Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Computing, Communication, and Simulation

Probing topological spin liquids on a programmable quantum simulator

Giulia Semeghini, Harry Levine, Alexander Keesling, Sepehr Ebadi, Tout T. Wang, Dolev Bluvstein, Ruben Verresen, Hannes Pichler, Marcin Kalinowski, Rhine Samajdar, Ahmed Omran, Subir Sachdev A, Ashvin Vishwanath, Markus Greiner, Vladan Vuletić, Mikhail D. Lukin

Published Mar 9, 2022• 84 citations
Publisher

Abstract

Quantum phases with topological order, such as quantum spin liquids, have been the focus of explorations for several decades. Such phases feature a number of remarkable properties including long-range quantum entanglement. Moreover, they can be potentially exploited for the realization of robust quantum computation, as exemplified by the paradigmatic toric code model. While some indications that such phases may be present in frustrated condensed matter systems have been previously reported, so far quantum spin liquids have eluded direct experimental detection. In this talk, I will show how a programmable quantum simulator based on Rydberg atom arrays can be used to realize and probe quantum spin liquid states. In our approach, atoms are placed on the links of a kagome lattice and coherent evolution under Rydberg blockade enables the transition into frustrated quantum states with no local order. We detect the onset of a quantum spin liquid phase of the toric code type by measuring topological string operators in two complementary bases. The properties of this state are further revealed using a lattice with non-trivial topology, representing a step towards the realization of a topological qubit. Our observations open the door to the controlled experimental exploration of topological quantum matter, and could enable the investigation of new methods for topologically protected quantum information processing.

DOI
10.1117/12.2615077

Related papers

Probing topological spin liquids on a programmable quantum simulator

Giulia Semeghini, Harry Levine, Alexander Keesling +13 more

Quantum spin liquids, exotic phases of matter with topological order, have been a major focus in physics for the past several decades. Such phases feature long-range quantum entanglement that can potentially be exploited to realize robust quantum computation. We used a 219-atom programmable quantum simulator to probe quantum spin liquid states. In our approach, arrays of atoms were placed on the links of a kagome lattice, and evolution under Rydberg blockade created frustrated quantum states with no local order. The onset of a quantum spin liquid phase of the paradigmatic toric code type was detected by using topological string operators that provide direct signatures of topological order and quantum correlations. Our observations enable the controlled experimental exploration of topological matter and protected quantum information processing.

arXiv:2104.04119•Science•Dec 2, 2021•778 citations

Non-Abelian Floquet Spin Liquids in a Digital Rydberg Simulator

Marcin Kalinowski, Nishad Maskara, Mikhail D. Lukin

Understanding topological matter is an outstanding challenge across several disciplines of physical science.Programmable quantum simulators have emerged as a powerful approach to studying such systems.While quantum spin liquids of paradigmatic toric code type have recently been realized in the laboratory, controlled exploration of topological phases with non-Abelian excitations remains an open problem.We introduce and analyze a new approach to simulating topological matter based on periodic driving.Specifically, we describe a model for a so-called Floquet spin liquid, obtained through a periodic sequence of parallel quantum gate operations that effectively simulates the Hamiltonian of the non-Abelian spin liquid in Kitaev's honeycomb model.We show that this approach, including the toolbox for preparation, control, and readout of topological states, can be efficiently implemented in state-of-the-art experimental platforms.One specific implementation scheme is based on Rydberg atom arrays and utilizes recently demonstrated coherent qubit transport combined with controlled-phase gate operations.We describe methods for probing the non-Abelian excitations, and the associated Majorana zero modes, and simulate possible fusion and braiding experiments.Our analysis demonstrates the potential of programmable quantum simulators for exploring topological phases of matter.Extensions including simulation of Kitaev materials and lattice gauge theories are also discussed.

arXiv:2211.00017•Physical Review X•Jul 21, 2023•59 citations

Quantum Spin Liquid State of a Dual-Species Atomic Array on Kagome Lattice

Ahmed M. Farouk, Ilya I. Beterov, Ghadeer Suliman +2 more

Dual-species arrays of ultracold neutral atoms have recently attracted increased interest due to the ability to independently control different atomic species and tune the interatomic interactions. This capability provides additional flexibility essential for both quantum computing and quantum simulation. In this work we theoretically investigate a quantum spin liquid (QSL) state to be simulated on a programmable quantum simulator based on a dual-species atomic array, arranged on a Kagome lattice. The Kagome lattice is formed by corner sharing triangles. This specific spatial arrangement enhances the competing interactions between atoms and is often considered as a model for realizing QSL states. When the atoms are excited into Rydberg states, long-range interactions result in Rydberg blockade. The geometric frustration of the Kagome lattice, combined with the Rydberg blockade, drives the system into exotic phases with topological order and long-range entanglement. To drive an array into the QSL state, we use a sweep-hold-sweep protocol, when the atoms are quasi-adiabatically excited into Rydberg state with individually controlled detuning from the resonance for each atomic species. The filling fraction, indicating emergence of a QSL state, is represented by a density of Rydberg excitations. We identified the conditions required for QSL state in a dual-species array with non-uniform interaction energies. We calculated the correlation length and studied the mutual information as a function of the size of the subset of the system. The existence of a topological order was proved by estimating the Kitaev-Preskill topological quantum entanglement entropy, and further confirmed by evaluating diagonal and off-diagonal topological string operators, which respectively probe the classical dimer-covering structure and the quantum coherence between distinct dimer configurations.

quant-pharXiv:2605.03579•Scientific Reports•May 6, 2026•0 citations

Exploring Topological Phases in Quantum Many-Body Physics

Teng, Yanting

Interactions among atoms can lead to emergent phenomena, one of the most fascinating being topological order. Topological phases are important in understanding high-temperature superconductors and fault-tolerant quantum computing. Quantum spin liquids, a key example of topologically ordered phases, exhibit unique properties such as long-range entanglement in the ground state and support of anyonic excitations, making them an exciting focus in the study of strongly correlated systems. This thesis explores the detection and learning of topological phases in quantum many-body systems, including quantum spin models, cuprate superconductors and ultracold atomic platform of Rydberg atom arrays. Guided by the experiments on Kitaev materials, we begin by using spinon mean-field theory of quantum spin liquids to explain the transition from a quantized thermal Hall effect to an unquantized values. Making closer connections to experiments in cuprates, we include additional interactions with phonons present in the system. We examine how spinon-phonon interactions, characterized by symmetry analysis, give rise to a chiral phonon Hall viscosity and can also contribute to the thermal Hall effect. In the second part, we turn to Rydberg atom arrays, which have recently been shown to realize a $\mathbb{Z}_2$ quantum spin liquid phase—an elusive state in conventional solid-state materials. We study how Rydberg interactions and lattice geometries lead to the emergence of $Z_2$ gauge theories and distinct classes of topological quantum spin liquids. Finally, we study a variational tensor network tomography method for learning topological states from randomized measurements on Rydberg atom arrays. We demonstrate its efficiency in characterizing complex two-dimensional states that could be realized in future experiments.

•Jan 1, 2024•0 citations

Prediction of Toric Code Topological Order from Rydberg Blockade

Ruben Verresen, Mikhail D. Lukin, Ashvin Vishwanath

The physical realization of Z 2 topological order as encountered in the paradigmatic toric code has proven to be an elusive goal.We predict that this phase of matter can be realized in a two-dimensional array of Rydberg atoms placed on the ruby lattice, at specific values of the Rydberg blockade radius.First, we show that the blockade model-also known as a "PXP" model-realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term.This model can be interpreted as a Z 2 gauge theory whose dynamics is generated by monomer fluctuations.We obtain its phase diagram using the numerical density matrix renormalization group method and find a topological quantum liquid (TQL) as evidenced by multiple measures including (i) a continuous transition between two featureless phases, (ii) a topological entanglement entropy of ln 2 as measured in various geometries, (iii) degenerate topological ground states, and (iv) the expected modular matrix from ground state overlap.Next, we show that the TQL persists upon including realistic, algebraically decaying van der Waals interactions VðrÞ ∼ 1=r 6 for a choice of lattice parameters.Moreover, we can directly access topological loop operators, including the Fredenhagen-Marcu order parameter.We show how these can be measured experimentally using a dynamic protocol, providing a "smoking gun" experimental signature of the TQL phase.Finally, we show how to trap an emergent anyon and realize different topological boundary conditions, and we discuss the implications for exploring fault-tolerant quantum memories.

arXiv:2011.12310•Physical Review X•Jul 8, 2021•193 citations

Trimer quantum spin liquid in a honeycomb array of Rydberg atoms

Milan Kornjača, Rhine Samajdar, Tommaso Macrì +3 more

Abstract Quantum spin liquids are elusive but paradigmatic examples of strongly correlated quantum states that are characterized by long-range quantum entanglement. Recently, signatures of a gapped topological $${{\mathbb{Z}}}_{2}$$ Z 2 spin liquid have been observed in a system of Rydberg atoms; however, the full capability of these platforms to realize quantum spin liquids extends far beyond this state alone. Here, we propose the realization of a different class of spin liquids in a honeycomb array of Rydberg atoms. Exploring the system’s quantum phase diagram using density-matrix renormalization group and exact diagonalization calculations, we identify several density-wave-ordered phases and a trimer spin liquid ground state with an emergent U(1) × U(1) local symmetry. This liquid state originates from superpositions of classical trimer configurations on the dual triangular lattice in the regime where third-nearest-neighbor atoms lie within the Rydberg blockade radius. Finally, we discuss the conditions to enhance the preparation fidelity of this state by a general Rydberg-blockade-based projection mechanism, test the robustness of the trimer spin liquid phase in a range of realistic parameters, and outline methods for its experimental detection.

arXiv:2211.00653•Communications Physics•Dec 13, 2023•19 citations
Quantum phases with topological order, such as quantum spin liquids, have been the focus of explorations for several decades. Such phases feature a number of remarkable properties including long-range quantum entanglement. Moreover, they can be potentially exploited for the realization of robust quantum computation, as exemplified by the paradigmatic toric code model. While some indications that such phases may be present in frustrated condensed matter systems have been previously reported, so far quantum spin liquids have eluded direct experimental detection. In this talk, I will show how a programmable quantum simulator based on Rydberg atom arrays can be used to realize and probe quantum spin liquid states. In our approach, atoms are placed on the links of a kagome lattice and coherent evolution under Rydberg blockade enables the transition into frustrated quantum states with no local order. We detect the onset of a quantum spin liquid phase of the toric code type by measuring topological string operators in two complementary bases. The properties of this state are further revealed using a lattice with non-trivial topology, representing a step towards the realization of a topological qubit. Our observations open the door to the controlled experimental exploration of topological quantum matter, and could enable the investigation of new methods for topologically protected quantum information processing.
Quantum spin liquids, exotic phases of matter with topological order, have been a major focus in physics for the past several decades. Such phases feature long-range quantum entanglement that can potentially be exploited to realize robust quantum computation. We used a 219-atom programmable quantum simulator to probe quantum spin liquid states. In our approach, arrays of atoms were placed on the links of a kagome lattice, and evolution under Rydberg blockade created frustrated quantum states with no local order. The onset of a quantum spin liquid phase of the paradigmatic toric code type was detected by using topological string operators that provide direct signatures of topological order and quantum correlations. Our observations enable the controlled experimental exploration of topological matter and protected quantum information processing.
Understanding topological matter is an outstanding challenge across several disciplines of physical science.Programmable quantum simulators have emerged as a powerful approach to studying such systems.While quantum spin liquids of paradigmatic toric code type have recently been realized in the laboratory, controlled exploration of topological phases with non-Abelian excitations remains an open problem.We introduce and analyze a new approach to simulating topological matter based on periodic driving.Specifically, we describe a model for a so-called Floquet spin liquid, obtained through a periodic sequence of parallel quantum gate operations that effectively simulates the Hamiltonian of the non-Abelian spin liquid in Kitaev's honeycomb model.We show that this approach, including the toolbox for preparation, control, and readout of topological states, can be efficiently implemented in state-of-the-art experimental platforms.One specific implementation scheme is based on Rydberg atom arrays and utilizes recently demonstrated coherent qubit transport combined with controlled-phase gate operations.We describe methods for probing the non-Abelian excitations, and the associated Majorana zero modes, and simulate possible fusion and braiding experiments.Our analysis demonstrates the potential of programmable quantum simulators for exploring topological phases of matter.Extensions including simulation of Kitaev materials and lattice gauge theories are also discussed.
Dual-species arrays of ultracold neutral atoms have recently attracted increased interest due to the ability to independently control different atomic species and tune the interatomic interactions. This capability provides additional flexibility essential for both quantum computing and quantum simulation. In this work we theoretically investigate a quantum spin liquid (QSL) state to be simulated on a programmable quantum simulator based on a dual-species atomic array, arranged on a Kagome lattice. The Kagome lattice is formed by corner sharing triangles. This specific spatial arrangement enhances the competing interactions between atoms and is often considered as a model for realizing QSL states. When the atoms are excited into Rydberg states, long-range interactions result in Rydberg blockade. The geometric frustration of the Kagome lattice, combined with the Rydberg blockade, drives the system into exotic phases with topological order and long-range entanglement. To drive an array into the QSL state, we use a sweep-hold-sweep protocol, when the atoms are quasi-adiabatically excited into Rydberg state with individually controlled detuning from the resonance for each atomic species. The filling fraction, indicating emergence of a QSL state, is represented by a density of Rydberg excitations. We identified the conditions required for QSL state in a dual-species array with non-uniform interaction energies. We calculated the correlation length and studied the mutual information as a function of the size of the subset of the system. The existence of a topological order was proved by estimating the Kitaev-Preskill topological quantum entanglement entropy, and further confirmed by evaluating diagonal and off-diagonal topological string operators, which respectively probe the classical dimer-covering structure and the quantum coherence between distinct dimer configurations.
Interactions among atoms can lead to emergent phenomena, one of the most fascinating being topological order. Topological phases are important in understanding high-temperature superconductors and fault-tolerant quantum computing. Quantum spin liquids, a key example of topologically ordered phases, exhibit unique properties such as long-range entanglement in the ground state and support of anyonic excitations, making them an exciting focus in the study of strongly correlated systems. This thesis explores the detection and learning of topological phases in quantum many-body systems, including quantum spin models, cuprate superconductors and ultracold atomic platform of Rydberg atom arrays. Guided by the experiments on Kitaev materials, we begin by using spinon mean-field theory of quantum spin liquids to explain the transition from a quantized thermal Hall effect to an unquantized values. Making closer connections to experiments in cuprates, we include additional interactions with phonons present in the system. We examine how spinon-phonon interactions, characterized by symmetry analysis, give rise to a chiral phonon Hall viscosity and can also contribute to the thermal Hall effect. In the second part, we turn to Rydberg atom arrays, which have recently been shown to realize a Z2\mathbb{Z}_2Z2​ quantum spin liquid phase—an elusive state in conventional solid-state materials. We study how Rydberg interactions and lattice geometries lead to the emergence of Z2Z_2Z2​ gauge theories and distinct classes of topological quantum spin liquids. Finally, we study a variational tensor network tomography method for learning topological states from randomized measurements on Rydberg atom arrays. We demonstrate its efficiency in characterizing complex two-dimensional states that could be realized in future experiments.
The physical realization of Z 2 topological order as encountered in the paradigmatic toric code has proven to be an elusive goal.We predict that this phase of matter can be realized in a two-dimensional array of Rydberg atoms placed on the ruby lattice, at specific values of the Rydberg blockade radius.First, we show that the blockade model-also known as a "PXP" model-realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term.This model can be interpreted as a Z 2 gauge theory whose dynamics is generated by monomer fluctuations.We obtain its phase diagram using the numerical density matrix renormalization group method and find a topological quantum liquid (TQL) as evidenced by multiple measures including (i) a continuous transition between two featureless phases, (ii) a topological entanglement entropy of ln 2 as measured in various geometries, (iii) degenerate topological ground states, and (iv) the expected modular matrix from ground state overlap.Next, we show that the TQL persists upon including realistic, algebraically decaying van der Waals interactions VðrÞ ∼ 1=r 6 for a choice of lattice parameters.Moreover, we can directly access topological loop operators, including the Fredenhagen-Marcu order parameter.We show how these can be measured experimentally using a dynamic protocol, providing a "smoking gun" experimental signature of the TQL phase.Finally, we show how to trap an emergent anyon and realize different topological boundary conditions, and we discuss the implications for exploring fault-tolerant quantum memories.
Abstract Quantum spin liquids are elusive but paradigmatic examples of strongly correlated quantum states that are characterized by long-range quantum entanglement. Recently, signatures of a gapped topological Z2{{\mathbb{Z}}}_{2}Z2​ Z 2 spin liquid have been observed in a system of Rydberg atoms; however, the full capability of these platforms to realize quantum spin liquids extends far beyond this state alone. Here, we propose the realization of a different class of spin liquids in a honeycomb array of Rydberg atoms. Exploring the system’s quantum phase diagram using density-matrix renormalization group and exact diagonalization calculations, we identify several density-wave-ordered phases and a trimer spin liquid ground state with an emergent U(1) × U(1) local symmetry. This liquid state originates from superpositions of classical trimer configurations on the dual triangular lattice in the regime where third-nearest-neighbor atoms lie within the Rydberg blockade radius. Finally, we discuss the conditions to enhance the preparation fidelity of this state by a general Rydberg-blockade-based projection mechanism, test the robustness of the trimer spin liquid phase in a range of realistic parameters, and outline methods for its experimental detection.