Periodic Reporting for period 1 - TOPORYD (Topological quantum matter with Rydberg atom arrays)
Reporting period: 2023-05-01 to 2025-12-31
Recent advances in experimental control have enabled the realization of programmable quantum simulators for interacting many-body systems. A central challenge in this setting is to understand which types of strongly correlated quantum states can arise in experimentally accessible platforms, and how such states can subsequently be prepared and characterized under realistic conditions. This includes, in particular, topologically ordered phases and quantum spin liquids, which are of fundamental interest in many-body physics and relevant to the long-term development of quantum technologies.
Rydberg atom arrays constitute a particularly versatile platform for addressing these questions. Their strong, tunable interactions and flexible geometry allow the implementation of constrained spin models that can give rise to frustration, collective effects, and a rich variety of correlated quantum phases. At the same time, the microscopic form of the interactions, finite system sizes, and experimental imperfections complicate both the identification of the relevant many-body states and the design of reliable preparation protocols.
The objective of this project is to develop theoretical and numerical tools to identify and analyze the strongly correlated many-body states that can emerge in Rydberg-based quantum simulators, design and study protocols for their preparation, and characterize their properties and dynamics. While the initial motivation is the realization of topological phases, the project more broadly addresses the structure, controllability, and observability of complex many-body states in experimentally realistic settings, both in and out of equilibrium.
Rydberg atom arrays constitute a particularly versatile platform for addressing these questions. Their strong, tunable interactions and flexible geometry allow the implementation of constrained spin models that can give rise to frustration, collective effects, and a rich variety of correlated quantum phases. At the same time, the microscopic form of the interactions, finite system sizes, and experimental imperfections complicate both the identification of the relevant many-body states and the design of reliable preparation protocols.
The objective of this project is to develop theoretical and numerical tools to identify and analyze the strongly correlated many-body states that can emerge in Rydberg-based quantum simulators, design and study protocols for their preparation, and characterize their properties and dynamics. While the initial motivation is the realization of topological phases, the project more broadly addresses the structure, controllability, and observability of complex many-body states in experimentally realistic settings, both in and out of equilibrium.
The work performed during the action focused on the theoretical and numerical study of quantum many-body systems, including their ground-state and dynamical properties, in programmable quantum simulators, with particular emphasis on Rydberg atom arrays. A central aspect of this work was the dynamical preparation of correlated quantum states, with the aim of understanding and designing protocols compatible with realistic experimental constraints. The research was organized along two main lines: (i) the identification and characterization of the quantum states and phases that can arise in experimentally relevant Rydberg-based models, and (ii) the development of optimal control methods for the design and analysis of state-preparation protocols.
Within the first research line, variational ground-state ansätze were developed and employed to analyze Rydberg atom models, enabling the study of chiral spin liquid phases and their associated topological properties, as well as the analysis of ground-state structure and phase transitions in two-dimensional and higher-dimensional blockade-constrained systems. In parallel, Rydberg gadgets were explored as a systematic approach to engineer effective constraints, providing access to quantum dimer models and spin liquid states on a variety of lattice geometries.
The second line of work focused on optimal control methods for dynamical state preparation. These techniques were first developed and tested in few-qubit settings, where they were used to engineer novel two-qubit gate protocols for quantum computation with neutral atoms. Building on this framework, optimal control methods were then extended to interacting many-body systems, enabling the design of robust preparation protocols for highly entangled states, including Greenberger–Horne–Zeilinger states, quantum spin liquid states, and many-body quantum scar states in Rydberg atom models. Finally, in collaboration with an experimental group, these theoretical developments were implemented on a Rydberg atom array and applied to the preparation of a 20-atom GHZ state.
Within the first research line, variational ground-state ansätze were developed and employed to analyze Rydberg atom models, enabling the study of chiral spin liquid phases and their associated topological properties, as well as the analysis of ground-state structure and phase transitions in two-dimensional and higher-dimensional blockade-constrained systems. In parallel, Rydberg gadgets were explored as a systematic approach to engineer effective constraints, providing access to quantum dimer models and spin liquid states on a variety of lattice geometries.
The second line of work focused on optimal control methods for dynamical state preparation. These techniques were first developed and tested in few-qubit settings, where they were used to engineer novel two-qubit gate protocols for quantum computation with neutral atoms. Building on this framework, optimal control methods were then extended to interacting many-body systems, enabling the design of robust preparation protocols for highly entangled states, including Greenberger–Horne–Zeilinger states, quantum spin liquid states, and many-body quantum scar states in Rydberg atom models. Finally, in collaboration with an experimental group, these theoretical developments were implemented on a Rydberg atom array and applied to the preparation of a 20-atom GHZ state.
The project produced several results that advance the state of the art in the theoretical description, control, and experimental implementation of correlated quantum states in programmable quantum simulators:
-Novel variational ansätze were developed for the description of chiral spin liquid phases in Rydberg arrays, as well as for the study of ground-state properties and dynamics of constrained models in two and three spatial dimensions. These approaches provide efficient and physically transparent tools for analyzing correlated phases emerging in Rydberg-based systems.
-The concept of Rydberg gadgets, originally introduced for the efficient encoding of optimization problems into Rydberg platforms, was applied to the engineering of constrained quantum many-body models. This enabled the realization of effective dimer constraints and quantum dimer models, opening a systematic route toward the dynamical preparation of quantum spin liquid states with Rydberg atoms.
-Optimal control techniques were applied to the design of new two-qubit gate protocols for neutral-atom digital quantum computers. These results demonstrate the potential of control-based strategies for improving the speed, robustness, and flexibility of entangling operations in Rydberg-based quantum processors.
-Results on many-body quantum scar states were obtained in constrained Rydberg models, clarifying mechanisms underlying non-ergodic dynamics. These results enabled the design of scar-state preparation protocols using optimal control techniques.
-Optimal control methods were extended from few-qubit systems to interacting many-body platforms. This led to the identification of a novel robust dynamical state-preparation strategy, termed the many-body adiabatic echo protocol, with applications ranging from the preparation of GHZ states to the generation of quantum spin liquid states in Rydberg arrays and beyond.
-In collaboration with an experimental group, the adiabatic echo protocol was implemented for the first time on an ytterbium Rydberg atom array, resulting in the generation of a 20-atom GHZ state. This provides an experimental validation of the robustness benefits predicted by the theoretical and optimal-control analysis in a many-body Rydberg platform.
-Novel variational ansätze were developed for the description of chiral spin liquid phases in Rydberg arrays, as well as for the study of ground-state properties and dynamics of constrained models in two and three spatial dimensions. These approaches provide efficient and physically transparent tools for analyzing correlated phases emerging in Rydberg-based systems.
-The concept of Rydberg gadgets, originally introduced for the efficient encoding of optimization problems into Rydberg platforms, was applied to the engineering of constrained quantum many-body models. This enabled the realization of effective dimer constraints and quantum dimer models, opening a systematic route toward the dynamical preparation of quantum spin liquid states with Rydberg atoms.
-Optimal control techniques were applied to the design of new two-qubit gate protocols for neutral-atom digital quantum computers. These results demonstrate the potential of control-based strategies for improving the speed, robustness, and flexibility of entangling operations in Rydberg-based quantum processors.
-Results on many-body quantum scar states were obtained in constrained Rydberg models, clarifying mechanisms underlying non-ergodic dynamics. These results enabled the design of scar-state preparation protocols using optimal control techniques.
-Optimal control methods were extended from few-qubit systems to interacting many-body platforms. This led to the identification of a novel robust dynamical state-preparation strategy, termed the many-body adiabatic echo protocol, with applications ranging from the preparation of GHZ states to the generation of quantum spin liquid states in Rydberg arrays and beyond.
-In collaboration with an experimental group, the adiabatic echo protocol was implemented for the first time on an ytterbium Rydberg atom array, resulting in the generation of a 20-atom GHZ state. This provides an experimental validation of the robustness benefits predicted by the theoretical and optimal-control analysis in a many-body Rydberg platform.