Benchmarking highly entangled states on a 60-atom analogue quantum simulator.

Quantum systems have entered a competitive regime in which classical computers must make approximations to represent highly entangled quantum states1,2. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices2-5, and it remains unsolved how to estimate the actual entanglement content of experiments6. Here, we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analogue Rydberg quantum simulator, reaching a high-entanglement entropy regime in which exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement6, finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution2-5. Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we use. Our results enable a new model for evaluating the ability of both analogue and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems.

Erasure conversion in a high-fidelity Rydberg quantum simulator.

Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices1 and for the quest towards fault-tolerant quantum computation2,3. Rydberg arrays have emerged as a prominent platform in this context4 with impressive system sizes5,6 and proposals suggesting how error-correction thresholds could be significantly improved by detecting leakage errors with single-atom resolution7,8, a form of erasure error conversion9-12. However, two-qubit entanglement fidelities in Rydberg atom arrays13,14 have lagged behind competitors15,16 and this type of erasure conversion is yet to be realized for matter-based qubits in general. Here we demonstrate both erasure conversion and high-fidelity Bell state generation using a Rydberg quantum simulator5,6,17,18. When excising data with erasure errors observed via fast imaging of alkaline-earth atoms19-22, we achieve a Bell state fidelity of [Formula: see text], which improves to [Formula: see text] when correcting for remaining state-preparation errors. We further apply erasure conversion in a quantum simulation experiment for quasi-adiabatic preparation of long-range order across a quantum phase transition, and reveal the otherwise hidden impact of these errors on the simulation outcome. Our work demonstrates the capability for Rydberg-based entanglement to reach fidelities in the 0.999 regime, with higher fidelities a question of technical improvements, and shows how erasure conversion can be utilized in NISQ devices. These techniques could be translated directly to quantum-error-correction codes with the addition of long-lived qubits7,22-24.

Benchmarking Quantum Simulators Using Ergodic Quantum Dynamics.

We propose and analyze a sample-efficient protocol to estimate the fidelity between an experimentally prepared state and an ideal target state, applicable to a wide class of analog quantum simulators without advanced spatiotemporal control. Our protocol relies on universal fluctuations emerging from generic Hamiltonian dynamics, which we discover in the present work. It does not require fine-tuned control over state preparation, quantum evolution, or readout capability, while achieving near optimal sample complexity: a percent-level precision is obtained with ∼10^{3} measurements, independent of system size. Furthermore, the accuracy of our fidelity estimation improves exponentially with increasing system size. We numerically demonstrate our protocol in a variety of quantum simulator platforms, including quantum gas microscopes, trapped ions, and Rydberg atom arrays. We discuss applications of our method for tasks such as multiparameter estimation of quantum states and processes.

Dark-State Enhanced Loading of an Optical Tweezer Array.

Neutral atoms and molecules trapped in optical tweezers have become a prevalent resource for quantum simulation, computation, and metrology. However, the maximum achievable system sizes of such arrays are often limited by the stochastic nature of loading into optical tweezers, with a typical loading probability of only 50%. Here we present a species-agnostic method for dark-state enhanced loading (DSEL) based on real-time feedback, long-lived shelving states, and iterated array reloading. We demonstrate this technique with a 95-tweezer array of ^{88}Sr atoms, achieving a maximum loading probability of 84.02(4)% and a maximum array size of 91 atoms in one dimension. Our protocol is complementary to, and compatible with, existing schemes for enhanced loading based on direct control over light-assisted collisions, and we predict it can enable close-to-unity filling for arrays of atoms or molecules.

Many-body cavity quantum electrodynamics with driven inhomogeneous emitters.

Quantum emitters coupled to optical resonators are quintessential systems for exploring fundamental phenomena in cavity quantum electrodynamics (cQED)1 and are commonly used in quantum devices acting as qubits, memories and transducers2. Many previous experimental cQED studies have focused on regimes in which a small number of identical emitters interact with a weak external drive3-6, such that the system can be described with simple, effective models. However, the dynamics of a disordered, many-body quantum system subject to a strong drive have not been fully explored, despite its importance and potential in quantum applications7-10. Here we study how a large, inhomogeneously broadened ensemble of solid-state emitters coupled with high cooperativity to a nanophotonic resonator behaves under strong excitation. We discover a sharp, collectively induced transparency (CIT) in the cavity reflection spectrum, resulting from quantum interference and collective response induced by the interplay between driven inhomogeneous emitters and cavity photons. Furthermore, coherent excitation within the CIT window leads to highly nonlinear optical emission, spanning from fast superradiance to slow subradiance11. These phenomena in the many-body cQED regime enable new mechanisms for achieving slow light12 and frequency referencing, pave a way towards solid-state superradiant lasers13 and inform the development of ensemble-based quantum interconnects9,10.

Preparing random states and benchmarking with many-body quantum chaos.

Producing quantum states at random has become increasingly important in modern quantum science, with applications being both theoretical and practical. In particular, ensembles of such randomly distributed, but pure, quantum states underlie our understanding of complexity in quantum circuits1 and black holes2, and have been used for benchmarking quantum devices3,4 in tests of quantum advantage5,6. However, creating random ensembles has necessitated a high degree of spatio-temporal control7-12 placing such studies out of reach for a wide class of quantum systems. Here we solve this problem by predicting and experimentally observing the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics, which we use to implement an efficient, widely applicable benchmarking protocol. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system, offering new insights into quantum thermalization13. Predicated on this discovery, we develop a fidelity estimation scheme, which we demonstrate for a Rydberg quantum simulator with up to 25 atoms using fewer than 104 experimental samples. This method has broad applicability, as we demonstrate for Hamiltonian parameter estimation, target-state generation benchmarking, and comparison of analogue and digital quantum devices. Our work has implications for understanding randomness in quantum dynamics14 and enables applications of this concept in a much wider context4,5,9,10,15-20.

Influence of Environmental Factors on the Swelling Capacities of Superabsorbent Polymers Used in Concrete.

Superabsorbent polymers (SAP) are of major interest as materials to control the cement hydration process. The swelling behavior of the SAPs significantly influences the performance of the resulting concrete by slowly releasing polymer-bound water in order to maintain a consistent w/c value. A round-robin test conducted by the RILEM Technical Committee 260-RSC showed that the same batch of polymer can lead to large deviations in concrete performance and this was assumed to originate in different storage conditions of the SAP. In this contribution the change in the performance of two SAPs, a crosslinked poly(acrylate) and a crosslinked poly(acrylate-co-acrylamide), was assessed after ageing in standard climate, at 50 °C, and under UV irradiation. During storage in standard climate or 50 °C, ageing led to dehydration of the SAP, and this subsequently led to a higher water uptake during swelling. By contrast, UV irradiation reduced the water uptake, most likely as a result of photo-crosslinking. Dynamic water vapor sorption experiments indicated a strong dependence of the water uptake on both the ambient humidity and the temperature. As a result, cement mixtures containing SAP must be calculated on the dry mass of the SAP rather than the actual weight on site. A standard procedure of how to pack and handle SAP to be used in concrete is also provided.

Integrating Neural Networks with a Quantum Simulator for State Reconstruction.

We demonstrate quantum many-body state reconstruction from experimental data generated by a programmable quantum simulator by means of a neural-network model incorporating known experimental errors. Specifically, we extract restricted Boltzmann machine wave functions from data produced by a Rydberg quantum simulator with eight and nine atoms in a single measurement basis and apply a novel regularization technique to mitigate the effects of measurement errors in the training data. Reconstructions of modest complexity are able to capture one- and two-body observables not accessible to experimentalists, as well as more sophisticated observables such as the Rényi mutual information. Our results open the door to integration of machine learning architectures with intermediate-scale quantum hardware.

2000-Times Repeated Imaging of Strontium Atoms in Clock-Magic Tweezer Arrays.

We demonstrate single-atom resolved imaging with a survival probability of 0.99932(8) and a fidelity of 0.99991(1), enabling us to perform repeated high-fidelity imaging of single atoms in tweezers thousands of times. We further observe lifetimes under laser cooling of more than seven minutes, an order of magnitude longer than in previous tweezer studies. Experiments are performed with strontium atoms in 813.4 nm tweezer arrays, which is at a magic wavelength for the clock transition. Tuning to this wavelength is enabled by off-magic Sisyphus cooling on the intercombination line, which lets us choose the tweezer wavelength almost arbitrarily. We find that a single not retroreflected cooling beam in the radial direction is sufficient for mitigating recoil heating during imaging. Moreover, this cooling technique yields temperatures below 5 µK, as measured by release and recapture. Finally, we demonstrate clock-state resolved detection with average survival probability of 0.996(1) and average state detection fidelity of 0.981(1). Our work paves the way for atom-by-atom assembly of large defect-free arrays of alkaline-earth atoms, in which repeated interrogation of the clock transition is an imminent possibility.

Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator.

Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations1. These fluctuations play a dominant part in the quantum critical region surrounding the transition point, where the dynamics is governed by the universal properties associated with the QPT. Although time-dependent phenomena associated with classical, thermally driven phase transitions have been extensively studied in systems ranging from the early Universe to Bose-Einstein condensates2-5, understanding critical real-time dynamics in isolated, non-equilibrium quantum systems remains a challenge6. Here we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations when crossing the QPT, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM)7-9 for an Ising-type QPT, explore scaling universality and observe corrections beyond QKZM predictions. This approach is subsequently used to measure the critical exponents associated with chiral clock models10,11, providing new insights into exotic systems that were not previously understood and opening the door to precision studies of critical phenomena, simulations of lattice gauge theories12,13 and applications to quantum optimization14,15.

Sorption-active transparent films based on chitosan.

In this paper we describe the preparation of alkanoic acid-based aqueous chitosan solutions, which show no sign of acid-catalysed depolymerisation over time - something commonly accompanying other preparation methods. Longer chitosan chains have previously been shown to exhibit more advantageous biological activities, and constant viscosities are essential for consistent quality in biomedical applications. Avoiding acid-catalysed depolymerisation requires careful control of the stoichiometry between the free amino groups of chitosan and the appropriate solubilising acid. Acetic and butyric acid are both suitable solubilising agents, but chitosan butyrate exhibits lower solution viscosities due to a combined electric and steric shielding of the chains. These solutions dry into clear transparent films that remain fully water soluble and absorb up to 70 wt% of water from 90%-RH vapour phase at 25 °C. The absorption follows simple first-order kinetics and the rate constants increase with increasing humidity up to approx. 71%-RH, where a metastable chitosan trihydrate salt appears to be formed. Desorption is slightly faster, but more complex, as it exhibits two distinct first-order processes. In addition, films prepared in this way are thermally more stable than the usual chitosan hydrochloride.

High-Fidelity Control and Entanglement of Rydberg-Atom Qubits.

Individual neutral atoms excited to Rydberg states are a promising platform for quantum simulation and quantum information processing. However, experimental progress to date has been limited by short coherence times and relatively low gate fidelities associated with such Rydberg excitations. We report progress towards high-fidelity quantum control of Rydberg-atom qubits. Enabled by a reduction in laser phase noise, our approach yields a significant improvement in coherence properties of individual qubits. We further show that this high-fidelity control extends to the multi-particle case by preparing a two-atom entangled state with a fidelity exceeding 0.97(3), and extending its lifetime with a two-atom dynamical decoupling protocol. These advances open up new prospects for scalable quantum simulation and quantum computation with neutral atoms.

Probing many-body dynamics on a 51-atom quantum simulator.

Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on classical approaches. Here we demonstrate a method for creating controlled many-body quantum matter that combines deterministically prepared, reconfigurable arrays of individually trapped cold atoms with strong, coherent interactions enabled by excitation to Rydberg states. We realize a programmable Ising-type quantum spin model with tunable interactions and system sizes of up to 51 qubits. Within this model, we observe phase transitions into spatially ordered states that break various discrete symmetries, verify the high-fidelity preparation of these states and investigate the dynamics across the phase transition in large arrays of atoms. In particular, we observe robust many-body dynamics corresponding to persistent oscillations of the order after a rapid quantum quench that results from a sudden transition across the phase boundary. Our method provides a way of exploring many-body phenomena on a programmable quantum simulator and could enable realizations of new quantum algorithms.

Corrigendum: Synthesis of Metal Nanoparticles and Metal Fluoride Nanoparticles from Metal Amidinate Precursors in 1-Butyl-3-Methylimidazolium Ionic Liquids and Propylene Carbonate.

[This corrects the article DOI: 10.1002/open.201600105.].

Synthesis of Metal Nanoparticles and Metal Fluoride Nanoparticles from Metal Amidinate Precursors in 1-Butyl-3-Methylimidazolium Ionic Liquids and Propylene Carbonate.

Decomposition of transition-metal amidinates [M{MeC(NiPr)2} n ] [M(AMD) n ; M=MnII, FeII, CoII, NiII, n=2; CuI, n=1) induced by microwave heating in the ionic liquids (ILs) 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIm][BF4]), 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIm][PF6]), 1-butyl-3-methylimidazolium trifluoromethanesulfonate (triflate) ([BMIm][TfO]), and 1-butyl-3-methylimidazolium tosylate ([BMIm][Tos]) or in propylene carbonate (PC) gives transition-metal nanoparticles (M-NPs) in non-fluorous media (e.g. [BMIm][Tos] and PC) or metal fluoride nanoparticles (MF2-NPs) for M=Mn, Fe, and Co in [BMIm][BF4]. FeF2-NPs can be prepared upon Fe(AMD)2 decomposition in [BMIm][BF4], [BMIm][PF6], and [BMIm][TfO]. The nanoparticles are stable in the absence of capping ligands (surfactants) for more than 6 weeks. The crystalline phases of the metal or metal fluoride synthesized in [BMIm][BF4] were identified by powder X-ray diffraction (PXRD) to exclusively Ni- and Cu-NPs or to solely MF2-NPs for M=Mn, Fe, and Co. The size and size dispersion of the nanoparticles were determined by transmission electron microscopy (TEM) to an average diameter of 2(±2) to 14(±4) nm for the M-NPs, except for the Cu-NPs in PC, which were 51(±8) nm. The MF2-NPs from [BMIm][BF4] were 15(±4) to 65(±18) nm. The average diameter from TEM is in fair agreement with the size evaluated from PXRD with the Scherrer equation. The characterization was complemented by energy-dispersive X-ray spectroscopy (EDX). Electrochemical investigations of the CoF2-NPs as cathode materials for lithium-ion batteries were simply evaluated by galvanostatic charge/discharge profiles, and the results indicated that the reversible capacity of the CoF2-NPs was much lower than the theoretical value, which may have originated from the complex conversion reaction mechanism and residue on the surface of the nanoparticles.

Atom-by-atom assembly of defect-free one-dimensional cold atom arrays.

The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical science. We use atom-by-atom assembly to implement a platform for the deterministic preparation of regular one-dimensional arrays of individually controlled cold atoms. In our approach, a measurement and feedback procedure eliminates the entropy associated with probabilistic trap occupation and results in defect-free arrays of more than 50 atoms in less than 400 milliseconds. The technique is based on fast, real-time control of 100 optical tweezers, which we use to arrange atoms in desired geometric patterns and to maintain these configurations by replacing lost atoms with surplus atoms from a reservoir. This bottom-up approach may enable controlled engineering of scalable many-body systems for quantum information processing, quantum simulations, and precision measurements.

Bloch state tomography using Wilson lines.

Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high-energy theories, quantum information, and condensed-matter physics. In condensed-matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multiband systems. Using an ultracold gas of rubidium atoms loaded in a honeycomb optical lattice, we realize strong-force dynamics in Bloch bands that are described by Wilson lines and observe an evolution in the band populations that directly reveals the band geometry. Our technique enables a full determination of band eigenstates, Berry curvature, and topological invariants, including single- and multiband Chern and Z2 numbers.

Landau Levels in Strained Optical Lattices.

We propose a hexagonal optical lattice system with spatial variations in the hopping matrix elements. Just like in the valley Hall effect in strained graphene, for atoms near the Dirac points the variations in the hopping matrix elements can be described by a pseudomagnetic field and result in the formation of Landau levels. We show that the pseudomagnetic field leads to measurable experimental signatures in momentum resolved Bragg spectroscopy, Bloch oscillations, cyclotron motion, and quantization of in situ densities. Our proposal can be realized by a slight modification of existing experiments. In contrast to previous methods, pseudomagnetic fields are realized in a completely static system avoiding common heating effects and therefore opening the door to studying interaction effects in Landau levels with cold atoms.

Spatially Resolved Detection of a Spin-Entanglement Wave in a Bose-Hubbard Chain.

Entanglement is an essential property of quantum many-body systems. However, its local detection is challenging and was so far limited to spin degrees of freedom in ion chains. Here we measure entanglement between the spins of atoms located on two lattice sites in a one-dimensional Bose-Hubbard chain which features both local spin- and particle-number fluctuations. Starting with an initially localized spin impurity, we observe an outwards propagating entanglement wave and show quantitatively how entanglement in the spin sector rapidly decreases with increasing particle-number fluctuations in the chain.

Microscopic observation of magnon bound states and their dynamics.

The existence of bound states of elementary spin waves (magnons) in one-dimensional quantum magnets was predicted almost 80 years ago. Identifying signatures of magnon bound states has so far remained the subject of intense theoretical research, and their detection has proved challenging for experiments. Ultracold atoms offer an ideal setting in which to find such bound states by tracking the spin dynamics with single-spin and single-site resolution following a local excitation. Here we use in situ correlation measurements to observe two-magnon bound states directly in a one-dimensional Heisenberg spin chain comprising ultracold bosonic atoms in an optical lattice. We observe the quantum dynamics of free and bound magnon states through time-resolved measurements of two spin impurities. The increased effective mass of the compound magnon state results in slower spin dynamics as compared to single-magnon excitations. We also determine the decay time of bound magnons, which is probably limited by scattering on thermal fluctuations in the system. Our results provide a new way of studying fundamental properties of quantum magnets and, more generally, properties of interacting impurities in quantum many-body systems.