Publications
Papers
Quantum doubles in symmetric blockade structures
Phys. Rev. B ?, ?? (2026)
DownloadarXiv2511.04414DOI10.1103/99sy-kggw
Abstract
Exactly solvable models of topologically ordered phases with non-abelian anyons typically require complicated many-body interactions which do not naturally appear in nature. This motivates the “inverse problem” of quantum many-body physics: given microscopic systems with experimentally realistic two-body interactions, how to design a Hamiltonian that realizes a desired topological phase? Here we solve this problem on a platform motivated by Rydberg atoms, where elementary two-level systems couple via simple blockade interactions. Within this framework, we construct Hamiltonians that realize topological orders described by non-abelian quantum double models. We analytically prove the existence of topological order in the ground state, and present efficient schemes to prepare these states. We also introduce protocols for the controlled adiabatic braiding of anyonic excitations to probe their non-abelian statistics. Our construction is generic and applies to quantum doubles $\mathcal{D}(G)$ for arbitrary finite groups $G$. We illustrate braiding for the simplest non-abelian quantum double $\mathcal{D}(S_3)$.Robust detection of an entanglement transition in the projective transverse-field Ising model
Phys. Rev. Lett. 136, 140403 (2026)
DownloadarXiv2511.17370DOI10.1103/5m5q-f7vc
Abstract
We propose a scalable and noise-resilient protocol for the detection of the entanglement transition in a projective version of the transverse field Ising model. Entanglement transitions are experimentally difficult to observe due to the inherent randomness of projective measurements and noise in large-scale experimental settings. Our approach combines error correction algorithms with classical shadow tomography to overcome both problems. This allows for experimentally accessible upper and lower bounds on the entanglement transition without postselection or full state tomography. These bounds remain robust under noise and their sharpness is a measure of the noise rate.Topological order in symmetric blockade structures
PRX Quantum 6, 030340 (2025)
DownloadarXiv2503.17123DOI10.1103/dtlf-2q82 Featured in Physics Talk
Abstract
The bottom-up design of strongly interacting quantum materials with prescribed ground-state properties is a highly nontrivial task, especially if only simple constituents with realistic two-body interactions are available on the microscopic level. Here we study two- and three-dimensional structures of two-level systems that interact via a simple blockade potential in the presence of a coherent coupling between the two states. For such strongly interacting quantum many-body systems, we introduce the concept of blockade graph automorphisms to construct symmetric blockade structures with strong quantum fluctuations that lead to equal-weight superpositions of tailored states. Drawing from these results, we design a quasi-two-dimensional periodic quantum system that — as we show rigorously — features a topological $\mathbb{Z}_2$ spin liquid as its ground state. Our construction is based on the implementation of a local symmetry on the microscopic level in a system with only two-body interactions.Absorbing State Phase Transition with Clifford Circuits
Phys. Rev. Research 6, 013278 (2024)
DownloadarXiv2303.05317DOI10.1103/PhysRevResearch.6.013278
Abstract
The role of quantum fluctuations in modifying the critical behavior of nonequilibrium phase transitions is a fundamental but unsolved question. In this study, we examine the absorbing state phase transition of a 1D chain of qubits undergoing a contact process that involves both coherent and classical dynamics. We adopt a discrete-time quantum model with states that can be described in the stabilizer formalism, and therefore allows for an efficient simulation of large system sizes. The extracted critical exponents indicate that the absorbing state phase transition of this Clifford circuit model belongs to the directed percolation universality class. This suggests that the inclusion of quantum fluctuations does not necessarily alter the critical behavior of nonequilibrium phase transitions of purely classical systems. Finally, we extend our analysis to a non-Clifford circuit model, where a tentative scaling analysis in small systems reveals critical exponents that are also consistent with the directed percolation universality class.Decoding the Projective Transverse Field Ising Model
Phys. Rev. B 107, 214201 (2023)
DownloadarXiv2303.03081DOI10.1103/PhysRevB.107.214201
Abstract
The competition between noncommuting projective measurements in discrete quantum circuits can give rise to entanglement transitions. It separates a regime where initially stored quantum information survives the time evolution from a regime where the measurements destroy the quantum information. Here we study one such system — the projective transverse field Ising model — with a focus on its capabilities as a quantum error correction code. The idea is to interpret one type of measurement as an error and the other type as a syndrome measurement. We demonstrate that there is a finite threshold below which quantum information encoded in an initially entangled state can be retrieved reliably. In particular, we implement the maximum likelihood decoder to demonstrate that the error correction threshold is distinct from the entanglement transition. This implies that there is a finite regime where quantum information is protected by the projective dynamics, but cannot be retrieved by using syndrome measurements.Functional completeness of planar Rydberg blockade structures
Phys. Rev. B 108, 085138 (2023)
DownloadarXiv2301.01508DOI10.1103/PhysRevB.108.085138
Abstract
The construction of Hilbert spaces that are characterized by local constraints as the low-energy sectors of microscopic models is an important step towards the realization of a wide range of quantum phases with long-range entanglement and emergent gauge fields. Here we show that planar structures of trapped atoms in the Rydberg blockade regime are functionally complete: Their ground-state manifold can realize any Hilbert space that can be characterized by local constraints in the product basis. We introduce a versatile framework, together with a set of provably minimal logic primitives as building blocks, to implement these constraints. As examples, we present lattice realizations of the string-net Hilbert spaces that underlie the surface code and the Fibonacci anyon model. We discuss possible optimizations of planar Rydberg structures to increase their geometrical robustness.Experimentally accessible scheme for a fractional Chern insulator in Rydberg atoms
PRX Quantum 3, 030302 (2022)
DownloadarXiv2202.00699DOI10.1103/PRXQuantum.3.030302
Abstract
We present a setup with Rydberg atoms for the realization of a bosonic fractional Chern insulator in artificial matter. The suggested setup relies on Rydberg atoms arranged in a honeycomb lattice, where excitations hop through the lattice by dipolar exchange interactions and can be interpreted as hard-core bosons. The quantum many-body Hamiltonian is studied within exact diagonalization and the density-matrix renormalization group. We identify experimentally accessible parameters where all signatures indicate the appearance of a fractional state with the same topological properties as the $\nu=1/2$ bosonic Laughlin state. We demonstrate an adiabatic ramping procedure, which allows for the preparation of the topological state in a finite system, and demonstrate an experimentally accessible smoking-gun signature for the fractional excitations.Entanglement Transition in the Projective Transverse Field Ising Model
Phys. Rev. B 102, 094204 (2020)
DownloadarXiv2006.09748DOI10.1103/PhysRevB.102.094204 Editor's Suggestion Talk
Abstract
Discrete quantum trajectories of systems under random unitary gates and projective measurements have been shown to feature transitions in the entanglement scaling that are not encoded in the density matrix. In this paper, we study the projective transverse field Ising model, a stochastic model with two noncommuting projective measurements and no unitary dynamics. We numerically demonstrate that their competition drives an entanglement transition between two distinct steady states that both exhibit area law entanglement, and introduce a classical but nonlocal model that captures the entanglement dynamics completely. Exploiting a map to bond percolation, we argue that the critical system in one dimension is described by a conformal field theory, and derive the universal scaling of the entanglement entropy and the critical exponent for the scaling of the mutual information of two spins exactly. We conclude with an interpretation of the entanglement transition in the context of quantum error correction.Realization of a density-dependent Peierls phase in a synthetic, spin-orbit coupled Rydberg system
Phys. Rev. X 10, 021031 (2020)
DownloadarXiv2001.10357DOI10.1103/PhysRevX.10.021031
Abstract
We experimentally realize a Peierls phase in the hopping amplitude of excitations carried by Rydberg atoms, and observe the resulting characteristic chiral motion in a minimal setup of three sites. Our demonstration relies on the intrinsic spin-orbit coupling of the dipolar exchange interaction combined with time-reversal symmetry breaking by a homogeneous external magnetic field. Remarkably, the phase of the hopping amplitude between two sites strongly depends on the occupancy of the third site, thus leading to a correlated hopping associated with a density-dependent Peierls phase. We experimentally observe this density-dependent hopping and show that the excitations behave as anyonic particles with a nontrivial phase under exchange. Finally, we confirm the dependence of the Peierls phase on the geometrical arrangement of the Rydberg atoms.Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms
Science 365, 775 (2019)
DownloadarXiv1810.13286DOI10.1126/science.aav9105 Talk
Abstract
The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states. The experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata
SciPost Phys. 4, 007 (2018)
DownloadarXiv1711.08196DOI10.21468/SciPostPhys.4.1.007
Abstract
Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In this work, we focus on the one-dimensional Majorana chain and construct a strictly local decoder based on a self-dual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. Our results pave the way for scalable and modular designs of actively corrected one-dimensional topological quantum memories.Topological networks for quantum communication between distant qubits
npj Quantum Information 3, 47 (2017)
DownloadarXiv1705.06901DOI10.1038/s41534-017-0047-x
Abstract
Efficient communication between qubits relies on robust networks which allow for fast and coherent transfer of quantum information. It seems natural to harvest the remarkable properties of systems characterized by topological invariants to perform this task. Here we show that a linear network of coupled bosonic degrees of freedom, characterized by topological bands, can be employed for the efficient exchange of quantum information over large distances. Important features of our setup are that it is robust against quenched disorder, all relevant operations can be performed by global variations of parameters, and the time required for communication between distant qubits approaches linear scaling with their distance. We demonstrate that our concept can be extended to an ensemble of qubits embedded in a two-dimensional network to allow for communication between all of them.Ising anyonic topological phase of interacting Fermions in one dimension
Phys. Rev. B 96, 121109(R) (2017)
DownloadarXiv1705.01786DOI10.1103/PhysRevB.96.121109
Abstract
We study a microscopic model of interacting fermions in a ladder setup, where the total number of particles is conserved. At a special point, the ground state is known and gives rise to a topological state of matter with edge modes obeying the statistics of Ising anyons. Using a combination of bosonization as well as full scale numerical density-matrix renormalization group analysis, we map out the full phase diagram. We find that the topological phase survives in an extended parameter regime. Remarkably, an additional symmetry is required to protect the topological phase.Topological states in a microscopic model of interacting fermions
Phys. Rev. B 92, 041118(R) (2015)
DownloadarXiv1504.04233DOI10.1103/PhysRevB.92.041118 Editor's Suggestion Poster Talk
Abstract
We present a microscopic model of interacting fermions where the ground state degeneracy is topologically protected. The model is based on a double-wire setup with local interactions in a particle number conserving setting. A compelling property of this model is the exact solvability for its ground states and low energy excitations. We demonstrate the appearance of topologically protected edge states and derive their braiding properties on a microscopic level. We find the non-Abelian statistics of Ising anyons, which can be interpreted as Majorana-like edge states.Topological flat bands with Chern number $C=2$ by dipolar exchange interactions
Phys. Rev. A 91, 053617 (2015)
DownloadarXiv1410.5667DOI10.1103/PhysRevA.91.053617
Abstract
We demonstrate the realization of topological band structures by exploiting the intrinsic spin-orbit coupling of dipolar interactions in combination with broken time-reversal symmetry. The system is based on polar molecules trapped in a deep optical lattice, where the dynamics of rotational excitations follows a hopping Hamiltonian which is determined by the dipolar exchange interactions. We find topological bands with Chern number $C=2$ on the square lattice, while a very rich structure of different topological bands appears on the honeycomb lattice. We show that the system is robust against missing molecules. For certain parameters we obtain flat bands, providing a promising candidate for the realization of hard-core bosonic fractional Chern insulators.Exploring quantum phases by driven dissipation
Phys. Rev. A 92, 012128 (2015)
DownloadarXiv1408.4616DOI10.1103/PhysRevA.92.012128 Poster Talk
Abstract
Dephasing and decay are the intrinsic dissipative processes prevalent in any open quantum system and the dominant mechanisms for the loss of coherence and entanglement. This inadvertent effect not only can be overcome but can even be capitalized on in a dissipative quantum simulation by means of tailored couplings between the quantum system and the environment. In this context it has been demonstrated that universal quantum computation can be performed using purely dissipative elements, and furthermore, the efficient preparation of highly entangled states is possible. In this article, we are interested in nonequilibrium phase transitions appearing in purely dissipative systems and the exploration of quantum phases in terms of a dissipative quantum simulation. To elucidate these concepts, we scrutinize exemplarily two paradigmatic models: the transverse-field Ising model and the considerably more complex $\mathbb{Z}_2$ lattice gauge theory. We show that the nonequilibrium phase diagrams parallel the quantum phase diagrams of the Hamiltonian “blueprint” theories.Majorana modes and p-wave superfluids for fermionic atoms in optical lattices
Nature Communications 5, 4504 (2014)
DownloadarXiv1403.0593DOI10.1038/ncomms5504
Abstract
We present a simple approach to create a strong p-wave interaction for fermions in an optical lattice. The crucial step is that the combination of a lattice setup with different orbital states and s-wave interactions can give rise to a strong induced p-wave pairing. We identify different topological phases and demonstrate that the setup offers a natural way to explore the transition from Kitaev’s Majorana wires to two-dimensional p-wave superfluids. We demonstrate how this design can induce Majorana modes at edge dislocations in the optical lattice, and we provide an experimentally feasible protocol for the observation of the non-Abelian statistics.Minimal instances for toric code ground states
Phys. Rev. A 86, 022336 (2012)
DownloadarXiv1206.6994DOI10.1103/PhysRevA.86.022336 Talk
Abstract
A decade ago Kitaev’s toric code model established the new paradigm of topological quantum computation. Due to remarkable theoretical and experimental progress, the quantum simulation of such complex many-body systems is now within the realms of possibility. Here we consider the question, to which extent the ground states of small toric code systems differ from local-unitary (LU)-equivalent graph states. We argue that simplistic (though experimentally attractive) setups obliterate the differences between the toric code and equivalent graph states; hence we search for the smallest setups on the square and triangular lattices, such that the quasilocality of the toric code Hamiltonian becomes a distinctive feature. To this end, a purely geometric procedure to transform a given toric code setup into a local-Clifford (LC)-equivalent graph state is derived. In combination with an algorithmic computation of LC-equivalent graph states, we find the smallest nontrivial setup on the square lattice to contain five plaquettes and 16 qubits; on the triangular lattice the number of plaquettes and qubits is reduced to four and nine, respectively.
Theses
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B.Sc. Thesis: Minimal Instance for Topological Matter
DownloadPages88Submitted2011
Abstract
Quantum information theory is a promising interdisciplinary field of both experimental and theoretical physics on the one hand and informatics on the other. However, the storage and protection of coherent quantum information proves much more challenging than in the classical analogue. This led to various approaches in order to protect quantum information from decoherence due to inevitable interactions with the environment.
Whereas classical quantum error correction codes take the approach of detecting and correcting errors algorithmically the investigation of topological phases gave rise to the notion of error correction on a physical level. These theories use degenerate ground states of topologically ordered systems to store quantum information reliably. For topologically ordered systems the successful description of phase transitions by means of spontaneous symmetry breaking and local order parameters fails. This leads to an inherent stability of such phases against local noise.
A well-established theory showing topological order is Kitaev’s Toric Code Model which was subject to intensive studies in recent years. This theory describes a square lattice of spins embedded into the surface of a torus and features a topology dependent ground state degeneracy. Since the Toric Code can be described in terms of stabilizers — a group theoretic formalism known from quantum information theory — its ground states may be expressed as graph states, a subclass of multi-qubit states described by mathematical graphs and introduced by Hein et al.
In the first part of this thesis the construction of ground states for small Toric Code systems is investigated. We show how ground states from larger systems may be derived from ground states of their smaller constituents. In the second part it is shown how a known algorithm, developed for stabilizer states in general, is applied to the special case of Toric Code Models. Furthermore a transformation rule stated in purely graph theoretic terms is provided. In the last section the existence of special, so called local graph states for certain Toric Code systems is investigated. We compute the smallest settings for Toric Code Models on triangular and square lattices that cannot be constructed from local graph states by means of local unitaries alone.
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M.Sc. Thesis: Phase Transitions and Topological Phases by Driven Dissipation
DownloadPages341Submitted2013
Abstract
One of the most fascinating phenomena in nature surely is the emergence of long range order in initially disordered systems caused by simple local interactions. Transitions between such qualitatively distinct phases are often accompanied by sharp changes in particular quantities of the system when specific parameters are varied. Such collective phenomena that can be triggered by small changes of the system’s configuration are usually referred to as phase transitions.
Whereas statistical physics accounts for the latter in the general framework of classical mechanics, there has also been intense interest in the emergence of phase transitions in quantum mechanical systems. There the critical fluctuations that are responsible for the appearance of collective order can be caused by quantum fluctuations only — at zero temperature! In this context one speaks of quantum phases and quantum phase transitions.
In recent years it was realized by the scientific community that there are quantum phases that elude a characterization by local properties. There the order is “hidden” in more intricate structures that are features of the incredible complexity that characterises various sectors of the system Hilbert spaces. Such systems are referred to as topologically ordered.
Another aspect of topology that has found broad acceptance in condensed matter physics is concerned with systems that exhibit a remarkable resilience about local disorder. Their ground states feature long range entanglement and their Hamiltonians are characterised by topological invariants that account for the aforementioned stability. This outlines the field of topological phases which has been (and is still) a vivid area of research.
A few years ago it was realized that both — topologically ordered systems and topological phases — may be applicable to the great quest of quantum engineering, namely the search for scalable and stable quantum memories that prevent coherent states from decoherence. The emergence of topological quantum memories bridged the domains of quantum information theory and condensed matter physics.
All these concepts are usually treated as part of the Hamiltonian framework of closed quantum systems. Originally promoted by the quantum optics community, the mathematical description and physical investigation of open quantum systems has seen considerable progress in the last decades. Only lately physicists started to think about combining features of dissipatively driven systems and topology related properties.
This thesis is concerned with various topics, all of which relate to the outlined subject matters above. The major structure is two-part: In the first and most comprehensive part, constituted by Chapter 2 and 3, we deal with quantum phases and their dissipative counterparts. In particular, we construct dissipative versions of the paradigmatic transverse field Ising model and a more sophisticated instance, the $\mathbb{Z}_2$-Gauge-Higgs model which is related to topological order.
In the additional second part, namely Chapter 4 and 5, we deal once more with the dissipative counterpart of a well-known Hamiltonian theory: the Majorana chain which is a paradigmatic example for a topological phase. We discuss and criticize recent results regarding the dissipative realization of the Majorana chain and subsequently investigate a possible dissipatively driven, self-correcting quantum memory. We conclude that the straightforward dissipative implementation of the Majorana chain does not yield a self-stabilizing quantum memory.
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PhD Thesis: One-Dimensional Topological States of Synthetic Quantum Matter
DownloadPages600Submitted2019
Abstract
This thesis is based on a collection of papers and addresses several questions on properties and applications of “topological matter,” a concept that drives a particularly active and increasingly complex field of condensed matter physics. If the reader is familiar with this field, there is nothing new I can tell in the few paragraphs of an abstract; if he or she is not familiar with the field, an abstract cannot do justice to the complexity of the field anyway. In any case, I recommend reading 1.1 and 1.3 which provide a self-contained and fairly comprehensive review of “topological matter,” its properties and possible applications.
So let me start right away with a structured abstract of the contents:
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In Chapter 1, we review the theoretical foundations of this thesis and locate it within the ever-growing field of condensed matter physics. We start with an introduction to the general concept of topological quantum phases and discuss the role played by symmetries in this context. We address the classification of topological phases with and without interactions between their fermionic or bosonic constituents. Then, we discuss two paradigmatic models — the Su-Schrieffer-Heeger chain and the Majorana chain — as examples of non-interacting topological phases in one dimension. Both models are closely related and used repeatedly in this thesis, either as motivation for or key element of the presented projects. Finally, we review various proposals for applications of topological phases — both quantum and classical — to demonstrate that the concept is more than a theorist’s delight. We briefly comment on experimental results to make contact with the real world.
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In Chapter 2, we study a microscopic model of interacting fermions with topologically protected ground state degeneracy. The model, introduced in Ref. [1], is based on a double-wire setup with local interactions in a number-conserving setting. A compelling property of this model is the exact solvability for its ground states and low-energy excitations. We demonstrate the appearance of topologically protected edge states and derive their braiding properties on a microscopic level. We find the non-abelian statistics of Ising anyons which can be interpreted as Majorana-like edge states. As a result, the model qualifies as a number-conserving relative of Kitaev’s paradigmatic Majorana chain.
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In Chapter 3, we show that a linear network of coupled bosonic degrees of freedom, characterized by topological bands, can be employed for the efficient exchange of quantum information. Features of the proposed setup, published in Ref. [2], are that it is robust against quenched disorder, all relevant operations can be performed by global variations of parameters, and the time required for communication between qubits approaches linear scaling with their distance. We show how the proposed concept can be extended to an ensemble of qubits embedded in a two-dimensional network to allow for communication between all of them.
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In Chapter 4, we focus on the application of the one-dimensional Majorana chain as a topological quantum memory and construct a strictly local decoder based on a self-dual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. These results, published in Ref. [3], pave the way for scalable and modular designs of actively corrected one-dimensional topological quantum memories.
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Chapter 5 is a safe haven for all projects that do not deserve their own chapter but are still interesting enough to be discussed somewhere. Some — mostly conceptual — are possible starting points for future projects, some are closely related to projects of the main part, and some are contributions to publications (in particular Ref. [4]) that are not covered in the other chapters.
See also my popular summaries in German or English (for non-physicists) or my brief summary (in German). -