Strong field terahertz pulses are increasingly used to excite and control quantum materials at the ultrafast timescale. They have found widespread application by enabling direct addressing of the superconducting gap or Josephson resonances and are essential in Higgs spectroscopy. Large non-linear optical signals can be induced by the strong coupling of the THz and superconducting degrees of freedom. However, far less attention has been paid to the strong bi-directional coupling between field and material this implies. Here, we use the framework of the time-dependent Ginzburg-Landau equations to study the full field and material evolution of a superconductor driven by strong field terahertz pulses. We find that at high field strengths, the backreaction of the superconductor induces large changes to the driving pulse, which in turn leads to a runaway melting of the superconducting condensate. This results in a surprisingly large sensitivity to the initial driving pulse chirp, enabling these purely dynamical changes to result in order of magnitude different levels of melting. We also find large-scale spectral shifting of the driving pulse to occur in just a few hundred nanometers of propagation through a superconductor. We attribute these effects to an inverse plasma redshift, in which the driving field breaks Cooper pairs and decreases the free-electron mobility, analogous to reducing the density of a plasma.

Gauge-field configurations with nontrivial topology have profound consequences for the physics of Abelian and non-Abelian gauge theories. Over time, arguments have been gathering for the existence of gauge-field configurations with fractional topological charge, called fractons. Ground-state properties of gauge theories can drastically change in presence of fractons in the path integral. However, understanding the origin of such fractons is usually restricted to semiclassical argumentation. Here, we show that fractons persist in strongly correlated many-body systems, using the multiflavor Schwinger model of quantum electrodynamics as a paradigm example. Through detailed numerical tensor-network analysis, we find strong fracton signatures even in highly discretized lattice models, at sizes that are implementable on already existing quantum-simulation devices. Our work sheds light on how the nontrivial topology of gauge theories persists in challenging nonperturbative regimes, and it shows a path forward to probing it in tabletop experiments.

Dynamical correlations reveal important out-of-equilibrium properties of the underlying quantum many-body system, yet they are notoriously difficult to measure in experiments. While measurement protocols for dynamical correlations based on Hadamard tests for qubit quantum devices exist, they do not straightforwardly extend to qudits. Here, we propose a modified protocol to overcome this limitation by decomposing qudit observables into unitary operations that can be implemented and probed in a quantum circuit. We benchmark our algorithm numerically at the example of quench dynamics in a spin-1 XXZ chain with finite shot noise and demonstrate advantages in terms of the signal-to-noise ratio over established protocols based on linear response. Our scheme can readily be implemented on various platforms and offers a wide range of applications like variational quantum optimization and probing thermalization in many-body systems.

Lattice gauge theories are fundamental to various fields, including particle physics, condensed matter, and quantum information theory. Recent progress in the control of quantum systems allows for studying Abelian lattice gauge theories in table-top experiments. However, several challenges remain, such as implementing dynamical fermions in higher spatial dimensions and magnetic field terms. Here, we map D-dimensional U(1) Abelian lattice gauge theories onto qudit systems with local interactions for arbitrary D. We propose a variational quantum simulation scheme for the qudit system with a local Hamiltonian, that can be implemented on a universal qudit quantum device as the one developed in [Nat. Phys. 18, 1053-1057 (2022)]. We describe how to implement the variational imaginary-time evolution protocol for ground state preparation as well as the variational real-time evolution protocol to simulate non-equilibrium physics on universal qudit quantum computers, supplemented with numerical simulations. Our proposal can serve as a way of simulating lattice gauge theories, particularly in higher spatial dimensions, with minimal resources, regarding both system sizes and gate count.

The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the experimental realization of such holographic codes now within reach. Formulating the hyperbolic pentagon code in terms of a stabilizer graph code, we give gate sequences that are tailored to systems with long-range interactions. We show how to obtain encoding and decoding circuits for the hyperbolic pentagon code, before focusing on a small instance of the holographic code on twelve qubits. Our approach allows to verify holographic properties by partial decoding operations, recovering bulk degrees of freedom from their nearby boundary.

Driven by growing computational power and algorithmic developments, machine learning methods have become valuable tools for analyzing vast amounts of data. Simultaneously, the fast technological progress of quantum information processing suggests employing quantum hardware for machine learning purposes. Recent works discuss different architectures of quantum perceptrons, but the abilities of such quantum devices remain debated. Here, we investigate the storage capacity of a particular quantum perceptron architecture by using statistical mechanics techniques and connect our analysis to the theory of classical spin glasses. We focus on a specific quantum perceptron model and explore its storage properties in the limit of a large number of inputs. Finally, we comment on using statistical physics techniques for further studies of neural networks.

Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter or quantum information theory. The recent progress in the control of artificial quantum systems already allows for studying Abelian lattice gauge theories in table-top experiments. However, the realization of non-Abelian models remains challenging. Here, we employ a coherent quantum control scheme to enforce non-Abelian gauge invariance, and discuss this idea in detail for a one dimensional SU(2) lattice gauge system. Finally, we comment on how to extend our scheme to other non-Abelian gauge symmetries and higher spatial dimensions, which summarized, provides a promising route for the quantum simulation of non-Abelian lattice gauge theories.

For bosons with flat energy dispersion, condensation can occur in different symmetry sectors. Here, we consider bosons in a kagome lattice with π-flux hopping, which, in the presence of mean-field interactions, exhibit degenerate condensates in the Γ and the K point. We analyze the excitation above both condensates and find strikingly different properties: For the K-point condensate, the Bogoliubov-de Gennes (BdG) Hamiltonian has broken particle-hole symmetry and exhibits a topologically trivial quasiparticle band structure. However, band flatness plays a key role in breaking the time-reversal symmetry of the BdG Hamiltonian for a Γ-point condensate. Consequently, its quasiparticle band structure exhibits nontrivial topology, characterized by nonzero Chern numbers and by the presence of edge states. Although quantum fluctuations energetically favor the K-point condensate, the interesting properties of the Γ-point condensate become relevant for anisotropic hopping. The topological properties of the Γ-point condensate get even richer in the presence of extended Bose-Hubbard interactions. We find a topological phase transition into a topological condensate characterized by high Chern number and also comment on the realization and detection of such excitations.

A frequent starting point of quantum computation platforms are two-state quantum systems, i.e., qubits. However, in the context of integer optimization problems, relevant to scheduling optimization and operations research, it is often more resource-efficient to employ quantum systems with more than two basis states, so-called qudits. Here, we discuss the quantum approximate optimization algorithm (QAOA) for qudit systems. We illustrate how the QAOA can be used to formulate a variety of integer optimization problems such as graph coloring problems or electric vehicle (EV) charging optimization. In addition, we comment on the implementation of constraints and describe three methods to include these into a quantum circuit of a QAOA by penalty contributions to the cost Hamiltonian, conditional gates using ancilla qubits, and a dynamical decoupling strategy. Finally, as a showcase of qudit-based QAOA, we present numerical results for a charging optimization problem mapped onto a max-k-graph coloring problem. Our work illustrates the flexibility of qudit systems to solve integer optimization problems.

We investigate an ultra-cold mixture of Bose gases interacting via spin-changing collisions by studying the dynamics of spin fluctuations. The experimental implementation employs $^{23}$Na and $^{7}$Li atoms, which are prepared out of equilibrium across a wide range of initial conditions. We identify three regimes in the dynamics of the system for different initial states: a long-lived metastable regime, an instability range with strong growth of fluctuations, and a fast relaxing regime approaching thermal equilibrium. Theoretical modelling of the data allows us to reconstruct effective potentials which characterize the different dynamical regimes of the system.

Quantum information platforms made great progress in the control of many-body entanglement and the implementation of quantum error correction, but it remains a challenge to realize both in the same setup. Here, we propose a mixture of two ultracold atomic species as a platform for universal quantum computation with long-range entangling gates, while providing a natural candidate for quantum error-correction. In this proposed setup, one atomic species realizes localized collective spins of tunable length, which form the fundamental unit of information. The second atomic species yields phononic excitations, which are used to entangle collective spins. Finally, we discuss a finite-dimensional version of the Gottesman-Kitaev-Preskill code to protect quantum information encoded in the collective spins, opening up the possibility to universal fault-tolerant quantum computation in ultracold atom systems.

Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter, and quantum information science. Their local symmetries enforce the charge conservation observed in the laws of physics. Impressive experimental progress has demonstrated that they can be engineered in table-top experiments using synthetic quantum systems. However, the challenges posed by the scalability of such lattice gauge simulators are pressing, thereby making the exploration of different experimental setups desirable. Here, we realize a U(1) lattice gauge theory with five matter sites and four gauge links in classical electric circuits employing nonlinear elements connecting LC oscillators. This allows for probing previously inaccessible spectral and transport properties in a multi-site system. We directly observe Gauss's law, known from electrodynamics, and the emergence of long-range interactions between massive particles in full agreement with theoretical predictions. Our work paves the way for investigations of increasingly complex gauge theories on table-top classical setups, and demonstrates the precise control of nonlinear effects within metamaterial devices.

Maciej Lewenstein1,2,∗ , Aikaterini Gratsea , Andreu Riera-Campeny , Albert Aloy , Valentin Kasper and Anna Sanpera2,3 1 ICFO Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain 2 ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain 3 Física Teòrica: Informaciò i Fenòmens Quàntics, Departament de Física Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain ∗ Author to whom any correspondence should be addressed.

Fractional quantum Hall systems are among the most exciting strongly correlated systems. Accessing them microscopically via quantum simulations with ultracold atoms would be an important achievement toward a better understanding of this strongly correlated state of matter. A promising approach is to confine a small number of bosonic atoms in a quasi-two-dimensional rotating trap, which mimics the magnetic field. For rotation frequencies close to the in-plane trapping frequency, the ground state is predicted to be a bosonic analog of the Laughlin state. Here, we study the problem of the adiabatic preparation of the Laughlin state by ramping the rotation frequency and controlling the ellipticity of the trapping potential. By employing adapted ramping speeds for rotation frequency and ellipticity, and large trap deformations, we improve the preparation time for high-fidelity Laughlin states by a factor of 10 in comparison to previous studies. With this improvement of the adiabatic protocol the Laughlin state can be prepared with current experimental technology.

Monika Aidelsburger, Luca Barbiero, Alejandro Bermudez, Titas Chanda, Alexandre Dauphin, Daniel González-Cuadra, Przemys law R. Grzybowski, Simon Hands, Fred Jendrzejewski, Johannes Jünemann, Gediminas Juzeliunas, Valentin Kasper, Angelo Piga, Shi-Ju Ran, Matteo Rizzi, Gérman Sierra, Luca Tagliacozzo, Emanuele Tirrito, Torsten V. Zache, Jakub Zakrzewski, Erez Zohar, Maciej Lewenstein Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 Munich, Germany 2 Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany 3 ICFO Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain 4 Departamento de F́ısica Teorica, Universidad Complutense, 28040 Madrid, Spain Institute of Theoretical Physics, Jagiellonian University in Kraków, 30-348 Kraków, Poland 6 Faculty of Physics, Adam Mickiewicz University in Poznań, Poznań, Poland Department of Physics, Faculty of Science and Engineering, Swansea University, Swansea SA28PP, United Kingdom Universität Heidelberg, Kirchhoff-Institut für Physik, 69120 Heidelberg, Germany Johannes Gutenberg-Universität, Institut für Physik, 55128 Mainz, Germany 10 Institute of Theoretical Physics and Astronomy, Vilnius University, LT-10257 Vilnius, Lithuania Department of Physics, Capital Normal University, 100048 Beijing, China Forschungszentrum Jülich, Institute of Quantum Control, Peter Grünberg Institut (PGI-8), 52425 Jülich, Germany Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany Instituto de F́ısica Teórica, UAM/CSIC, Universidad Autònoma de Madrid, Madrid, Spain Departament de F́ısica Quàntica i Astrof́ısica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, 08028 Barcelona, Catalonia, Spain International School for Advanced Studies (SISSA), 34136 Trieste, Italy Center for Quantum Physics, University of Innsbruck, 6020 Innsbruck, Austria Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel ICREA, Passeig Lluis Companys 23, 08010 Barcelona, Spain

We study the storage capacity of quantum neural networks (QNNs), described by completely positive trace preserving (CPTP) maps acting on an N -dimensional Hilbert space. We demonstrate that attractor QNNs can store in a non-trivial manner up to N linearly independent pure states. For n qubits, QNNs can reach an exponential storage capacity, O ( 2 n ) , clearly outperforming standard classical neural networks whose storage capacity scales linearly with the number of neurons n . We estimate, employing the Gardner program, the relative volume of CPTP maps with M ⩽ N stationary states and show that this volume decreases exponentially with M and shrinks to zero for M ⩾ N + 1. We generalize our results to QNNs storing mixed states as well as input–output relations for feed-forward QNNs. Our approach opens the path to relate storage properties of QNNs to the quantum features of the input–output states. This paper is dedicated to the memory of Peter Wittek.

The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more 'accessible' and easier to manipulate for experimentalists, but this 'substitution' also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or [Formula: see text] Bose-Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz-Hubbard ladder, or Gross-Neveu-Wilson and Wilson-Hubbard models. This article is not a general review of the rapidly growing field-it reviews activities related to quantum simulations for lattice field theories performed by the Quantum Optics Theory group at ICFO and their collaborators from 19 institutions all over the world. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics. This article is part of the theme issue 'Quantum technologies in particle physics'.

We study a transition between a homogeneous and an inhomogeneous phase in a system of one-dimensional, Raman tunnel-coupled Bose gases. The homogeneous phase shows a flat density and phase profile, whereas the inhomogeneous ground state is characterized by periodic density ripples and a soliton staircase in the phase difference. We show that under experimentally viable conditions the transition can be tuned by the wave-vector difference Q of the Raman beams and can be described by the Pokrovsky-Talapov model for the relative phase between the two condensates. Local imaging available in atom chip experiments allows us to observe the soliton lattice directly, while modulation spectroscopy can be used to explore collective modes, such as the phonon mode arising from breaking of translation symmetry by the soliton lattice. In addition, we investigate regimes where the cold atom experiment deviates from the Pokrovsky-Talapov field theory. We predict unusual mesoscopic effects arising from the finite size of the system, such as quantized injection of solitons upon increasing Q , or the system size. For moderate values of Q above criticality, we find that the density modulations in the two gases interplay with the relative phase profile and introduce novel features in the spatial structure of the mode wave functions. Using an inhomogeneous Bogoliubov theory, we show that spatial quantum fluctuations are intertwined with the emerging soliton staircase. Finally, we comment on the prospects of the ultracold atom setup.