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Fault-tolerant quantum error correction provides a strategy to protect information processed by a quantum computer against noise which would otherwise corrupt the data. A fault-tolerant universal quantum computer must implement a universal gate set on the logical level in order to perform arbitrary calculations to in principle unlimited precision. We characterize the recent demonstration of a fault-tolerant universal gate set in a trapped-ion quantum computer [Postler et al. Nature 605.7911 (2022)] and identify aspects to improve the design of experimental setups to reach an advantage of logical over physical qubit operation. We show that various criteria to assess the break-even point for fault-tolerant quantum operations are within reach for the ion trap quantum computing architecture under consideration. We analyze the influence of crosstalk in entangling gates for logical state preparation circuits. These circuits can be designed to respect fault tolerance for specific microscopic noise models. We find that an experimentally-informed depolarizing noise model captures the essential noise dynamics of the fault-tolerant experiment, and crosstalk is negligible in the currently accessible regime of physical error rates. For deterministic Pauli state preparation, we provide a fault-tolerant unitary logical qubit initialization circuit, which can be realized without in-sequence measurement and feed-forward of classical information. We show that non-deterministic state preparation schemes for logical Pauli and magic states perform with higher logical fidelity over their deterministic counterparts for the current and anticipated future regime of physical error rates. Our results offer guidance on improvements of physical qubit operations and validate the experimentally-informed noise model as a tool to predict logical failure rates in quantum computing architectures based on trapped ions., 36 pages, 26 figures

Quantum computing systems are developing rapidly as powerful solvers for a variety of real-world calculations. Traditionally, many of these same applications are solved using conventional high-performance computing (HPC) systems, which have progressed sharply through decades of hardware and software improvements. Here, we present a perspective on the motivations and challenges of pairing quantum computing systems with modern HPC infrastructure. We outline considerations and requirements for the use cases, macroarchitecture, microarchitecture, and programming models needed to integrate near-term quantum computers with HPC system, and we conclude with the expectation that such efforts are well within reach of current technology.

Quantum information carriers, just like most physical systems, naturally occupy high-dimensional Hilbert spaces. Instead of restricting them to a two-level subspace, these high-dimensional (qudit) quantum systems are emerging as a powerful resource for the next generation of quantum processors. Yet harnessing the potential of these systems requires efficient ways of generating the desired interaction between them. Here, we experimentally demonstrate an implementation of a native two-qudit entangling gate in a trapped-ion qudit system up to dimension $5$. This is achieved by generalizing a recently proposed light-shift gate mechanism to generate genuine qudit entanglement in a single application of the gate. The gate seamlessly adapts to the local dimension of the system with a calibration overhead that is independent of the dimension., 9 pages, 5 figures

A major challenge for the realization of useful universal quantum computers is achieving high fidelity two-qubit entangling gate operations. However, calibration errors can affect the quantum gate operations and limit their fidelity. To reduce such errors it is desirable to have an analytical understanding and quantitative predictions of the effects that miscalibrations of gate parameters have on the gate performance. In this work, we study a systematic perturbative expansion in miscalibrated parameters of the Mølmer-Sørensen entangling gate, which is widely used in trapped-ion quantum processors. Our analytical treatment particularly focuses on systematic center-line detuning miscalibrations. Via a unitary Magnus expansion, we compute the gate evolution operator, which allows us to obtain relevant key properties such as relative phases, electronic populations, quantum state purity and fidelities. These quantities, subsequently, are used to assess the performance of the gate using the fidelity of entangled states as performance metric. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor. The method and the results presented here can help design and calibrate high-fidelity gate operations of large-scale quantum computers.

Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers, which naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to classical simulation Here, we present a cross-verification technique that exploits the principles of measurement-based quantum computation to link quantum circuits of different input size, depth, and structure. Our technique enables consistency checks of quantum computations between independent devices, as well as within a single device. We showcase our protocol by applying it to five state-of-the-art quantum processors, based on four distinct physical architectures: nuclear magnetic resonance, superconducting circuits, trapped ions, and photonics, with up to six qubits and up to 200 distinct circuits.

Quantum sensors are an established technology that has created new opportunities for precision sensing across the breadth of science. Using entanglement for quantum-enhancement will allow us to construct the next generation of sensors that can approach the fundamental limits of precision allowed by quantum physics. However, determining how state-of-the-art sensing platforms may be used to converge to these ultimate limits is an outstanding challenge. In this work we merge concepts from the field of quantum information processing with metrology, and successfully implement experimentally a *programmable quantum sensor* operating close to the fundamental limits imposed by the laws of quantum mechanics. We achieve this by using low-depth, parametrized quantum circuits implementing optimal input states and measurement operators for a sensing task on a trapped ion experiment. With 26 ions, we approach the fundamental sensing limit up to a factor of 1.45(1), outperforming conventional spin-squeezing with a factor of 1.87(3). Our approach reduces the number of averages to reach a given Allan deviation by a factor of 1.59(6) compared to traditional methods not employing entanglement-enabled protocols. We further perform on-device quantum-classical feedback optimization to `self-calibrate' the programmable quantum sensor with comparable performance. This ability illustrates that this next generation of quantum sensor can be employed without prior knowledge of the device or its noise environment., Comment: Main: 10 pages including Methods, 4 figures. Supplementary Material: 6 pages, 2 figures, separate references

The successful operation of quantum computers relies on protecting qubits from decoherence and noise, which - if uncorrectet - will lead to erroneous results. Because these errors accumulate during an algorithm, correcting them becomes a key requirement for large-scale and fault-tolerant quantum information processors. Besides computational errors, which can be addressed by quantum error correction [2] – [8] , the carrier of the information can also be completely lost or the information can leak out of the computational space [9] – [13] .

Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by imperfect operations do not spread uncontrollably through the quantum register. This requires that all operations on the quantum register obey a fault-tolerant circuit design which, in general, increases the complexity of the implementation. Here, we demonstrate a fault-tolerant universal set of gates on two logical qubits in a trapped-ion quantum computer. In particular, we make use of the recently introduced paradigm of flag fault tolerance, where the absence or presence of dangerous errors is heralded by usage of few ancillary 'flag' qubits. We perform a logical two-qubit CNOT-gate between two instances of the seven qubit color code, and we also fault-tolerantly prepare a logical magic state. We then realize a fault-tolerant logical T-gate by injecting the magic state via teleportation from one logical qubit onto the other. We observe the hallmark feature of fault tolerance, a superior performance compared to a non-fault-tolerant implementation. In combination with recently demonstrated repeated quantum error correction cycles these results open the door to error-corrected universal quantum computation., Comment: v3 with updated acknowledgements, 14 pages, 7 figures

Today's quantum computers operate with a binary encoding that is the quantum analog of classical bits. Yet, the underlying quantum hardware consists of information carriers that are not necessarily binary, but typically exhibit a rich multilevel structure, which is artificially restricted to two dimensions. A wide range of applications from quantum chemistry to quantum simulation, on the other hand, would benefit from access to higher-dimensional Hilbert spaces, which conventional quantum computers can only emulate. Here we demonstrate a universal qudit quantum processor using trapped ions with a local Hilbert space dimension of up to 7. With a performance similar to qubit quantum processors, this approach enables native simulation of high-dimensional quantum systems, as well as more efficient implementation of qubit-based algorithms., Comment: 5+9 pages, many figures

We investigate the energy dynamics of non-crystallized (melted) ions, confined in a Paul trap. The non-periodic Coulomb interaction experienced by melted ions forms a medium for non-conservative energy transfer from the radio-frequency (rf) field to the ions, a process known as rf heating. We study rf heating by analyzing numerical simulations of non-crystallized ion motion in Paul trap potentials, in which the energy of the ions' secular motion changes at discrete intervals, corresponding to ion-ion collisions. The analysis of these collisions is used as a basis to derive a simplified model of rf heating energy dynamics, from which we conclude that the rf heating rate is predominantly dependent on the rf field strength. We confirm the predictability of the model experimentally: Two trapped $^{40}$Ca$^{+}$ ions are deterministically driven to melt, and their fluorescence rate is used to infer the ions' energy. From simulation and experimental results, we generalize which experimental parameters are required for efficient recrystallization of melted trapped ions.

Quantum information processing is steadily progressing from a purely academic discipline towards applications throughout science and industry. Transitioning from lab-based, proof-of-concept experiments to robust, integrated realizations of quantum information processing hardware is an important step in this process. However, the nature of traditional laboratory setups does not offer itself readily to scaling up system sizes or allow for applications outside of laboratory-grade environments. This transition requires overcoming challenges in engineering and integration without sacrificing the state-of-the-art performance of laboratory implementations. Here, we present a 19-inch rack quantum computing demonstrator based on Ca-40(+) optical qubits in a linear Paul trap to address many of these challenges. We outline the mechanical, optical, and electrical subsystems. Furthermore, we describe the automation and remote access components of the quantum computing stack. We conclude by describing characterization measurements relevant to quantum computing including site-resolved single-qubit interactions, and entangling operations mediated by the Molmer-Sorensen interaction delivered via two distinct addressing approaches. Using this setup, we produce maximally entangled Greenberger-Horne-Zeilinger states with up to 24 ions without the use of postselection or error mitigation techniques; on par with well-established conventional laboratory setups., PRX Quantum, 2 (2), ISSN:2691-3399

Trapped-ion quantum computers have demonstrated high-performance gate operations in registers of about ten qubits. However, scaling up and parallelizing quantum computations with long one-dimensional (1D) ion strings is an outstanding challenge due to the global nature of the motional modes of the ions which mediate qubit-qubit couplings. Here, we devise methods to implement scalable and parallel entangling gates by using engineered localized phonon modes. We propose to tailor such localized modes by tuning the local potential of individual ions with programmable optical tweezers. Localized modes of small subsets of qubits form the basis to perform entangling gates on these subsets in parallel. We demonstrate the inherent scalability of this approach by presenting analytical and numerical results for long 1D ion chains and even for infinite chains of uniformly spaced ions. Furthermore, we show that combining our methods with optimal coherent control techniques allows to realize maximally dense universal parallelized quantum circuits., 24 pages, 12 figures

An important building block for large-scale quantum computation with trapped ions is experimentally realized. The investigation is crucial for transport-based quantum logic.

The successful operation of quantum computers relies on protecting qubits from decoherence and noise, which-if uncorrected-will lead to erroneous results. Because these errors accumulate during an algorithm, correcting them is a key requirement for large-scale and fault-tolerant quantum information processors. Besides computational errors, which can be addressed by quantum error correction1-9, the carrier of the information can also be completely lost or the information can leak out of the computational space10-14. It is expected that such loss errors will occur at rates that are comparable to those of computational errors. Here we experimentally implement a full cycle of qubit loss detection and correction on a minimal instance of a topological surface code15,16 in a trapped-ion quantum processor. The key technique used for this correction is a quantum non-demolition measurement performed via an ancillary qubit, which acts as a minimally invasive probe that detects absent qubits while imparting the smallest quantum mechanically possible disturbance to the remaining qubits. Upon detecting qubit loss, a recovery procedure is triggered in real time that maps the logical information onto a new encoding on the remaining qubits. Although the current demonstration is performed in a trapped-ion quantum processor17, the protocol is applicable to other quantum computing architectures and error correcting codes, including leading two- and three-dimensional topological codes. These deterministic methods provide a complete toolbox for the correction of qubit loss that, together with techniques that mitigate computational errors, constitute the building blocks of complete and scalable quantum error correction.

Quantum computers promise to solve certain problems more efficiently than their digital counterparts. A major challenge towards practically useful quantum computing is characterizing and reducing the various errors that accumulate during an algorithm running on large-scale processors. Current characterization techniques are unable to adequately account for the exponentially large set of potential errors, including cross-talk and other correlated noise sources. Here we develop cycle benchmarking, a rigorous and practically scalable protocol for characterizing local and global errors across multi-qubit quantum processors. We experimentally demonstrate its practicality by quantifying such errors in non-entangling and entangling operations on an ion-trap quantum computer with up to 10 qubits, and total process fidelities for multi-qubit entangling gates ranging from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$99.6(1)\%$$\end{document}99.6(1)% for 2 qubits to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$86(2)\%$$\end{document}86(2)% for 10 qubits. Furthermore, cycle benchmarking data validates that the error rate per single-qubit gate and per two-qubit coupling does not increase with increasing system size., Checking the quality of operations of quantum computers in a reliable and scalable way is still an open challenge. Here, the authors show how to characterise multi-qubit operations in a way that scales favourably with the system’s size, and demonstrate it on a 10-qubit ion-trap device.

Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a cross-platform benchmark for multi-qubit quantum simulators., 22 pages, 14 figures, close to published version (freely available at PRX)

Residential buildings account for approximately one fifth of the total energy consumption and 12 % of the overall CO2 emissions in the OECD countries. Replacing conventional boilers by a co-generation of heat and power in decentralized plants on site promises a great benefit. Especially, micro gas turbine (MGT) based combined heat and power systems are particularly suitable due to their low pollutant emissions without exhaust gas treatment. Hence, the overall aim of this work is the development of a recuperated inverted MGT as heat and power supply for a single family house with 1 kWel. First, an inverted MGT on a Brayton cycle MGT was developed and experimentally characterized, in previous work by the authors. This approach allows exploiting the potential of using the same components for both cycles. As a next step, the applicability of the Brayton cycle components operated in inverted mode needs to be evaluated and the requirements for a component optimization need to be defined, both, by pursuing thermodynamic cycle simulations. This paper presents a parametrization and validation of in-house 1D steady state simulation tool for an inverted MGT, based on experimental data from the inverted Brayton cycle test rig. Moreover, a sensitivity analysis is conducted to estimate the influence of every major component on the overall system and to identify the necessary optimizations. Finally, the component requirements for an optimized inverted MGT with 1 kWel and 16 % of electrical efficiency are defined. This work demonstrates the high potential of an inverted MGT for a decentralized heat and power generation when optimizing the system components.

Measuring and understanding electric field noise from bulk material and surfaces is important for many areas of physics. In this work, we introduce a method to detect in situ different sources of electric field noise using a single trapped ion as a sensor. We demonstrate the probing of electric field noise as small as $S_E = 5.2(11)\times 10^{-16}\,\text{V}^2\text{m}^{-2}\text{Hz}^{-1}$, the lowest noise level observed with a trapped ion to our knowledge. Our setup incorporates a controllable noise source utilizing a high-temperature superconductor. This element allows us, first, to benchmark and validate the sensitivity of our probe. Second, to probe non-invasively bulk properties of the superconductor, observing for the first time a superconducting transition with an ion. For temperatures below the transition, we use our setup to assess different surface noise processes. The measured noise shows a crossover regime in the frequency domain, which cannot be explained by existing surface noise models. Our results open perspectives for new models in surface science and pave the way to test them experimentally., Comment: 7 pages, 6 figures, 2 tables

Correlations between different partitions of quantum systems play a central role in a variety of many-body quantum systems, and they have been studied exhaustively in experimental and theoretical research. Here, we investigate dynamical correlations in the time evolution of multiple parts of a composite quantum system. A rigorous measure to quantify correlations in quantum dynamics based on a full tomographic reconstruction of the quantum process has been introduced recently [\'A. Rivas et al., New Journal of Physics, 17(6) 062001 (2015).]. In this work, we derive a lower bound for this correlation measure, which does not require full knowledge of the quantum dynamics. Furthermore we also extend the correlation measure to multipartite systems. We directly apply the developed methods to a trapped ion quantum information processor to experimentally characterize the correlations in quantum dynamics for two- and four-qubit systems. The method proposed and demonstrated in this work is scalable, platform-independent and applicable to other composite quantum systems and quantum information processing architectures. We apply the method to estimate spatial correlations in environmental noise processes, which are crucial for the performance of quantum error correction procedures., Comment: 17 pages, 9 figures, V2: Minor changes

Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in 1994 that Peter Shor came up with an algorithm that is able to calculate the prime factors of a large number vastly more efficiently than known possible with a classical computer. This paradigmatic algorithm stimulated the flourishing research in quantum information processing and the quest for an actual implementation of a quantum computer. Over the last fifteen years, using skillful optimizations, several instances of a Shor algorithm have been implemented on various platforms and clearly proved the feasibility of quantum factoring. For general scalability, though, a different approach has to be pursued. Here, we report the realization of a fully scalable Shor algorithm as proposed by Kitaev. For this, we demonstrate factoring the number fifteen by effectively employing and controlling seven qubits and four "cache-qubits", together with the implementation of generalized arithmetic operations, known as modular multipliers. The scalable algorithm has been realized with an ion-trap quantum computer exhibiting success probabilities in excess of 90%., 5 pages, 3 figures, 4 pages suppl. material (incl. 1 figure)

Jet-stabilized combustion is a promising technology for fuel flexible, reliable, highly efficient combustion systems. The aim of this work is a reduction of NOx emissions of a previously published two-staged MGT combustor [1, 2], where the pilot stage of the combustor was identified as the main contributor to NOx emissions. The geometry optimization was carried out regarding the shape of the pilot dome and the interface between pilot and main stage in order to prevent the formation of high temperature recirculation zones. Both stages have been run separately to allow a detailed understanding of the flame stabilization within the combustor, its range of stable combustion, the interaction between both stages and the influence of the modified geometry. All experiments were conducted at atmospheric pressure and an air preheat temperature of 650 °C. The flame was analyzed in terms of shape, length and lift-off height, using OH* chemiluminescence images. Emission measurements for NOx, CO and UHC emissions were carried out. At a global air number of λ = 2, a fuel split variation was carried out from 0 (only pilot-stage) to 1 (only main stage). The modification of the geometry lead to a decrease in NOx and CO emissions throughout the fuel split variation in comparison with the previous design. Regarding CO emissions, the pilot stage operations is beneficial for a fuel split above 0.8. The local maximum in NOx emissions observed for the previous combustor design at a fuel split of 0.78 was not apparent for the modified design. NOx emissions were increasing, when the local air number of the pilot stage was below the global air number. In order to evaluate the influence of the modified design on the flow field and identify the origin of the emission reduction compared to the previous design, unsteady RANS simulations were carried out for both geometries at fuel splits of 0.93 and 0.78, respectively, using the DLR in-house code THETA with the k-w SST turbulence model and the DRM22 [3] detailed reaction mechanism. The numerical results showed a strong influence of the recirculation zones on the pilot stage reaction zone.

Strings of trapped ions are applied to investigate the dynamics and propagation of entanglement in an analogue fashion. With a small trapped-ion quantum computer a digital quantum simulation of a lattice gauge theory is performed.

41 pags., 32 figs., 7 tabs. -- Open Access funded by Creative Commons Atribution Licence 4.0, A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the well-known QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trapped-ion quantum processors and, more importantly, to guide the future hardware developments that will be required in order to demonstrate beneficial QEC with small topological quantum codes. In doing so, we present a thorough description of a realistic trapped-ion toolbox for QEC and a physically motivated error model that goes beyond standard simplifications in the QEC literature. We focus on laser-based quantum gates realized in two-species trapped-ion crystals in high-optical aperture segmented traps. Our large-scale numerical analysis shows that, with the foreseen technological improvements described here, this platform is a very promising candidate for fault-tolerant quantum computation., The research is based upon work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via the U.S. Army Research Office Grant No. W911NF-16-1-0070. . The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. . We also acknowledge support by U.S. ARO through Grant No. W911NF-14-1-010. A. B. acknowledges support from Spanish MINECO Project No. FIS2015-70856-P, and CAM Regional Research Consortium QUITEMAD+. P. S., T. M., and R. B. acknowledge support from the Austrian Science Fund (FWF), through the SFB FoQus (FWF Project No. F4002-N16) and the Institut für Quanteninformation GmbH. S. C. B. acknowledges support from EPSRC Grant No. EP/M013243/1

Decentralized heat and power (CHP) production constitutes a promising solution to reduce the primary energy consumption and greenhouse gas emissions. Here, micro gas turbine (MGT) based CHP systems are particularly suitable due to their low pollutant emissions without exhaust gas treatment. Typically, the electrical power demand for single houses ranges from 1 to several kWel. However, downsizing turbocharger components of a conventional MGT CHP system can reduce electrical efficiencies since losses like seal and tip leakages, generally do not scale proportionally with size. By introducing an inverted Brayton Cycle (IBC) based MGT this potential can be exploited. The IBC keeps the volumetric flows constant while mass flow and thermodynamic work are scaled by the ratio of pressure level. Since the performance of turbocharger components is mainly driven by the volumetric flow they should be applicable for both cycles. Hence, smaller power outputs can be achieved. The overall aim of this work, is the development of a recuperated inverted MGT CHP unit for a single family house with 1 kWel. This paper presents an experimental study of the applicability and feasibility of a conventional MGT operated in IBC mode. The demonstrator was based on a single shaft, single stage conventional MGT. Reliable start up and stable operation within the entire operating range from 180 000 rpm to 240 000 rpm are demonstrated. The turbine outlet pressure varied between 0,5 bar (part load) and 0,3 bar absolute (full load). All relevant parameters such as pressure losses and efficiencies of the main components are investigated. Moreover, the power output and the mechanical and thermal losses were analyzed in detail. Although the results indicated that the mechanical and heat losses have a high influence on the performance and economic efficiency of the system, the prototype shows great potential for further development.

Dynamical maps are well known in the context of classical nonlinear dynamics and chaos theory. A trapped-ion quantum simulator can be used to study the generalized version of dynamical maps for many-body dissipative quantum systems.

Micro gas turbine (MGT) technology is evolving toward a large variety of novel applications, such as weak gas electrification, inverted Brayton cycles, and fuel cell hybrid cycles; however, many of these systems show very different dynamic behaviors compared to conventional MGTs. In addition, some applications impose more stringent requirements on transient maneuvers, e.g., to limit temperature and pressure gradients in a fuel cell hybrid cycle. Besides providing operational safety, optimizing system dynamics to meet the variable power demand of modern energy markets is also of increasing significance. Numerical cycle simulation programs are crucial tools to analyze these dynamics without endangering the machines, and to meet the challenges of automatic control design. For these tasks, complete cycle simulations of transient maneuvers lasting several minutes need to be calculated. Moreover, sensitivity analysis and optimization of dynamic properties like automatic control systems require many simulation runs. To perform these calculations in an acceptable timeframe, simplified component models based on lumped volume or one-dimensional discretization schemes are necessary. The accuracy of these models can be further improved by parameter identification, as most novel applications are modifications of well-known MGT systems and rely on proven, characterized components. This paper introduces a modular in-house simulation tool written in fortran to simulate the dynamic behavior of conventional and novel gas turbine cycles. Thermodynamics, gas composition, heat transfer to the casing and surroundings, shaft rotation and control system dynamics as well as mass and heat storage are simulated together to account for their interactions. While the presented models preserve a high level of detail, they also enable calculation speeds up to five times faster than real-time. The simulation tool is explained in detail, including a description of all component models, coupling of the elements and the ODE solver. Finally, validation results of the simulator based on measurement data from the DLR Turbec T100 recuperated MGT test rig are presented, including cold start-up and shutdown maneuvers.

Jet-stabilized combustion is a promising technology for fuel flexible, reliable, highly efficient combustion systems. In this work, experiments have been carried out on a two-staged combustor, with a jet-stabilized main stage and a swirl-stabilized pilot stage. Both stages have been run separately to allow a more detailed understanding of the flame stabilization within the combustor and its range of stable operation. All experiments were conducted at atmospheric pressure and preheating temperatures of 650 °C. The air was fed to both stages of the combustor for all experiments. The flame was analyzed in terms of shape, length and lift-off height, using the OH* chemiluminescence signal detected by an ICCD-camera. Emission measurements for NOx, CO and UHC emissions were carried out. The pilot stage was examined at a local air number between 0.14 and 1.43, which corresponds to a global air number of 2.0 to 20.7. For lowest air numbers, the combustor works with the RQL principle with lowest emissions in pilot stage only operation. This is because the remaining fuel fed to the pilot stage mixes rapidly with the air from the main stage and reacts under lean conditions. The optimum operating range of the main stage is at global air numbers between 3 and 3.2 with a blow-off limit beyond λg = 4.0. At a global air number of λg = 2, a fuel split variation was carried out from 0 (only pilot stage) to 1 (only main stage). In combined operation and at higher fuel splits, the NOx emissions are reduced compared to the main stage only operation, while the opposing effect on NOx emissions was observed for lower fuel splits. CFD simulations of the combustor test rig showed higher residence times in the pilot stage compared to the main stage which facilitates higher NOx formation rates in the pilot stage. This could be improved by a geometry optimization. The operation of the pilot stage was beneficial at fuel splits above 90 %, especially concerning an extended operating range to higher global air numbers. In addition, the capability of the combustor to operate at higher thermal power inputs was investigated. Originally designed for the Turbec T100 micro gas turbine, the combustor was operated at 160% of the original design point. At a constant air number, this led to a decrease in NOx and to an increase in CO emissions, caused by shorter residence times in the combustion chamber at higher power input. An operation strategy of constant pilot air number increases the envelope of a stable operation regime further.

Trapping ions in Paul traps requires high radio-frequency voltages, which are generated using resonators. When operating traps in a cryogenic environment, an in-vacuum resonator showing low loss is crucial to limit the thermal load to the cryostat. In this study, we present a guide for the design and production of compact, shielded cryogenic resonators. We produced and characterized three different types of resonators and furthermore demonstrate efficient impedance matching of these resonators at cryogenic temperatures., Comment: 13 pages, 12 figures, 1 table

Electromagnetically-induced-transparency (EIT) cooling is a ground-state cooling technique for trapped particles. EIT offers a broader cooling range in frequency space compared to more established methods. In this work, we experimentally investigate EIT cooling in strings of trapped atomic ions. In strings of up to 18 ions, we demonstrate simultaneous ground-state cooling of all radial modes in under 1 ms. This is a particularly important capability in view of emerging quantum simulation experiments with large numbers of trapped ions. Our analysis of the EIT cooling dynamics is based on a technique enabling single-shot measurements of phonon numbers, by rapid adiabatic passage on a vibrational sideband of a narrow transition.

A digital quantum simulation of a lattice gauge theory is performed on a quantum computer that consists of a few trapped-ion qubits; the model simulated is the Schwinger mechanism, which describes the creation of electron–positron pairs from vacuum. Quantum simulations promise to provide solutions to problems where classical computational methods fail. An example of a challenging computational problem is the real-time dynamics in gauge theories — field theories paramount to modern particle physics. This paper presents a digital quantum simulation of a lattice gauge theory on a quantum computer consisting of a few qubits comprising trapped calcium controlled by electromagnetic fields. The specific model that the authors simulate is the Schwinger mechanism, which describes the creation of electron–positron pairs from vacuum. As an early example of a particle-physics theory simulated with an atomic physics experiment, this could potentially open the door to simulating more complicated and otherwise computationally intractable models. Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons1,2. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman’s idea of a quantum simulator3,4, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented5,6,7. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model8,9) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism10,11, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron–positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields12 in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture13. We explore the Schwinger mechanism of particle–antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments—the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.