From Spin Liquids to non-Abelions in Synthetic Quantum Systems

• Ashvin Vishwanath (Harvard U.)

Strategies for simulating gauge theories with NISQ machines

• Alessio Celi (Universitat Autònoma de Brcelona)

Gauge theories represent a fierce challenge and an amazing opportunity for quantum simulation. Up to date, proof-of-principle experiments have been limited to gauge theories in one spatial dimension. In this talk, I will focus on three key problems encountered in simulating gauge theories beyond one spatial dimension: I) the realization of magnetic interactions, II) the ability to “take the continuum limit” with finite resources, and III) the preparation of a targeted state. I will also report about the simulation of topological gauge theories in the continuum.

Initializing the ground state of lattice gauge theories with the quantum approximate optimization algorithm

• Michele Burrello (Niels Bohr Institute (Copenhagen))

I discuss the implementation of a two-dimensional $Z_2$ lattice gauge theory on a shallow quantum circuit, suitable for near-term quantum computers. The ground state preparation of this model is numerically analyzed on a small lattice with a variational quantum algorithm, the quantum approximate optimization algorithm, which requires a small number of parameters to reach high fidelities and can be efficiently scaled up on larger systems. Despite the reduced size of the considered lattices (up to 5x5), a transition between confined and deconfined regimes can be detected by measuring the expectation values of Wilson loop operators or the topological entropy. Moreover, if periodic boundary conditions are implemented, the same optimal solution is transferable among all four different topological sectors, without any need for further optimization on the variational parameters. These results show that variational quantum algorithms provide a useful technique to be added in the growing toolbox for digital simulations of lattice gauge theories.

Hardware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms

• Torsten Zache (Institute for Theoretical Physics, University of Innsbruck & IQOQI, Austrian Academy of Sciences)

Non-abelian gauge theories underlie our understanding of fundamental forces in nature, and developing tailored quantum hardware and algorithms to simulate them is an outstanding challenge in the rapidly evolving field of quantum simulation. In this talk, I will present an approach where gauge fields, discretized in spacetime, are represented by qudits and are time-evolved in Trotter steps with multiqudit quantum gates. This maps naturally and hardware-efficiently to an architecture based on Rydberg tweezer arrays, where long-lived internal atomic states represent qudits, and the required quantum gates are performed as error-tolerant holonomic operations supported by a Rydberg blockade mechanism. Our proposal is illustrated for a minimal digitization of non-abelian gauge fields via a finite subgroup of SU(2). Ref.: arXiv:2203.15541

Fifty years of Ising lattice gauge theory

• Franz Wegner (Ruprecht-Karls University Heidelberg)

I review the introduction of the gauge invariant Ising model and my motivation based on my 1971 paper "Duality in generalized Ising Models and Phase Transitions without Local Order Parameter". I start with the exact determination of the critical temperature of the two-dimensional Ising model on the square lattice by Kramers and Wannier 1941 before Onsager gave the exact solution for this model in 1944. The basic idea was that this model was self-dual. Therefore I thought whether something similar could be done for the three-dimensional model. I realized that the dual model is a gauge-invariant model , but it is not self-dual. Increasing the number of dimensions from three to four the gauge-invariant model is self-dual and its critical temperature is the same as for the two-dimensional conventional model. The gauge-invariant model has the property that it has no local order parameter. Non-vanishing correlations are given by products of spins along a loop, called Wilson loop. The expectation value obeys at high temperatures an area law and at low temperatures a perimeter law I mention the dual of the correlations and if time permits some further related work.

Z2 gauge theory: self-duality, criticality, and emergent order parameters

• Adam Nahum (CNRS & Ecole Normale Superieure Paris)

Simulatable models of Quantum Criticality in Heavy Fermion Systems

• Tarun Grover (University of California San Diego)

The fermion sign problem tends to stymie exploration of highly entangled phases of matter such as interacting fermions at finite density. In this talk, I will present recent progress in simulating Fermi and non-Fermi liquids in the context of Kondo lattice systems. I will also discuss analytical results on quantum criticality in related models, and a few ideas on diagnosing Kondo breakdown.

DYNAMITE: Next Generation Quantum Simulators: From DYNAMIcal Gauge Fields to Lattice Gauge ThEory

• Maciej Lewenstein (ICFO and ICREA)

I will present review of recent progress on theory of quantum simulators of gauge theories in the Quantum Optic Group at ICFO. In particular, I will talk about the following papers: 1) Titas Chanda, Maciej Lewenstein, Jakub Zakrzewski, and Luca Tagliacozzo, On the phase diagram of 1+1D Abelian-Higgs model and its critical point, Phys. Rev. Lett. 128, 090601 (2022); 2) Adith Sai Aramthottil, Utso Bhattacharya, Daniel González-Cuadra, Maciej Lewenstein, Luca Barbiero, and Jakub Zakrzewski, Scar States in Deconfined Z2 Lattice Gauge Theories, arXiv:2201.10260v1; 3) L. Ziegler, E. Tirrito, M. Lewenstein, S. Hands, and A. Bermudez, Correlated Chern insulators in two-dimensional Raman lattices: a cold-atom regularization of strongly-coupled four-Fermi field theories; arXiv:2011.08744.

Quantum simulation of Z2 lattice gauge theory with dynamical matter

• Fabian Grusdt (LMU Munich)

Z2 lattice gauge theories (LGTs) coupled to dynamical matter show rich physics, including topological phases with anyons (toric code) and fractionalized Fermi liquids, with potential realizations in strongly correlated quantum matter. In this talk I report on recent progress — theoretical and experimental — in performing analog quantum simulations of such models. Starting from several distinct zero-dimensional building blocks I will move on to discuss extensions to extended 1D and 2D systems, including the realization of the plaquette operators in 2D. Next I will discuss how experimental imperfects, such as gauge-symmetry breaking errors, impact quantum simulations, and how they can be overcome. Then I will show how the insights gained lead us to an inherently stable protocol for quantum simulations of Z2 LGTs with dynamical matter with existing Rydberg tweezer arrays. I will close with an outlook and by discussing possible near-term experimental goals ranging from disorder-free localization to finite-temperature deconfinement transitions.

Insight on gauge theories from MPS

• Luca Tagliacozzo (Instituto de Fisica Fundamental IFF-CSIC)

I will review some of the recent results we have obtained by performing MPS simulations of Abelian gauge theories in 1D

Stabilization and engineering of exotic far-from-equilibrium gauge-theory phenomena

• Jad Halimeh (Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig Maximilian University of Munich)

In recent years, exotic far-from-equilibrium phenomena have been discovered that lead to novel paradigms in condensed matter and particle physics, with salient examples ranging from string breaking to quantum many-body scarred dynamics and disorder-free localization. Underlying many of these phenomena are gauge symmetries, which endow their host models with rich dynamical behavior arising from the plethora of underlying local constraints. The high level of control and precision in today’s synthetic quantum matter experiments has facilitated first attempts at realizing gauge theories. However, a major challenge in this endeavor is stabilizing the core property of these models, gauge symmetry. We will discuss our recent work on gauge protection schemes based on the concept of quantum Zeno dynamics, which reliably stabilize gauge symmetries and also protect salient dynamical features such as disorder-free localization. We will also discuss the concept of local pseudogenerators, which are experimentally feasible simplifications of the actual gauge-symmetry generators. In concert with the quantum Zeno effect, they can be used to enhance disorder-free localization through the dynamical emergence of a gauge theory with an enriched local symmetry. Finally, we discuss recent experimental work based on our schemes, and also present our new experimental proposals that are undergoing implementation.

Qubit Regularization, Qubit Embedding Algebra and Asymptotic Freedom

• Shailesh Chandrasekharan (Duke University)

Quantum computation of quantum field theories requires one to regularize the local lattice Hilbert space. We define this type of regularization as Qubit Regularization. This naturally leads to the concept of a Qubit Embedding Algebra (QEA) which replaces the traditional symmetry algebra. We derive some QEAs for lattice spin models and gauge theories. We discover a simple qubit regularization of the two dimensional O(3) non-linear sigma model and show asymptotic freedom emerging from it. We contrast this discovery with the D-theory approach to asymptotic freedom.

Cold-atom regularizations of relavistic 4-Fermi QFTs: Exploring correlated topological phases

• Alejandro Bermudez (Instituto de Fisica Teorica, CSIC-UAM)

Theory of Oblique Topological Insulators

• Eduardo Fradkin (University of Illinois)

I will discuss a theory of topological insulators with topological order. The topological field theory exhibits oblique confinement with a universal "magneto-electric" response to background two-form probe fields. I will discuss the relation of this system with a lattice gauge theory of Z_N gauge fields with a 𝜃 term.

Probing confinement in a Z2 lattice gauge theory on a Sycamore chip

• Philipp Hauke (University of Trento)

Digital quantum simulators provide a table-top platform for addressing salient questions in lattice gauge theories (LGTs). In this talk, I will present a recent work where we implemented a Z2 lattice gauge theory on the Google Sycamore chips within the Google Early Access Program. We synthesize the charge--gauge-field interaction using only 6 native two-qubit gates, enabling us to reach simulation times of up to 25 Trotter steps. We observe how tuning a term that couples only to the electric field confines the charges, a manifestation of the tight bond that the local gauge constraint generates between both. Moreover, we study a different mechanism, where a modification of the gauge constraint from a Z2 to U(1) symmetry freezes the system dynamics. This modification is achieved by the addition of a linear symmetry protecting term, illustrating also the potential power of protecting gauge symmetries via energy penalties. Our work showcases the dramatic restriction that the underlying gauge constraint imposes on the dynamics of an LGT and it illustrates how gauge constraints can be modified and protected.

Trimer resonating-valence-bond states with $Z_3$ topological order in Rydberg atom arrays

• Federica Maria Surace (Caltech)

When quantum fluctuations meet an extensive classical degeneracy, exotic strongly correlated states can arise. Paradigmatic examples are resonating valence bond (RVB) states of hard dimers. They are defined as equal weight quantum superpositions of all dimer coverings with one dimer entering each vertex of a lattice. In this work, we consider RVB states of hard trimers (tRVB), which are objects made up of two nearest-neighbor edges of a lattice that cannot share a common vertex. On certain lattices, tRVB states are known to be gapped and to possess a form of topological order with emergent $Z_3$ gauge symmetry, and thus to be good representatives of a quantum phase with $Z_3$ topological order. Here, we identify a necessary condition for having a gapped tRVB state with $Z_3$ topological order, similar to the condition of non-bipartite lattices for dimer models. Moreover, we propose and analyze a possible implementation of the trimer constraint in an array of Rydberg atoms.

Numerical simulations of Dirac Systems

• Fakher Assaad (University of Würzburg)

Exploring fermionic deconfinement in near-term quantum simulators

• Daniel González-Cuadra (University of Innsbruck, IQOQI)

Topologically ordered phases of matter, although stable against local perturbations, are usually restricted to relatively small regions in phase diagrams. Thus, their preparation requires a precise fine-tunning of the system’s parameters, a very challenging task in most experimental setups. In this talk, I will present a model of spinless fermions interacting with dynamical Z2 gauge fields on a cross-linked ladder [1] and show evidence of topological order throughout the full parameter space. In particular, I will show how a magnetic flux is spontaneously generated through the ladder due to an Aharonov-Bohm instability, giving rise to topological order even in the absence of a plaquette term. Moreover, the latter coexists here with a symmetry-protected topological phase in the matter sector, which displays fractionalized gauge-matter edge states and intertwines with it by a flux-threading phenomenon. Finally, I will explain the robustness of these features through a gauge frustration mechanism, akin to geometric frustration in spin liquids, allowing topological order to survive to arbitrarily large quantum fluctuations. In particular, I will show how, at finite chemical potential, topological solitons are created in the gauge field configuration, which bound to fermions and form Z2 deconfined quasiparticles. The simplicity of the model makes it an ideal candidate for 2D gauge theory phenomena, as well as exotic topological effects, to be investigated using cold-atom quantum simulators. [1] D. González-Cuadra et al., Phys. Rev. X 10, 041007 (2020)

Deconfined Z2 gauge theory in Rydberg atom arrays

• Subir Sachdev (Harvard University)

Pumped Rydberg atoms trapped in arrays of optical tweezers realize systems of individually controllable qubits with strong interactions. I will describe recent theory and experiments on Z2 spin liquids, which are deconfined phases of Z2 gauge theory in 2+1 dimensions

Hyperbolic band theory

• Joseph Maciejko (University of Alberta)

Translation enriched Z2 topological orders and thermal hall from topological vison bands

• Xueyang Song (MIT)

Motivated by recent thermal hall measurements in a putative quantum spin liquid state(alpha-RuCl3), we explore Z_2 gauge theory where vison excitations induce thermal hall currents. We classify the symmetry-enriched Z2 topological(SET) order with translations. Among the 9 SET classes, we identify classes where a chern band for visons is forbidden. Applied to spin-1/2 systems with a slave-particle construction, we construct vison models which describe fully frustrated Ising paramagnet (FFIM), on square, honeycomb and Kagome lattices, that yield a Chern band and could contribute to thermal hall effects. Last, a Z2 gauge model with background visons, that aligns with the phenomenology of alpha-RuCl3 is demonstrated to yield thermal hall conductivity from visons similar to measured.

Gauge theoretic origin of Rydberg spin liquids

• Marcello Dalmonte (ICTP)

TBA

• Zi Yang Meng (The University of Hong Kong)

Disorder-free localization in lattice gauge theories

• Markus Heyl (University of Augsburg)

Gauge theories play an interdisciplinary, fundamental role in physics, ranging from the study of elementary particles all the way to strongly correlated and topological quantum matter. While their equilibrium properties have been explored extensively for decades, their nonequilibrium quantum real-time dynamics has attracted significant attention rather recently, driven particularly by strong experimental efforts in so-called quantum simulators. In this talk I will show how the inherent local gauge symmetries can impose such a strong constraint so that lattice gauge theories exhibit a new form of localization without the need of disorder. I will discuss how even interacting two-dimensional lattice gauge theories can become nonergodic and I will present an accurate characterization of the associated quantum localization transition. I will further outline the potential to realize new phase structures both in quantum simulators and solid state systems.

Can long-range entangled deconfined gauge theories be created with finite-depth unitaries and single-site measurements?

• Ruben Verresen (Harvard University)

RVB and Z2 topological order in a simple spin model

• Ribhu Kaul (University of Kentucky)

Many-body quantum scars in Abelian lattice gauge theories

• Debasish Banerjee (Saha Institute of Nuclear Physics)

Exploring topological matter and lattice gauge theories using programmable quantum simulators

• Mikhail Lukin (Harvard)

We will discuss the recent advances and new opportuning involving programmable, coherent manipulation of quantum many-body systems for probing topological matter and simulating lattice gauge theories. As a specific example, we will consider neutral atom arrays excited into Rydberg states and we will describe the realization and probing of quantum spin liquid states - the exotic topological states of matter have thus far evaded direct experimental detection. In addition, we will discuss a hybrid analog-digital quantum architecture that can be used for probing entanglement dynamics, simulating complex models and exploring both abelian and non-abelian braiding statistics. Prospects for using these techniques to enable large-scale quantum simulations of lattice gauge theories will be discussed.

Towards quantum simulation of U(1) LGTs with alkaline-earth-like atoms

• Monika Aidelsburger (LMU Munich)

One of the main challenges for the simulation of lattice gauge theories with cold atoms in optical lattices is to find resource-efficient implementations of the required local symmetries. Despite the recent experimental progress, there is no clear path towards implementations of lattice gauge theories in extended systems beyond one dimension or with non-Abelian symmetries. Here, I report on the development of a new hybrid optical lattice-tweezer platform that combines local state-dependent control of tunnel couplings with the unique properties of fermionic alkaline-earth-like atoms to realize U(1) lattice gauge theories coupled to matter. Moreover, the SU(N) symmetric interactions of fermionic 173Yb atoms pave the way towards novel schemes for the realization of more complex non-Abelian symmetries. Our scheme relies on correlated tunneling of fermionic atoms in a state-dependent programmable optical lattice. We have performed ab initio calculations of the lattice gauge theory dynamics, identifying suitable parameter regimes. On the experimental side we have performed measurements of the required laser wavelengths, which is the first step towards building the final lattice setup.

Disorder-free localisation and confinement dynamics

• Johannes Knolle (TU Munich)

Qubit alive thanks to the anomaly

• Enrique Rico Ortega (Ikerbasque & UPV/EHU)

We present an exact full symmetry analysis of the 0-π superconducting circuit. We identify points in control parameter space of enhanced anomalous symmetry, which imposes robust twofold degeneracy of its ground state, that is for all values of the energy parameters of the model. We show, both analytically and numerically, how this anomalous symmetry is maintained in the low-energy sector, thus providing us with a strong candidate for robust qubit engineering.

Properties of the winding number sectors in the U(1) quantum link model

• Paolo Stornati (ICFO)

Discussion