J. Q. You, Franco Nori
Superconducting circuits can behave like atoms making transitions between two levels. Such circuits can test quantum mechanics at macroscopic scales and be used to conduct atomic-physics experiments on a silicon chip.
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We propose a new quantization method for superconducting electronic circuits involving a Josephson junction device coupled to a linear microwave environment. The method is based on an exact impedance synthesis of the microwave environment considered as a blackbox with impedance function Z(s). The synthesized circuit captures dissipative dynamics of the system with resistors coupled to the reactive part of the circuit in a non-trivial way. We quantize the circuit and compute relaxation rates following previous formalisms for lumped element circuit quantization. Up to the errors in the fit our m…
Based on a network graph analysis of the underlying circuit, a quantum theory of arbitrary superconducting charge qubits is derived. Describing the dissipative elements of the circuit with a Caldeira-Leggett model, we calculate the decoherence and leakage rates of a charge qubit. The analysis includes decoherence due to a dissipative circuit element such as a voltage source or the quasiparticle resistances of the Josephson junctions in the circuit. The theory presented here is dual to the quantum circuit theory for superconducting flux qubits. In contrast to spin-boson models, the full Hilbert…
Hybrid quantum circuits combine two or more physical systems, with the goal of harnessing the advantages and strengths of the different systems in order to better explore new phenomena and potentially bring about novel quantum technologies. This article presents a brief overview of the progress achieved so far in the field of hybrid circuits involving atoms, spins and solid-state devices (including superconducting and nanomechanical systems). How these circuits combine elements from atomic physics, quantum optics, condensed matter physics, and nanoscience is discussed, and different possible a…
The intriguing appeal of circuits lies in their modularity and ease of fabrication. Based on a toolbox of simple building blocks, circuits present a powerful framework for achieving new functionality by combining circuit elements into larger networks. It is an open question to what degree modularity also holds for quantum circuits -- circuits made of superconducting material, in which electric voltages and currents are governed by the laws of quantum physics. If realizable, quantum coherence in larger circuit networks has great potential for advances in quantum information processing including…
We consider a superconducting quantum point contact in a circuit quantum electrodynamics setup. We study three different configurations, attainable with current technology, where a quantum point contact is coupled galvanically to a coplanar waveguide resonator. Furthermore, we demonstrate that the strong and ultrastrong coupling regimes can be achieved with realistic parameters, allowing the coherent exchange between a superconducting quantum point contact and a quantized intracavity field.
We propose the analog-digital quantum simulation of the quantum Rabi and Dicke models using circuit quantum electrodynamics (QED). We find that all physical regimes, in particular those which are impossible to realize in typical cavity QED setups, can be simulated via unitary decomposition into digital steps. Furthermore, we show the emergence of the Dirac equation dynamics from the quantum Rabi model when the mode frequency vanishes. Finally, we analyze the feasibility of this proposal under realistic superconducting circuit scenarios.
We propose the implementation of a digital quantum simulator for prototypical spin models in a circuit quantum electrodynamics architecture. We consider the feasibility of the quantum simulation of Heisenberg and frustrated Ising models in transmon qubits coupled to coplanar waveguide microwave resonators. Furthermore, we analyze the time evolution of these models and compare the ideal spin dynamics with a realistic version of the proposed quantum simulator. Finally, we discuss the key steps for developing the toolbox of digital quantum simulators in superconducting circuits.
This paper provides an overview of the first experimental realizations of quantum-mechanical Maxwell's demons based on superconducting circuits. The principal results of these experiments are recalled and put into context. We highlight the versatility offered by superconducting circuits for studying quantum thermodynamics.
We derive a theory for the generation of arbitrary spin-spin interactions in superconducting circuits via periodic time modulation of the individual qubits or the qubit-qubit interactions. The modulation frequencies in our approach are in the microwave or radio frequency regime so that the required fields can be generated with standard generators. Among others, our approach is suitable for generating spin lattices that exhibit quantum spin liquid behavior such as Kitaev's honeycomb model.
Superconducting circuit quantum electrodynamics experiments with propagating microwaves require devices acting as beam splitters. Using niobium thin films on silicon and sapphire substrates, we fabricated superconducting 180° microstrip hybrid ring couplers, acting as beam splitters with center frequencies of about 6GHz. For the magnitude of the coupling and isolation we find -3.5+/-0.5dB and at least -15dB, respectively, in a bandwidth of 2GHz. We also investigate the effect of reflections at the superconductor-normal conductor contact by means of low temperature laser scanning microscopy. Ou…
Circuit simulation of readout process toward large-scale superconducting quantum circuits
针对器件参数波动影响大规模超导量子电路保真度的问题，提出基于传统 SPICE 的经典电路仿真方法，可在普通笔记本上评估万量子比特电路性能。
In this paper we investigate a linear chain of qubits and determine that it can be configured into a conditional two-qubit swapping gate, where the first and last qubits of the chain are the swapped qubits, and the remaining middle ancilla qubits are controlling the state of the gate. The swapping gate introduces different phases on the final states depending on the initial states. In particular we focus on a chain of four qubits and show the swapping gate it implements. We simulate the chain with realistic parameters, and decoherence noise and leakage to higher excited states, and find an ave…
We propose an efficient protocol for digital quantum simulation of quantum chemistry problems and enhanced digital-analog quantum simulation of transport phenomena in biomolecules with superconducting circuits. Along these lines, we optimally digitize fermionic models of molecular structure with single-qubit and two-qubit gates, by means of Trotter-Suzuki decomposition and Jordan-Wigner transformation. Furthermore, we address the modelling of system-environment interactions of biomolecules involving bosonic degrees of freedom with a digital-analog approach. Finally, we consider gate-truncated …
We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi-Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses thro…
Superconducting circuit quantum electrodynamics (QED) architecture composed of superconducting qubit and resonator is a powerful platform for exploring quantum physics and quantum information processing. By employing techniques developed for superconducting quantum computing, we experimentally investigate phase-sensitive Landau-Zener-Stückelberg (LZS) interference phenomena in a circuit QED. Our experiments cover a large range of LZS transition parameters, and demonstrate the LZS induced Rabi-like oscillation as well as phase-dependent steady-state population.
We propose a tunable on-chip micromaser using a superconducting quantum circuit (SQC). By taking advantage of externally controllable state transitions, a state population inversion can be achieved and preserved for the two working levels of the SQC and, when needed, the SQC can generate a single photon. We can regularly repeat these processes in each cycle when the previously generated photon in the cavity is decaying, so that a periodic sequence of single photons can be produced persistently. This provides a controllable way for implementing a persistent single-photon source on a microelectr…
We introduce a systematic formalism for two-resonator circuit QED, where two on-chip microwave resonators are simultaneously coupled to one superconducting qubit. Within this framework, we demonstrate that the qubit can function as a quantum switch between the two resonators, which are assumed to be originally independent. In this three-circuit network, the qubit mediates a geometric second-order circuit interaction between the otherwise decoupled resonators. In the dispersive regime, it also gives rise to a dynamic second-order perturbative interaction. The geometric and dynamic coupling stre…
We study the effect of non-equilibrium quasiparticles on the operation of a superconducting device (a qubit or a resonator), including heating of the quasiparticles by the device operation. Focusing on the competition between heating via low-frequency photon absorption and cooling via photon and phonon emission, we obtain a remarkably simple non-thermal stationary solution of the kinetic equation for the quasiparticle distribution function. We estimate the influence of quasiparticles on relaxation and excitation rates for transmon qubits, and relate our findings to recent experiments.
Circuit-level-configurable Zero-field Superconducting Diodes: A Universal Platform Beyond Intrinsic Symmetry Breaking
本文提出一种基于外部电路线电阻引起化学势移动的零场超导二极管效应，该效应电路级可配置，可通过栅极电压和电路重构精确调控极性与效率，为可扩展超导电子学提供通用平台。
The superconducting circuit companion -- an introduction with worked examples
本教程面向物理背景入门者，系统讲解超导量子比特电路分析方法，从电路图到量子化哈密顿量，附单/多量子比特实例，还补充高阶电路设计技术。
We report on the investigation of a superconducting anharmonic multi-level circuit that is coupled to a harmonic readout resonator. We observe multi-photon transitions via virtual energy levels of our system up to the fifth excited state. The back-action of these higher-order excitations on our readout device is analyzed quantitatively and demonstrated to be in accordance with theoretical expectation. By applying a strong microwave drive we achieve multi-photon dressing within our anharmonic circuit which is dynamically coupled by a weak probe tone. The emerging higher-order Rabi sidebands and…
Superconducting circuit technologies have recently achieved quantum protocols involving closed feedback loops. Quantum artificial intelligence and quantum machine learning are emerging fields inside quantum technologies which may enable quantum devices to acquire information from the outer world and improve themselves via a learning process. Here we propose the implementation of basic protocols in quantum reinforcement learning, with superconducting circuits employing feedback-loop control. We introduce diverse scenarios for proof-of-principle experiments with state-of-the-art superconducting …
We introduce a toolbox for the quantum simulation of superluminal motion with superconducting circuits. We show that it is possible to simulate the motion of a superconducting qubit at constant velocities that exceed the speed of light in the electromagnetic medium and the subsequent emission of Ginzburg radiation. We consider as well possible setups for simulating the superluminal motion of a mirror, finding a link with the superradiant phase transition of the Dicke model.
We investigate the circuit quantum electrodynamics of anharmonic superconducting nanowire oscillators. The sample circuit consists of a capacitively shunted nanowire with a width of about 20 nm and a varying length up to 350 nm, capacitively coupled to an on-chip resonator. By applying microwave pulses we observe Rabi oscillations, measure coherence times and the anharmonicity of the circuit. Despite the very compact design, simple top-down fabrication and high degree of disorder in the oxidized (granular) aluminum material used, we observe lifetimes in the microsecond range.
Superconducting qubits connected in an array can form quantum many-body systems such as the quantum Ising model. By coupling the qubits to a superconducting resonator, the combined system forms a circuit QED system. Here, we study the nonlinear behavior in the many-body state of the qubit array using a semiclassical approach. We show that sudden switchings as well as a bistable regime between the ferromagnetic phase and the paramagnetic phase can be observed in the qubit array. A superconducting circuit to implement this system is presented with realistic parameters .
Measurement of Many-Body Quantum Correlations in Superconducting Circuits
提出一种基于Josephson结非线性的探针电路，用于读取超导电路模拟量子模拟器中的多体量子关联，并验证其在LC梯形网络中测量压缩等量子关联的能力。
Flux-charge symmetric theory of superconducting circuits
本文提出一种磁通-电荷对称的超导电路量子化理论，结合拓扑图论与辛几何方法，使电荷和磁通在相空间上对称处理，并探讨电路对偶性从平面到非平面电路的推广。
Adiabatic manipulation of the quantum state is an essential tool in modern quantum information processing. Here we demonstrate the speed-up of the adiabatic population transfer in a three-level superconducting transmon circuit by suppressing the spurious non-adiabatic excitations with an additional two-photon microwave pulse. We apply this superadiabatic method to the stimulated Raman adiabatic passage, realizing fast and robust population transfer from the ground state to the second excited state of the quantum circuit.
We describe a superconducting-circuit lattice design for the implementation and simulation of dynamical lattice gauge theories. We illustrate our proposal by analyzing a one-dimensional U(1) quantum-link model, where superconducting qubits play the role of matter fields on the lattice sites and the gauge fields are represented by two coupled microwave resonators on each link between neighboring sites. A detailed analysis of a minimal experimental protocol for probing the physics related to string breaking effects shows that despite the presence of decoherence in these systems, distinctive phen…
We present a protected superconducting qubit based on an effective circuit element that only allows pairs of Cooper pairs to tunnel. These dynamics give rise to a nearly degenerate ground state manifold indexed by the parity of tunneled Cooper pairs. We show that, when the circuit element is shunted by a large capacitance, this manifold can be used as a logical qubit that we expect to be insensitive to multiple relaxation and dephasing mechanisms.
We theoretically study a circuit quantum electrodynamics (QED) architecture with superconducting flux qubits. The qubit is coupled to the transmission line resonator by an ac current originating from the current mode of the resonator. Ultrastrong coupling can be obtained by varying the capacitance between the qubit and the resonator. We propose a scalable design where the two-qubit coupling can be achieved.
Exploiting the intrinsic nonlinearity of superconducting Josephson junctions, we propose a scalable circuit with superconducting qubits (SCQs) which is very similar to the successful one now being used for trapped ions. The SCQs are coupled to the "vibrational" mode provided by a superconducting LC circuit or its equivalent (e.g., a SQUID). Both single-qubit rotations and qubit-LC-circuit couplings/decouplings can be controlled by the frequencies of the time-dependent magnetic fluxes. The circuit is scalable since the qubit-qubit interactions, mediated by the LC circuit, can be selectively per…
We investigate the validity of two common assumptions in the modelling of superconducting circuits: first, that the superconducting qubits are pointlike, and second, that the UV behaviour of the transmission line is not relevant to the qubit dynamics. We show that in the experimentally accessible ultra-strong coupling regime and for short (but attainable) times, the use of an inaccurate cutoff model (such as sharp, or none at all) could introduce very significant inaccuracies in the model's predictions.
We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure $SU(2)$ gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulatio…
A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging wh…
We show that electromagnetically-induced transparency and lasing without inversion are simultaneously achieved for microwave fields by using a fluxonium superconducting circuit. As a result of the $Δ$ energy-level structure of this artificial three-level atom, we find the surprising phenomenon that the electromagnetically-induced transparency window in the frequency domain is sandwiched between absorption on one side and amplification on the other side.
We present an approach to achieve efficient single-photon frequency conversion in the microwave domain based on coherent control in superconducting quantum circuits, which consist of a driven artificial atom coupled to a semi-infinite transmission line. Using the full quantum-mechanical method, we analyze the single-photon scattering process in this system and find that single-photon frequency up- or down-conversion with efficiency close to unity can be achieved by adjusting the parameters of the control field applied to the artificial atom. We further show that our approach is experimentally …
Parametrically induced strong coupling between a superconducting quantum circuit and a solid-state spin ensemble
本文通过参数泵浦实现约瑟夫森电路与稀土自旋系综之间的动态可控强耦合，为超导量子处理器提供高相干量子存储器。
We propose a superconducting circuit architecture suitable for digital-analog quantum computing (DAQC) based on an enhanced NISQ family of nearest-neighbor interactions. DAQC makes a smart use of digital steps (single qubit rotations) and analog blocks (parametrized multiqubit operations) to outperform digital quantum computing algorithms. Our design comprises a chain of superconducting charge qubits coupled by superconducting quantum interference devices (SQUIDs). Using magnetic flux control, we can activate/deactivate exchange interactions, double excitation/de-excitations, and others. As a …
We realize a superconducting circuit analog of the generic cavity-optomechanical Hamiltonian by longitudinally coupling two superconducting resonators, which are an order of magnitude different in frequency. We achieve longitudinal coupling by embedding a superconducting quantum interference device (SQUID) into a high frequency resonator, making its resonance frequency depend on the zero point current fluctuations of a nearby low frequency LC-resonator. By employing sideband drive fields we enhance the intrinsic coupling strength of about 15 kHz up to 280 kHz by controlling the amplitude of th…
The study of quantum heat transport in superconducting circuits is significant for further understanding the connection between quantum mechanics and thermodynamics, and for possible applications for quantum information. The first experimental realisations of devices demonstrating photonic heat transport mediated by a qubit have already been designed and measured. Motivated by the analysis of such experimental results, and for future experimental designs, we numerically evaluate the photonic heat transport of qubit-resonator devices in the linear circuit regime through electromagnetic simulati…
The quantum behaviour of mechanical resonators is a new and emerging field driven by recent experiments reaching the quantum ground state. The high frequency, small mass, and large quality-factor of carbon nanotube resonators make them attractive for quantum nanomechanical applications. A common element in experiments achieving the resonator ground state is a second quantum system, such as coherent photons or superconducting device, coupled to the resonators motion. For nanotubes, however, this is a challenge due to their small size. Here, we couple a carbon nanoelectromechanical (NEMS) device…
Majorana fermions are long-sought exotic particles that are their own antiparticles. Here we propose to utilize superconducting circuits to construct two superconducting-qubit arrays where Majorana modes can occur. A so-called Majorana qubit is encoded by using the unpaired Majorana modes, which emerge at the left and right ends of the chain in the Majorana-fermion representation. We also show this Majorana qubit in the spin representation and its advantage, over a single superconducting qubit, regarding quantum coherence. Moreover, we propose to use four superconducting qubits as the smallest…
Higgs gap modes in superconducting circuit quantisation
本文提出了一种基于电路量化的框架，用于研究超导体中与间隙动力学相关的Higgs模式，推导了Higgs质量、弹簧常数和振荡频率的解析表达式，并通过数值验证和与长波长计算的对比验证了非谐振修正。
We present a theoretical description for circuits consisting of weak anharmonic qubits coupled to cavity multimodes. We obtain a unitary transformation that diagonalizes harmonic sector of the circuit. Weak anharmonicity does not alter the normal mode basis, however it can modify energy levels. We study two examples of a transmon and two transmons coupled to bus resonator, and we determine dressed frequencies and Kerr nonlinearities in closed form formulas. Our results are valid for arbitrary frequency detuning and coupling within and beyond dispersive regime.
Acceptor-induced bulk dielectric loss in superconducting circuits on silicon
本文揭示硅中硼受主是限制超导电路性能的强耦合两能级系统来源，通过扫描硼浓度和施加磁场展示了体介电损耗极限及其抑制方法，证明下一代超导量子处理器需要超高纯度衬底。
We present a semi-classical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions coupled to electromagnetic environments made of an arbitrary combination of distributed and lumped elements. A convenient basis, capturing the multi-mode physics, is given by the quantized eigenmodes of the linearized circuit and is fully determined by a classical linear response function. The method is used to calculate numerically the low-energy spectrum of a 3D-transmon system, and quantitative agreement with …
Quantum simulators are attractive as a means to study many-body quantum systems that are not amenable to classical numerical treatment. A versatile framework for quantum simulation is offered by superconducting circuits. In this perspective, we discuss how superconducting circuits allow the engineering of a wide variety of interactions, which in turn allows the simulation of a wide variety of model Hamiltonians. In particular we focus on strong photon-photon interactions mediated by nonlinear elements. This includes on-site, nearest-neighbour and four-body interactions in lattice models, allow…
Coherent pulse control for quantum memory is viable in the optical domain but nascent in microwave quantum circuits. We show how to realize coherent storage and on-demand pulse retrieval entirely within a superconducting circuit by exploiting and extending existing electromagnetically induced transparency technology in superconducting quantum circuits. Our scheme employs a linear array of superconducting artificial atoms coupled to a microwave transmission line.
We report the experimental realization of a hybrid quantum circuit combining a superconducting qubit and an ensemble of electronic spins. The qubit, of the transmon type, is coherently coupled to the spin ensemble consisting of nitrogen-vacancy (NV) centers in a diamond crystal via a frequency-tunable superconducting resonator acting as a quantum bus. Using this circuit, we prepare arbitrary superpositions of the qubit states that we store into collective excitations of the spin ensemble and retrieve back later on into the qubit. These results constitute a first proof of concept of spin-ensemb…
We theoretically investigate the simulation of moving cavities in a superconducting circuit setup. In particular, we consider a recently proposed experimental scenario where the phase of the cavity field is used as a moving clock. By computing the error made when simulating the cavity trajectory with SQUIDs, we identify parameter regimes where the correspondence holds, and where time dilation, as well as corrections due to clock size and particle creation coefficients, are observable. These findings may serve as a guideline when performing experiments on simulation of moving cavities in superc…
The dynamical Lamb effect is predicted to arise in superconducting circuits when the coupling of a superconducting qubit with a resonator is periodically switched "on" and "off" nonadiabatically. We show that by using a superconducting circuit which allows to switch between longitudinal and transverse coupling of a qubit to a resonator, it is possible of to observe the dynamical Lamb effect. {The switching between longitudinal and transverse coupling can be achieved by modulating the magnetic flux through the circuit loops.} By solving the Schrödinger equation for a qubit coupled to a resonato…
We present low-temperature measurements of low-loss superconducting nanowire-embedded resonators in the low-power limit relevant for quantum circuits. The superconducting resonators are embedded with superconducting nanowires with widths down to 20nm using a neon focused ion beam. In the low-power limit, we demonstrate an internal quality factor up to 3.9x10^5 at 300mK [implying a two-level-system-limited quality factor up to 2x10^5 at 10 mK], not only significantly higher than in similar devices but also matching the state of the art of conventional Josephson-junction-embedded resonators. We …
Improving the accuracy of circuit quantization using the electromagnetic properties of superconductors
本文提出一种改进的超导电路量化方法，结合材料和几何依赖的动能电感，提升哈密顿量预测精度，实验显示模式频率误差从5.4%降至1.1%。
We report the realization of quantum microwave circuits using hybrid superconductor-semiconductor Josephson elements comprised of InAs nanowires contacted by NbTiN. Capacitively-shunted single elements behave as transmon qubits with electrically tunable transition frequencies. Two-element circuits also exhibit transmon-like behavior near zero applied flux, but behave as flux qubits at half the flux quantum, where non-sinusoidal current-phase relations in the elements produce a double-well Josephson potential. These hybrid Josephson elements are promising for applications requiring microwave su…
Elimination of Flux Trapping in Superconducting Circuits in Ambient Magnetic Fields
通过集成片上电阻加热器产生局部热梯度，将磁通涡旋驱赶至刻蚀槽中，从而消除环境磁场冷却或电路运行中捕获的磁通，提升超导电路性能。
Three-wave mixing in second-order nonlinear optical processes cannot occur in atomic systems due to the electric-dipole selection rules. In contrast, we demonstrate that second-order nonlinear processes can occur in a superconducting quantum circuit (i.e., a superconducting artificial atom) when the inversion symmetry of the potential energy is broken by simply changing the applied magnetic flux. In particular, we show that difference- and sum-frequencies (and second harmonics) can be generated in the microwave regime in a controllable manner by using a single three-level superconducting flux …
It is shown that strong driving of a quantum system substantially enhances the Lamb shift induced by broadband reservoirs which are typical for solid-state devices. By varying drive parameters the impact of environmental vacuum fluctuations with continuous spectral distribution onto system observables can be tuned in a distinctive way. This provides experimentally feasible measurement schemes for the Lamb shift in superconducting circuits based on Cooper pair boxes, where it can be detected either in shifted dressed transition frequencies or in pumped charge currents.
We propose an architecture based on superconducting qubits and resonators for the implementation of a variety of exotic lattice systems, such as spin and Hubbard models in higher or fractal dimensions and higher-genus topologies. Spin systems are realized naturally using qubits, while superconducting resonators can be used for the realization of Bose-Hubbard models. Fundamental requirements for these designs, such as controllable interactions between arbitrary qubit pairs, have recently been implemented in the laboratory, rendering our proposals feasible with current technology.
We present a circuit design composed of a non-reciprocal device and Josephson junctions whose ground space is doubly degenerate and the ground states are approximate codewords of the Gottesman-Kitaev-Preskill (GKP) code. We determine the low-energy dynamics of the circuit by working out the equivalence of this system to the problem of a single electron confined in a two-dimensional plane and under the effect of strong magnetic field and of a periodic potential. We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux…
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