-
M. K. Joshi, C. Kokail, R. van Bijnen, F. Kranzl, T. Zache, R. Blatt, C. F. Roos, P. Zoller Exploring Large-Scale Entanglement in Quantum Simulation,
Nature 624 539 (2023-11-29),
http://dx.doi.org/10.1038/s41586-023-06768-0 doi:10.1038/s41586-023-06768-0 (ID: 721080)
Toggle Abstract
Entanglement is a distinguishing feature of quantum many-body 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 51-ion programmable quantum simulator and perform sample-efficient `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 spatially-varying temperature profile as a signature of entanglement. Our results also show the transition from area to volume-law 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 wide-ranging applicability to revealing and understanding entanglement in many-body problems with local interactions including higher spatial dimensions.
-
T. Zache, D. Gonzalez Cuadra, P. Zoller Quantum and classical spin network algorithms for q-deformed Kogut-Susskind gauge theories,
Phys. Rev. Lett. 131 171902 (2023-10-24),
http://dx.doi.org/10.1103/PhysRevLett.131.171902 doi:10.1103/PhysRevLett.131.171902 (ID: 721075)
Toggle Abstract
Treating the infinite-dimensional Hilbert space of non-abelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we introduce q-deformed Kogut-Susskind 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 infinite-dimensional local Hilbert space while preserving essential symmetry-related properties. This enables the development of both quantum as well as quantum-inspired classical Spin Network Algorithms for q-deformed 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) Kogut-Susskind model as k→∞. In particular, we demonstrate that this formulation is well suited for efficient tensor network representations by variational ground-state 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 real-time evolution by analytically diagonalizing the SU(2)k plaquette interactions. Our work gives a new perspective for the application of tensor network methods to high-energy physics and paves the way for quantum simulations of non-abelian gauge theories far from equilibrium where no other methods are currently available.
-
T. Zache, D. González-Cuadra, P. Zoller Fermion-qudit quantum processors for simulating lattice gauge theories with matter,
Quantum 7 1140 (2023-10-16),
http://dx.doi.org/10.22331/q-2023-10-16-1140 doi:10.22331/q-2023-10-16-1140 (ID: 721067)
Toggle Abstract
Simulating the real-time 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 Rydberg-based architecture, co-designed to digitally simulate the dynamics of general gauge theories coupled to matter fields in a hardware-efficient manner. Ref. [1] showed how a qudit processor, where non-abelian gauge fields are locally encoded and time-evolved, considerably reduces the required simulation resources compared to standard qubit-based 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 gauge-matter interactions. We exemplify the flexibility of such a fermion-qudit processor by focusing on two paradigmatic high-energy phenomena. First, we present a resource-efficient protocol to simulate the Abelian-Higgs 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 non-abelian 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 experimentally-relevant quantities in particle physics.
-
D. González-Cuadra, 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 (2023-08-22),
http://dx.doi.org/10.1073/pnas.2304294120 doi:10.1073/pnas.2304294120 (ID: 721066)
Toggle Abstract
Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics. Although qubit-based quantum computers can potentially tackle this problem more efficiently than classical devices, encoding non-local fermionic statistics introduces an overhead in the required resources, limiting their applicability on near-term architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement non-local tunneling gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydberg-mediated 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 fermion-qubit 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 far-from-equilibrium quantum link models,
Quantum 6 878 (2022-12-19),
http://dx.doi.org/10.22331/q-2022-12-19-878 doi:10.22331/q-2022-12-19-878 (ID: 720766)
Toggle Abstract
Realizations of gauge theories in setups of quantum synthetic matter open up the possibility of probing salient exotic phenomena in condensed matter and high-energy 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 low-energy 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 far-from-equilibrium 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 half-integer and integer link spin lengths, we find that criticality emerging in the Loschmidt return rate is fundamentally different between half-integer and integer spin quantum link models in the regime of strong electric-field coupling. Our results further affirm that state-of-the-art finite-size ultracold-atom and NISQ-device implementations of quantum link lattice gauge theories have the real potential to simulate their quantum field theory limit even in the far-from-equilibrium regime.
-
A. Kruckenhauser, R. van Bijnen, T. Zache, M. Di Liberto, P. Zoller High-dimensional SO(4)-symmetric Rydberg manifolds for quantum simulation,
Quantum Sci. Technol. 8 (2022-12-19),
http://dx.doi.org/10.1088/2058-9565/aca996 doi:10.1088/2058-9565/aca996 (ID: 720885)
Toggle Abstract
We develop a toolbox for manipulating arrays of Rydberg atoms prepared in high-dimensional hydrogen-like 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 well-structured manifolds of states with principal quantum number n. This enables us to construct generalized large-spin Heisenberg models for which we develop state-preparation 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 sine-Gordon and massive Schwinger models. Moreover, these high-dimensional manifolds also offer the opportunity to perform quantum information processing operations for qudit-based quantum computing, which we exemplify with an entangling gate and a state-transfer 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 spin-S U(1) quantum link models,
Phys. Rev. B 106 (2022-12-08),
http://dx.doi.org/10.1103/PhysRevB.106.245110 doi:10.1103/PhysRevB.106.245110 (ID: 721052)
Toggle Abstract
Dynamical quantum phase transitions (DQPTs) are a powerful concept of probing far-from-equilibrium criticality in quantum many-body 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 far-from-equilibrium properties. In this work, we use infinite matrix product state techniques to study DQPTs in spin-S 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 Wilson-Kogut-Susskind 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 (2022-11-03),
http://dx.doi.org/10.1103/PhysRevD.106.L091502 doi:10.1103/PhysRevD.106.L091502 (ID: 720772)
Toggle Abstract
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 finite-dimensional Hilbert spaces of quantum spin-S 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 half-integer 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 González-Cuadra , T. Zache, J. Carrasco, Barbara Kraus, Peter Zoller Hardware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms,
Phys. Rev. Lett. 129 160501 (2022-10-13),
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 Li-Haldane Conjecture in Topological Quantum Matter,
Quantum 6 702 (2022-04-27),
http://dx.doi.org/10.22331/q-2022-04-27-702 doi:10.22331/q-2022-04-27-702 (ID: 720692)
Toggle Abstract
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 quasi-local 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 non-interacting 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 many-body 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 out-of-time-ordered correlators at finite temperature,
Phys. Rev. Lett. 128 (2022-04-06),
http://dx.doi.org/10.1103/PhysRevLett.128.140601 doi:10.1103/PhysRevLett.128.140601 (ID: 720746)
Toggle Abstract
Out-of-time-ordered correlators (OTOCs) are a key observable in a wide range of interconnected fields including many-body physics, quantum information science, and quantum gravity. The ability to measure OTOCs using near-term 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 temperature-dependent decay rate. Measuring this decay rate opens up the possibility of testing the fundamental temperature-dependent bounds on quantum information scrambling.
-
V. Kuzmin, T. Zache, L. Pastori, A. Celi, M. Baranov, P. Zoller Probing infinite many-body quantum systems with finite size quantum simulators,
PRX Quantum 3 20304 (2022-04-06),
http://dx.doi.org/10.1103/PRXQuantum.3.020304 doi:10.1103/PRXQuantum.3.020304 (ID: 720681)
Toggle Abstract
Experimental studies of synthetic quantum matter are necessarily restricted to approximate ground states prepared on finite-size 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 translation-invariant infinite-sized 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 quasi-particle transport towards the system's boundaries while retaining the bulk "vacuum". For the example of a non-integrable extended Su-Schrieffer-Heeger 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 out-of-time-ordered correlators at finite temperature with coupled spin chains,
New J. Phys. 24 23037 (2022-02-25),
http://dx.doi.org/10.1088/1367-2630/ac5002 doi:10.1088/1367-2630/ac5002 (ID: 720675)
Toggle Abstract
Information scrambling, which is the spread of local information through a system's many-body degrees of freedom, is an intrinsic feature of many-body dynamics. In quantum systems, the out-of-time-ordered 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 moderately-sized coupled spin chains. We consider a spin Hamiltonian with particle-hole symmetry, for which we show that the OTOC can be measured without needing sign-reversal 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 (2022-01-26),
http://dx.doi.org/10.1103/PhysRevA.105.013320 doi:10.1103/PhysRevA.105.013320 (ID: 720770)
Toggle Abstract
We perform a dynamical finite-size 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 one-dimensional setups of quenched ultracold quantum gases.