodic drives with tunable symmetries. The realization of higher dimensional spin models offers new opportunities ranging from studying topological phases of matter or quantum spin glasses to future fault-tolerant quantum computation.