We show that a family of secret communication challenge games naturally define a hierarchy of emergent quasiparticle statistics in three-dimensional (3D) topological phases. The winning strategies exploit a special class of the recently proposed $R$-paraparticles to allow nonlocal secret communication between the two participating players. We first give a high-level, axiomatic description of emergent $R$-paraparticles, and show that any physical system hosting such particles admits a winning strategy. We then analyze the games using the categorical description of topological phases (where point-like excitations in 3D are described by symmetric fusion categories), and show that only $R$-paraparticles can win the 3D challenge in a noise-robust way, and the winning strategy is essentially unique. This analysis associates emergent $R$-paraparticles to deconfined gauge theories based on an exotic class of finite groups. Thus, even though this special class of $R$-paraparticles are fermions or bosons under the categorical classification, their exchange statistics can still have nontrivial physical consequences in the presence of appropriate defects, and the $R$-paraparticle language offers a more convenient description of the winning strategies. Finally, while a subclass of non-Abelian anyons can win the game in 2D, we introduce twisted variants that exclude anyons, thereby singling out $R$-paraparticles in 2D as well. Our results establish the secret communication challenge as a versatile diagnostic for both identifying and classifying exotic exchange statistics in topological quantum matter.

Distributed quantum information processing seeks to overcome the scalability limitations of monolithic quantum devices by interconnecting multiple quantum processing nodes via classical and quantum communication. This approach extends the capabilities of individual devices, enabling access to larger problem instances and novel algorithmic techniques. Beyond increasing qubit counts, it also enables qualitatively new capabilities, such as joint measurements on multiple copies of high-dimensional quantum states. The distinction between single-copy and multi-copy access reveals important differences in task complexity and helps identify which computational problems stand to benefit from distributed quantum resources. At the same time, it highlights trade-offs between classical and quantum communication models and the practical challenges involved in realizing them experimentally. In this review, we contextualize recent developments by surveying the theoretical foundations of distributed quantum protocols and examining the experimental platforms and algorithmic applications that realize them in practice.

The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum computer can be built in a 1D chain with a fixed, translationally invariant Hamitonian consisting of nearest--neighbor interactions only. The result of the computation is obtained after a prescribed time with high probability.

The advent of digital neutral-atom quantum computers relies on the development of fast and robust protocols for high-fidelity quantum operations. In this work, we introduce a novel scheme for entangling gates using four atomic levels per atom: a ground-state qubit and two Rydberg states. A laser field couples the qubit to one of the two Rydberg states, while a microwave field drives transitions between the two Rydberg states, enabling a resonant dipole-dipole interaction between different atoms. We show that controlled-Z gates can be realized in this scheme without requiring optical phase modulation and relying solely on a microwave field with time-dependent phase and amplitude. We demonstrate that such gates are faster and less sensitive to Rydberg decay than state-of-the-art Rydberg gates based on van der Waals interactions. Moreover, we systematically stabilize our protocol against interatomic distance fluctuations and analyze its performance in realistic setups with rubidium or cesium atoms. Our results open up new avenues to the use of microwave-driven dipolar interactions for quantum computation with neutral atoms.

Metastable atomic qubits are a highly promising platform for the realization of quantum computers, owing to their scalability and the possibility of converting leakage errors to erasure errors mid-circuit. Here, we demonstrate and characterize a universal gate set for the metastable fine-structure qubit encoded between the $^3\text{P}_0$ and $^3\text{P}_2$ states in bosonic strontium-88. We find single-qubit gate fidelities of 0.993(1), and two-qubit gate fidelities of 0.9945(6) after correcting for losses during the gate operation. Furthermore, we present a novel state-resolved detection scheme for the two fine-structure states that enables high-fidelity detection of qubit loss. Finally, we leverage the existence of a stable ground state outside the qubit subspace to perform mid-circuit erasure conversion using fast destructive imaging. Our results establish the strontium fine-structure qubit as a promising candidate for near-term error-corrected quantum computers, offering unique scaling perspectives.

The Loschmidt echo - the probability of a quantum many-body system to return to its initial state following a dynamical evolution - generally contains key information about a quantum system, relevant across various scientific fields including quantum chaos, quantum many-body physics, or high-energy physics. However, it is typically exponentially small in system size, posing an outstanding challenge for experiments. Here, we experimentally investigate the subsystem Loschmidt echo, a quasi-local observable that captures key features of the Loschmidt echo while being readily accessible experimentally. Utilizing quantum gas microscopy, we study its short- and long-time dynamics. In the short-time regime, we observe a dynamical quantum phase transition arising from genuine higher-order correlations. In the long-time regime, the subsystem Loschmidt echo allows us to quantitatively determine the effective dimension and structure of the accessible Hilbert space in the thermodynamic limit. Performing these measurements in the ergodic regime and in the presence of emergent kinetic constraints, we provide direct experimental evidence for ergodicity breaking due to fragmentation of the Hilbert space. Our results establish the subsystem Loschmidt echo as a novel and powerful tool that allows paradigmatic studies of both non-equilibrium dynamics and equilibrium thermodynamics of quantum many-body systems, applicable to a broad range of quantum simulation and computing platforms.

The transverse folding algorithm [Phys. Rev. Lett. 102, 240603] is a tensor network method to compute time-dependent local observables in out-of-equilibrium quantum spin chains that can sometimes overcome the limitations of matrix product states. We present a contraction strategy that makes use of the exact light cone structure of the tensor network representing the observables. The strategy can be combined with the hybrid truncation proposed for global quenches in [Phys. Rev. A 91, 032306], which significantly improves the efficiency of the method. We demonstrate the performance of this transverse light cone contraction also for transport coefficients, and discuss how it can be extended to other dynamical quantities.

Quantum batteries, composed of quantum cells, are expected to outperform their classical analogs. The origin of such advantages lies in the role of quantum correlations, which may arise during the charging and discharging processes performed on the battery. In this theoretical work, we introduce a systematic characterization of the relevant quantities of quantum batteries, i.e., the capacity and the power, in relation to such correlations. For these quantities, we derive upper bounds for batteries that are a collection of noninteracting quantum cells with fixed Hamiltonians. The capacity, that is, a bound on the stored or extractable energy, is derived with the help of the energy-entropy diagram, and this bound is respected as long as the charging and discharging processes are entropy preserving. While studying power, we consider a geometric approach for the evolution of the battery state in the energy eigenspace of the battery Hamiltonian. Then, an upper bound for power is derived for arbitrary charging process, in terms of the Fisher information and the energy variance of the battery. The former quantifies the speed of evolution, and the latter encodes the nonlocal character of the battery state. Indeed, due to the fact that the energy variance is bounded by the multipartite entanglement properties of batteries composed of qubits, we establish a fundamental bound on power imposed by quantum entanglement. We also discuss paradigmatic models for batteries that saturate the bounds both for the stored energy and power. Several experimentally realizable quantum batteries, based on integrable spin chains, the Lipkin-Meshkov-Glick and the Dicke models, are also studied in the light of these newly introduced bounds.

Many-body systems arising in condensed matter physics and quantum optics inevitably couple to the environment and need to be modelled as open quantum systems. While near-optimal algorithms have been developed for simulating many-body quantum dynamics, algorithms for their open system counterparts remain less well investigated. We address the problem of simulating geometrically local many-body open quantum systems interacting with a stationary Gaussian environment. Under a smoothness assumption on the system-environment interaction, we develop near-optimal algorithms that, for a model with $N$ spins and evolution time $t$, attain a simulation error $\delta$ in the system-state with $\mathcal{O}(Nt(Nt/\delta)^{o(1)})$ gates, $\mathcal{O}(t(Nt/\delta)^{o(1)})$ parallelized circuit depth and $\tilde{\mathcal{O}}(N(Nt/\delta)^{o(1)})$ ancillas. We additionally show that, if only simulating local observables is of interest, then the circuit depth of the digital algorithm can be chosen to be independent of the system size $N$. This provides theoretical evidence for the utility of these algorithms for simulating physically relevant models, where typically local observables are of interest, on pre-fault tolerant devices. Finally, for the limiting case of Markovian dynamics with commuting jump operators, we propose two algorithms based on sampling a Wiener process and on a locally dilated Hamiltonian construction, respectively. These algorithms reduce the asymptotic gate complexity on $N$ compared to currently available algorithms in terms of the required number of geometrically local gates.

Geometric frustration can significantly increase the complexity and richness of many-body physics and, for instance, suppress antiferromagnetic order in quantum magnets. Here, we employ ultracold bosonic $^{39}$K atoms in a triangular optical lattice to study geometric frustration by stabilizing the gas at the frustrated upper band edge using negative absolute temperatures. We find that geometric frustration suppresses the critical interaction strength for the (chiral-)superfluid to Mott insulator ($\chi$-SF-MI) quantum phase transition by a factor of 2.7(3) and furthermore changes the critical dynamics of the transition. Although the emergence of coherence during fast ramps from MI to the ($\chi$-)SF regime is continuous in both cases, for ramps longer than a few tunnelling times, significant differences emerge. In the \frs case, no long-range order emerges on the studied timescales, highlighting a significantly reduced rate or even saturation of the emerging coherence. This work opens the door to quantum simulations of frustrated systems that are often intractable by classical simulations.

Parton distribution functions (PDFs) describe universal properties of bound states and allow us to calculate scattering amplitudes in processes with large momentum transfer. Calculating PDFs involves the evaluation of matrix elements with a Wilson line in a light-cone direction. In contrast to Monte Carlo methods in Euclidean spacetime, these matrix elements can be directly calculated in Minkowski-space using the Hamiltonian formalism. The necessary spatial- and time-evolution can be efficiently applied using established tensor network methods. We present PDFs in the Schwinger model calculated with matrix product states.

Classical theory asserts that several electromagnetic waves cannot interact with matter if they interfere destructively to zero, whereas quantum mechanics predicts a nontrivial light-matter dynamics even when the average electric field vanishes. Here we show that in quantum optics classical interference emerges from collective bright and dark states of light, \textit{i.e.}, entangled superpositions of multi-mode photon-number states. This makes it possible to explain wave interference using the particle description of light and the superposition principle for linear systems.

One of the most fascinating properties of topological phases of matter is their robustness to disorder and imperfections. Although several experimental techniques have been developed to probe the geometric properties of engineered topological Bloch bands with cold atoms, they almost exclusively rely on the translational invariance of the underlying lattice. This prevents direct studies of topology in the presence of disorder, further hindering an extension to disordered interacting topological phases. Here, we identify disorder-driven phase transitions between two distinct Floquet topological phases using the characteristic properties of topological edge modes with ultracold atoms in periodically-driven two-dimensional (2D) optical lattices. Our results constitute an important step towards studying the rich interplay between topology and disorder with cold atoms. Moreover, our measurements confirm that disorder indeed favors the anomalous Floquet topological regime over conventional Hall systems, indicating an enhanced robustness and paving the way towards observing exotic out-of-equilibrium phases such as the anomalous Floquet Anderson insulator.

Quantum many-body (QMB) systems are generally computationally hard: the computing resources necessary to simulate them exactly can often exceed the existing computation resources by orders of magnitude. For this reason, Richard Feynman proposed the concept of a quantum simulator: quantum systems engineered to obey a prescribed evolution equation and repeating the experiment multiple times. Experimentally, however, as we explain below, the vast majority of observables describing the system are inaccessible. Thus, while Feynman's idea addresses the problem of simulating quantum dynamics, it leaves unsolved the equally fundamental problem of inferring the underlying physics from the limited observables accessible in experiments. Indeed, many complex phenomena associated with QMB systems remain elusive. Perhaps, the most important example is identifying phase transitions in QMB systems when no simple order-parameter exists, which poses major challenges to this day. Complicating the problem further is the fact that, in most cases, it is impossible to learn from numerical simulations, as the underlying systems are often too large to be computable, and small QMB can show strong finite size effects, masking the presence of the transition. Here, we present an unsupervised machine learning approach to study QMB experiments, specifically aimed at detecting phase transitions and crossovers directly from raw experimental measurements. We demonstrate our methodology on systems undergoing Many-Body Localization cross-over and Mott-to-Superfluid phase-transition, showing that it reveals collective phenomena from the very partial experimental data and without any model-specific prior knowledge of the system. This approach offers a general and scalable route for data-driven discovery of emergent phenomena in complex quantum many-body systems.

Quantum simulations of electronic structure and strongly correlated quantum phases are widely regarded as among the most promising applications of quantum computing. These simulations require the accurate implementation of motion and entanglement of fermionic particles. Instead of the commonly applied costly mapping to qubits, fermionic quantum computers offer the prospect of directly implementing electronic structure problems. Ultracold neutral atoms have emerged as a powerful platform for spin-based quantum computing, but quantum information can also be processed via the motion of bosonic or fermionic atoms offering a distinct advantage by intrinsically conserving crucial symmetries like electron number. Here we demonstrate collisional entangling gates with fidelities up to 99.75(6)% and lifetimes of Bell states beyond $10\,s$ via the control of fermionic atoms in an optical superlattice. Using quantum gas microscopy, we characterize both spin-exchange and pair-tunneling gates locally, and realize a robust, composite pair-exchange gate, a key building block for quantum chemistry simulations. Our results enable the preparation of complex quantum states and advanced readout protocols for a new class of scalable analog-digital hybrid quantum simulators. Once combined with local addressing, they mark a key step towards a fully digital fermionic quantum computer based on the controlled motion and entanglement of fermionic neutral atoms.

One of the most important quantities characterizing the microscopic properties of quantum systems are dynamical correlation functions. These correlations are obtained by time-evolving a perturbation of an eigenstate of the system, typically the ground state. In this work, we study approximations of these correlation functions that do not require time dynamics. We show that having access to a circuit that prepares an eigenstate of the Hamiltonian, it is possible to approximate the dynamical correlation functions up to exponential accuracy in the complex frequency domain $\omega=\Re(\omega)+i\Im(\omega)$, on a strip above the real line $\Im(\omega)=0$. We achieve this by exploiting the continued fraction representation of the dynamical correlation functions as functions of frequency $\omega$, where the level $k$ approximant can be obtained by measuring a weight $O(k)$ operator on the eigenstate of interest. In the complex $\omega$ plane, we show how this approach allows to determine approximations to correlation functions with accuracy that increases exponentially with $k$. We analyse two algorithms to generate the continuous fraction representation in scalar or matrix form, starting from either one or many initial operators. We prove that these algorithms generate an exponentially accurate approximation of the dynamical correlation functions on a region sufficiently far away from the real frequency axis. We present numerical evidence of these theoretical results through simulations of small lattice systems. We comment on the stability of these algorithms with respect to sampling noise in the context of quantum simulation using quantum computers.

Nonstabilizerness, also known as ``magic'', stands as a crucial resource for achieving a potential advantage in quantum computing. Its connection to many-body physical phenomena is poorly understood at present, mostly due to a lack of practical methods to compute it at large scales. We present a novel approach for the evaluation of nonstabilizerness within the framework of matrix product states (MPS), based on expressing the MPS directly in the Pauli basis. Our framework provides a powerful tool for efficiently calculating various measures of nonstabilizerness, including stabilizer Rényi entropies, stabilizer nullity, and Bell magic, and enables the learning of the stabilizer group of an MPS. We showcase the efficacy and versatility of our method in the ground states of Ising and XXZ spin chains, as well as in circuits dynamics that has recently been realized in Rydberg atom arrays, where we provide concrete benchmarks for future experiments on logical qubits up to twice the sizes already realized.

A fundamental principle of chaotic quantum dynamics is that local subsystems eventually approach a thermal equilibrium state. Large subsystems thermalize slower: their approach to equilibrium is limited by the hydrodynamic build-up of large-scale fluctuations. For classical out-of-equilibrium systems, the framework of macroscopic fluctuation theory (MFT) was recently developed to model the hydrodynamics of fluctuations. We perform large-scale quantum simulations that monitor the full counting statistics of particle-number fluctuations in hard-core boson ladders, contrasting systems with ballistic and chaotic dynamics. We find excellent agreement between our results and MFT predictions, which allows us to accurately extract diffusion constants from fluctuation growth. Our results suggest that large-scale fluctuations of isolated quantum systems display emergent hydrodynamic behavior, expanding the applicability of MFT to the quantum regime.

TeNPy (short for 'Tensor Network Python') is a python library for the simulation of strongly correlated quantum systems with tensor networks. The philosophy of this library is to achieve a balance of readability and usability for new-comers, while at the same time providing powerful algorithms for experts. The focus is on MPS algorithms for 1D and 2D lattices, such as DMRG ground state search, as well as dynamics using TEBD, TDVP, or MPO evolution. This article is a companion to the recent version 1.0 release of TeNPy and gives a brief overview of the package.