PROgramming Gauge-invariant Rydberg AtoM arrays

Project Information

PROGRAM

Grant agreement ID: 101150724

DOI

10.3030/101150724

Project terminated on 30 April 2025

EC signature date 5 April 2024

Start date 1 November 2024

End date 30 April 2027

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 216 699,60

Coordinated by

AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS
Spain

Periodic Reporting for period 1 - PROGRAM (PROgramming Gauge-invariant Rydberg AtoM arrays)

Reporting period: 2024-11-01 to 2026-04-30

Summary of the context and overall objectives of the project

The simulation of quantum systems is one of the most promising near-term applications of quantum technologies. In particular, lattice gauge theories (LGTs), which underpin the Standard Model of particle physics, describe a vast range of strongly interacting phenomena, from the behaviour of quarks and gluons in high-energy physics to exotic states of matter in condensed matter systems. However, many important questions in this field remain unanswered, as they are beyond the reach of classical computational methods.

PROGRAM (PROgramming Gauge-invariant Rydberg AtoM arrays) addresses this challenge by developing new quantum simulation strategies for lattice gauge theories using arrays of neutral atoms. These platforms are among the most advanced quantum technologies available today, capable of controlling hundreds of atoms with high precision. The goal is to design protocols that fully exploit the capabilities of these devices to explore complex gauge-theoretic phenomena that are currently inaccessible.

The project focuses on two major research objectives:

1) Scaling gauge-matter interactions beyond one-dimensional systems using analog simulators, and develop protocols to simulate relevant non-equilibrium phenomena driven by these interactions.

2) Develop hardware-efficient digital quantum simulation protocols that account for non-abelian gauge fields as well as fermionic matter, co-designed for qudit and fermionic architectures, respectively.

By advancing these goals, PROGRAM aims to establish practical quantum simulation protocols that can be implemented in current and near-term devices, ultimately contributing to the long-term vision of quantum technologies delivering insights into fundamental physics.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

PROGRAM has made substantial progress toward its two main objectives, delivering key theoretical and experimental advances in quantum simulation of lattice gauge theories (LGTs).

The first objective, scaling gauge-matter interactions beyond 1D, was successfully achieved through a collaborative effort with QuEra Computing and Harvard University. In this work, we implemented an analog quantum simulation of a U(1) lattice gauge theory with scalar matter in (2+1) dimensions using a Rydberg atom array arranged in a Kagome lattice. The experiment enabled the direct observation of string breaking in a two-dimensional gauge theory, a hallmark of confinement dynamics. The results were reported in a joint theory-experiment preprint [arXiv:2410.16558] demonstrating the viability of programmable neutral-atom arrays for exploring complex non-perturbative phenomena in high-energy physics.

The second objective, developing hardware-efficient digital quantum simulation strategies for gauge theories, advanced along two parallel lines. On one front, we formulated a framework for simulating non-Abelian lattice gauge theories using high-dimensional qudit encodings. We found schemes that significantly reduce the circuit complexity and leverage the intrinsic capabilities of atomic platforms. The corresponding experiment is now underway in Martin Ringbauer’s trapped-ion quantum computer in Innsbruck, targeting real-time dynamics of SU(2) gauge fields.

In parallel, we addressed the challenge of simulating fermionic matter in gauge theories by developing variational protocols for extended Fermi-Hubbard models based on ultracold fermionic atoms in optical lattices. These protocols are optimized for near-term quantum simulators and lay the foundation for incorporating fermionic matter into digital simulations of LGTs. These results were reported in a theory preprint [arXiv:2502.05067]. Ongoing work aims to extend these methods to full fermionic lattice gauge theories, further bridging high-energy theory and quantum simulation platforms.

These results represent a significant step forward in the realization of scalable, flexible, and hardware-aware quantum simulators of gauge theories, combining both analog and digital approaches.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

PROGRAM has delivered results that go significantly beyond the state of the art in quantum simulation of lattice gauge theories, a field at the intersection of quantum information science and high-energy physics. The project introduced new theoretical frameworks and experimental implementations that make it possible to simulate more complex and realistic gauge theories on currently available quantum hardware.

The observation of string breaking in (2+1) dimensions marks a major milestone: it is the first demonstration of this phenomenon for a U(1) gauge theory in two spatial dimensions using programmable quantum simulators. This advance required novel encoding strategies and experimental control techniques, pushing the limits of existing Rydberg-atom platforms.

On the digital front, PROGRAM developed hardware-efficient simulation methods that reduce the quantum resources needed to simulate gauge theories. This includes compact qudit-based encodings for non-Abelian gauge fields and variational strategies for fermionic lattice models using ultracold atoms. These methods allow for a substantial reduction in circuit depth, enabling experiments on noisy intermediate-scale quantum (NISQ) devices.

To ensure the success and uptake of these results, further research is needed in three main directions: (i) scaling up system sizes while maintaining coherence and control, allowing to simulate in particular longer evolution times, (ii) extending protocols to include dynamical gauge fields and fermions in (3+1) dimensions, and (iii) integrating error mitigation and correction strategies for digital simulations. Advances in these areas will be key for realizing practical quantum simulations that can address open questions in particle physics and strongly correlated quantum matter.

Experimental realization of a (2+1)D gauge theory using a programmable array of Rydberg atoms