High-dimensional SO(4)-symmetric Rydberg manifolds for quantum simulation

TL;DR

This paper introduces a method to manipulate high-dimensional Rydberg atom manifolds with SO(4) symmetry, enabling quantum simulation of field theories and qudit-based quantum computing.

Contribution

It develops a framework for controlling high-dimensional Rydberg states using symmetry properties, facilitating quantum simulation and information processing.

Findings

Constructed generalized large-spin Heisenberg models.

Demonstrated simulation of sine-Gordon and Schwinger models.

Proposed quantum gates and state transfer protocols for qudits.

Abstract

We develop a toolbox for manipulating arrays of Rydberg atoms prepared in high-dimensional hydrogen-like manifolds in the regime of linear Stark and Zeeman effect. We exploit the SO(4) symmetry to characterize the action of static electric and magnetic fields as well as microwave and optical fields on the well-structured manifolds of states with principal quantum number $n$. This enables us to construct generalized large-spin Heisenberg models for which we develop state-preparation and readout schemes. Due to the available large internal Hilbert space, these models provide a natural framework for the quantum simulation of Quantum Field Theories, which we illustrate for the case of the sine-Gordon and massive Schwinger models. Moreover, these high-dimensional manifolds also offer the opportunity to perform quantum information processing operations for qudit-based quantum computing, which we exemplify with an entangling gate and a state-transfer protocol for the states in the neighborhood of the circular Rydberg level.