
M. K. Joshi, C. Kokail, R. van Bijnen, F. Kranzl, T. Zache, R. Blatt, C. F. Roos, P. Zoller Exploring LargeScale Entanglement in Quantum Simulation,
Nature 624 539 (20231129),
http://dx.doi.org/10.1038/s41586023067680 doi:10.1038/s41586023067680 (ID: 721080)
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Entanglement is a distinguishing feature of quantum manybody systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science. Here we perform experimental investigations of entanglement based on the entanglement Hamiltonian, as an effective description of the reduced density operator for large subsystems. We prepare ground and excited states of a 1D XXZ Heisenberg chain on a 51ion programmable quantum simulator and perform sampleefficient `learning' of the entanglement Hamiltonian for subsystems of up to 20 lattice sites. Our experiments provide compelling evidence for a local structure of the entanglement Hamiltonian. This observation marks the first instance of confirming the fundamental predictions of quantum field theory by Bisognano and Wichmann, adapted to lattice models that represent correlated quantum matter. The reduced state takes the form of a Gibbs ensemble, with a spatiallyvarying temperature profile as a signature of entanglement. Our results also show the transition from area to volumelaw scaling of Von Neumann entanglement entropies from ground to excited states. As we venture towards achieving quantum advantage, we anticipate that our findings and methods have wideranging applicability to revealing and understanding entanglement in manybody problems with local interactions including higher spatial dimensions.

T. Zache, D. Gonzalez Cuadra, P. Zoller Quantum and classical spin network algorithms for qdeformed KogutSusskind gauge theories,
Phys. Rev. Lett. 131 171902 (20231024),
http://dx.doi.org/10.1103/PhysRevLett.131.171902 doi:10.1103/PhysRevLett.131.171902 (ID: 721075)
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Treating the infinitedimensional Hilbert space of nonabelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we introduce qdeformed KogutSusskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. In contrast to other formulations, our proposal simultaneously provides a controlled regularization of the infinitedimensional local Hilbert space while preserving essential symmetryrelated properties. This enables the development of both quantum as well as quantuminspired classical Spin Network Algorithms for qdeformed gauge theories (SNAQs). To be explicit, we focus on SU(2)k gauge theories, that are controlled by the deformation parameter k and converge to the standard SU(2) KogutSusskind model as k→∞. In particular, we demonstrate that this formulation is well suited for efficient tensor network representations by variational groundstate simulations in 2D, providing first evidence that the continuum limit can be reached with k=O(10). Finally, we develop a scalable quantum algorithm for Trotterized realtime evolution by analytically diagonalizing the SU(2)k plaquette interactions. Our work gives a new perspective for the application of tensor network methods to highenergy physics and paves the way for quantum simulations of nonabelian gauge theories far from equilibrium where no other methods are currently available.

T. Zache, D. GonzálezCuadra, P. Zoller Fermionqudit quantum processors for simulating lattice gauge theories with matter,
Quantum 7 1140 (20231016),
http://dx.doi.org/10.22331/q202310161140 doi:10.22331/q202310161140 (ID: 721067)
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Simulating the realtime dynamics of lattice gauge theories, underlying the Standard Model of particle physics, is a notoriously difficult problem where quantum simulators can provide a practical advantage over classical approaches. In this work, we present a complete Rydbergbased architecture, codesigned to digitally simulate the dynamics of general gauge theories coupled to matter fields in a hardwareefficient manner. Ref. [1] showed how a qudit processor, where nonabelian gauge fields are locally encoded and timeevolved, considerably reduces the required simulation resources compared to standard qubitbased quantum computers. Here we integrate the latter with a recently introduced fermionic quantum processor [2], where fermionic statistics are accounted for at the hardware level, allowing us to construct quantum circuits that preserve the locality of the gaugematter interactions. We exemplify the flexibility of such a fermionqudit processor by focusing on two paradigmatic highenergy phenomena. First, we present a resourceefficient protocol to simulate the AbelianHiggs model, where the dynamics of confinement and string breaking can be investigated. Then, we show how to prepare hadrons made up of fermionic matter constituents bound by nonabelian gauge fields, and show how to extract the corresponding hadronic tensor. In both cases, we estimate the required resources, showing how quantum devices can be used to calculate experimentallyrelevant quantities in particle physics.

D. GonzálezCuadra, D. Bluvstein, M. Kalinowski, C. R. Kaubrügger, N. Maskara, P. Naldesi, T. Zache, A. Kaufman, M. Lukin, H. Pichler, B. Vermersch, J. Ye, P. Zoller Fermionic quantum processing with programmable neutral atom arrays,
PNAS 120 e2304294120 (20230822),
http://dx.doi.org/10.1073/pnas.2304294120 doi:10.1073/pnas.2304294120 (ID: 721066)
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Simulating the properties of manybody fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics. Although qubitbased quantum computers can potentially tackle this problem more efficiently than classical devices, encoding nonlocal fermionic statistics introduces an overhead in the required resources, limiting their applicability on nearterm architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardwareefficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement nonlocal tunneling gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydbergmediated interaction gates, to find efficient circuit decompositions for digital and variational quantum simulation algorithms, illustrated here for molecular energy estimation. Finally, we consider a combined fermionqubit architecture, where both the motional and internal degrees of freedom of the atoms are harnessed to efficiently implement quantum phase estimation, as well as to simulate lattice gauge theory dynamics.

J. . Halimeh, M. Van Damme, T. Zache, D. Banerjee, P. Hauke Achieving the quantum field theory limit in farfromequilibrium quantum link models,
Quantum 6 878 (20221219),
http://dx.doi.org/10.22331/q20221219878 doi:10.22331/q20221219878 (ID: 720766)
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Realizations of gauge theories in setups of quantum synthetic matter open up the possibility of probing salient exotic phenomena in condensed matter and highenergy physics, along with potential applications in quantum information and science technologies. In light of the impressive ongoing efforts to achieve such realizations, a fundamental question regarding quantum link model regularizations of lattice gauge theories is how faithfully they capture the quantum field theory limit of gauge theories. Recent work [Zache, Van Damme, Halimeh, Hauke, and Banerjee, (arXiv:2104.00025)] has shown through analytic derivations, exact diagonalization, and infinite matrix product state calculations that the lowenergy physics of U(1) quantum link models approaches the quantum field theory limit already at small link spin length S. Here, we show that the approach to this limit also lends itself to the farfromequilibrium quench dynamics of lattice gauge theories, as demonstrated by our numerical simulations of the Loschmidt return rate and the chiral condensate in infinite matrix product states, which work directly in the thermodynamic limit. Similar to our findings in equilibrium that show a distinct behavior between halfinteger and integer link spin lengths, we find that criticality emerging in the Loschmidt return rate is fundamentally different between halfinteger and integer spin quantum link models in the regime of strong electricfield coupling. Our results further affirm that stateoftheart finitesize ultracoldatom and NISQdevice implementations of quantum link lattice gauge theories have the real potential to simulate their quantum field theory limit even in the farfromequilibrium regime.

A. Kruckenhauser, R. van Bijnen, T. Zache, M. Di Liberto, P. Zoller Highdimensional SO(4)symmetric Rydberg manifolds for quantum simulation,
Quantum Sci. Technol. 8 (20221219),
http://dx.doi.org/10.1088/20589565/aca996 doi:10.1088/20589565/aca996 (ID: 720885)
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We develop a toolbox for manipulating arrays of Rydberg atoms prepared in highdimensional hydrogenlike manifolds in the regime of linear Stark and Zeeman effect. We exploit the SO(4) symmetry to characterize the action of static electric and magnetic fields as well as microwave and optical fields on the wellstructured manifolds of states with principal quantum number n. This enables us to construct generalized largespin Heisenberg models for which we develop statepreparation and readout schemes. Due to the available large internal Hilbert space, these models provide a natural framework for the quantum simulation of Quantum Field Theories, which we illustrate for the case of the sineGordon and massive Schwinger models. Moreover, these highdimensional manifolds also offer the opportunity to perform quantum information processing operations for quditbased quantum computing, which we exemplify with an entangling gate and a statetransfer protocol for the states in the neighborhood of the circular Rydberg level.

M. Van Damme, T. Zache, D. Banerjee, P. Hauke, J. . Halimeh Dynamical quantum phase transitions in spinS U(1) quantum link models,
Phys. Rev. B 106 (20221208),
http://dx.doi.org/10.1103/PhysRevB.106.245110 doi:10.1103/PhysRevB.106.245110 (ID: 721052)
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Dynamical quantum phase transitions (DQPTs) are a powerful concept of probing farfromequilibrium criticality in quantum manybody systems. With the strong ongoing experimental drive to quantum simulate lattice gauge theories, it becomes important to investigate DQPTs in these models in order to better understand their farfromequilibrium properties. In this work, we use infinite matrix product state techniques to study DQPTs in spinS U(1) quantum link models. Although we are able to reproduce literature results directly connecting DQPTs to a sign change in the dynamical order parameter in the case of S=1/2 for quenches starting in a vacuum initial state, we find that for different quench protocols or different values of the link spin length S>1/2 this direct connection is no longer present. In particular, we find that there is an abundance of different types of DQPTs not directly associated with any sign change of the order parameter. Our findings indicate that DQPTs are fundamentally different between the WilsonKogutSusskind limit and its representation through the quantum link formalism.

T. Zache, M. Van Damme, J. . Halimeh, P. Hauke, D. Banerjee Toward the continuum limit of a (1+1)D quantum link Schwinger model,
Phys. Rev. D 106 L091502 (20221103),
http://dx.doi.org/10.1103/PhysRevD.106.L091502 doi:10.1103/PhysRevD.106.L091502 (ID: 720772)
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The solution of gauge theories is one of the most promising applications of quantum technologies. Here, we discuss the approach to the continuum limit for U(1) gauge theories regularized via finitedimensional Hilbert spaces of quantum spinS operators, known as quantum link models. For quantum electrodynamics (QED) in one spatial dimension, we numerically demonstrate the continuum limit by extrapolating the ground state energy, the scalar, and the vector meson masses to large spin lengths S, large volume N, and vanishing lattice spacing a. By exactly solving Gauss’s law for arbitrary S, we obtain a generalized PXP spin model and count the physical Hilbert space dimension analytically. This allows us to quantify the required resources for reliable extrapolations to the continuum limit on quantum devices. We use a functional integral approach to relate the model with large values of halfinteger spins to the physics at topological angle Θ=π. Our findings indicate that quantum devices will in the foreseeable future be able to quantitatively probe the QED regime with quantum link models.

Daniel GonzálezCuadra , T. Zache, J. Carrasco, Barbara Kraus, Peter Zoller Hardware efficient quantum simulation of nonabelian gauge theories with qudits on Rydberg platforms,
Phys. Rev. Lett. 129 160501 (20221013),
http://dx.doi.org/10.1103/PhysRevLett.129.160501 doi:10.1103/PhysRevLett.129.160501 (ID: 720827)

T. Zache, C. Kokail, B. Sundar, P. Zoller Entanglement Spectroscopy and probing the LiHaldane Conjecture in Topological Quantum Matter,
Quantum 6 702 (20220427),
http://dx.doi.org/10.22331/q20220427702 doi:10.22331/q20220427702 (ID: 720692)
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Topological phases are characterized by their entanglement properties, which is manifest in a direct relation between entanglement spectra and edge states discovered by Li and Haldane. We propose to leverage the power of synthetic quantum systems for measuring entanglement via the Entanglement Hamiltonian to probe this relationship experimentally. This is made possible by exploiting the quasilocal structure of Entanglement Hamiltonians. The feasibility of this proposal is illustrated for two paradigmatic examples realizable with current technology, an integer quantum Hall state of noninteracting fermions on a 2D lattice and a symmetry protected topological state of interacting fermions on a 1D chain. Our results pave the road towards an experimental identification of topological order in strongly correlated quantum manybody systems.

A. M. Green, A. Elben, C. Huerta Alderete, L. K. Joshi, N. H. Nguyen, T. Zache, Y. Zhu, B. Sundar, N. M. Linke Experimental measurement of outoftimeordered correlators at finite temperature,
Phys. Rev. Lett. 128 (20220406),
http://dx.doi.org/10.1103/PhysRevLett.128.140601 doi:10.1103/PhysRevLett.128.140601 (ID: 720746)
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Outoftimeordered correlators (OTOCs) are a key observable in a wide range of interconnected fields including manybody physics, quantum information science, and quantum gravity. The ability to measure OTOCs using nearterm quantum simulators will extend our ability to explore fundamental aspects of these fields and the subtle connections between them. Here, we demonstrate the first experimental measurement of OTOCs at finite temperatures and study their temperature dependence. These measurements are performed on a digital quantum computer running a simulation of the transverse field Ising model. Our flexible method, based on the creation of a thermofield double state, can be extended to other models and enables us to probe the OTOC's temperaturedependent decay rate. Measuring this decay rate opens up the possibility of testing the fundamental temperaturedependent bounds on quantum information scrambling.

V. Kuzmin, T. Zache, L. Pastori, A. Celi, M. Baranov, P. Zoller Probing infinite manybody quantum systems with finite size quantum simulators,
PRX Quantum 3 20304 (20220406),
http://dx.doi.org/10.1103/PRXQuantum.3.020304 doi:10.1103/PRXQuantum.3.020304 (ID: 720681)
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Experimental studies of synthetic quantum matter are necessarily restricted to approximate ground states prepared on finitesize quantum simulators, which limits their reliability for strongly correlated systems, for instance in the vicinity of a quantum phase transition (QPT). Here, we propose a protocol that makes optimal use of a given finite system size by directly preparing, via coherent evolution with a local deformation of the system Hamiltonian, a part of the translationinvariant infinitesized system as a mixed state representing the reduced density operator. For systems of free fermions in one and two spatial dimensions, we illustrate and explain the underlying physics, which consists of quasiparticle transport towards the system's boundaries while retaining the bulk "vacuum". For the example of a nonintegrable extended SuSchriefferHeeger model, we demonstrate that our protocol enables a more accurate study of QPTs.

B. Sundar, A. Elben, L. K. Joshi, T. Zache Proposal for measuring outoftimeordered correlators at finite temperature with coupled spin chains,
New J. Phys. 24 23037 (20220225),
http://dx.doi.org/10.1088/13672630/ac5002 doi:10.1088/13672630/ac5002 (ID: 720675)
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Information scrambling, which is the spread of local information through a system's manybody degrees of freedom, is an intrinsic feature of manybody dynamics. In quantum systems, the outoftimeordered correlator (OTOC) quantifies information scrambling. Motivated by experiments that have measured the OTOC at infinite temperature and a theory proposal to measure the OTOC at finite temperature using the thermofield double state, we describe a protocol to measure the OTOC in a finite temperature spin chain that is realized approximately as one half of the ground state of two moderatelysized coupled spin chains. We consider a spin Hamiltonian with particlehole symmetry, for which we show that the OTOC can be measured without needing signreversal of the Hamiltonian. We describe a protocol to mitigate errors in the estimated OTOC, arising from the finite approximation of the system to the thermofield double state. We show that our protocol is also robust to main sources of decoherence in experiments.

L. Gresista, T. Zache, J. Berges Dimensional crossover for universal scaling far from equilibrium,
Phys. Rev. A 105 13320 (20220126),
http://dx.doi.org/10.1103/PhysRevA.105.013320 doi:10.1103/PhysRevA.105.013320 (ID: 720770)
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We perform a dynamical finitesize scaling analysis of a nonequilibrium Bose gas which is confined in the transverse plane. Varying the transverse size, we establish a dimensional crossover for universal scaling properties far from equilibrium. Our results suggest that some aspects of the dynamical universal behavior of anisotropic systems can be classified in terms of fractional spatial dimensions. We discuss our findings in view of recent experimental results with quasi onedimensional setups of quenched ultracold quantum gases.