In the upcoming decades quantum technologies, especially quantum computation, will have a strong influence on industrial, technological, economic, and social progress and are, therefore, considered to be one of the key technologies. The fundamental building blocks for quantum computation are quantum bits (qubits). The superconducting platform offers one of the most promising implementations due to its monolithic character and potential for scalability. Present research around the world primarily focusses on scaling up the number of qubits, so reliable wafer-scale fabrication technologies are mandatory. In this paper, we present our recent developments on wafer-scale fabrication of superconducting quantum circuits including Josephson junctions by the Manhattan-type technology. We discuss fabrication parameters as well as electrical characterization. For arrays out of 50 Josephson junctions with structure dimensions of 200 nm x 200 nm, we achieve a critical current standard deviation of approx. 3% on-chip and 7% on-wafer. We also show first measurement results of so fabricated transmon-type qubits with relaxation and decoherence times of T-1 = 12.5 mu s and T-2 = 15.0 mu s, respectively. With an increasing number of superconducting qubits and, thus, their input and read-out lines, new challenges arise: Crosstalk between qubits, unwanted modes in the qubit environment, and required interconnections. One way to counteract is the implementation of low inductance connections across coplanar waveguides. This can be realized by aluminum air bridges. In this paper we discuss the air bridges' fabrication parameters and the impact on the integrated circuits' elements, e.g., Josephson junctions. We show electrical and superconducting measurements with critical temperatures and critical currents of T-c > 1.0 K and I-c > 0.6 mA, respectively.

Josephson tunnel junctions represent a key element in superconducting electronics and quantum circuits. For many years, shadow evaporation by means of Dolan-type bridges has been the state-of-the-art for deep sub- micrometer sized structures. Increasing demand in the number of Josephson junctions, e.g., in qubit circuits and travelling wave parametric amplifiers, requests for a wafer-scale fabrication process with precise control of junction parameters and have led to an advanced lift-off technique called Manhattan-type junction technology in recent years. Herein, we report on the development of a 100 mm wafer-scale fabrication technology for deep sub-micrometer sized Al Josephson junctions with linear dimensions down to 180 nm. The critical current IC of the junctions ranges from about 10 to 120 nA scaling with their linear dimensions. Low temperature transport measurements as well as room-temperature characterization has been used for IC and process homogeneity determination of series arrays of up to 50 Josephson junctions. We discuss technology parameters such as yield, on-chip and on-wafer reproducibility of the junction's critical currents as well as main process limitations. Moreover, we present experimental results on the characterization of first transmon-type qubits fabricated using this technology.

Controllable coupling between the odd and even fundamental modes of an asymmetric half-wavelength superconducting coplanar waveguide resonator is demonstrated. The resonant frequency of the even mode Ωe could be tuned by an external magnetic field, while the resonant frequency of the odd mode Ωo is field independent. To realize the tunability of Ωe, the central conductor of the NbN-based resonator was galvanically coupled to an array of Al-based rf-SQUIDs (radio frequency superconducting quantum interferometer device). These rf-SQUIDs are placed in only one resonator gap, ensuring its strong asymmetry. By adjusting the appropriate external magnetic flux Φ, equal frequencies of both modes were obtained. At this resonant point Ωo(Φ)=Ωe(Φ) an avoided level crossing of the eigenfrequencies was observed, demonstrating the coupling between the odd and even fundamental modes.

The operating principle of traveling-wave parametric amplifiers is typically understood in terms of the standard coupled mode theory, which describes the evolution of forward propagating waves without any reflections, i.e. for perfect impedance matching. However, in practice, superconducting microwave amplifiers are unmatched nonlinear finite-length devices, where the reflecting waves undergo complex parametric processes, not described by the standard coupled mode theory. Here, we present an analytical solution for the TWPA gain, which includes the interaction of reflected waves. These reflections result in corrections to the well-known results of the standard coupled mode theory, which are obtained for both 3-wave and 4-wave mixing processes. Due to these reflections, gain is enhanced and unwanted nonlinear phase modulations are suppressed. Predictions of the model are experimentally demonstrated on two types of unmatched TWPA, based on coplanar waveguides with a central wire consisting of i) a high kinetic inductance superconductor, and ii) an array of 2000 Josephson junctions.

S. Kern, P. Neilinger, 2 E. Il’ichev, A. Sultanov, M. Schmelz, S. Linzen, J. Kunert, G. Oelsner, R. Stolz, A. Danilov, S. Mahashabde, A. Jayaraman, V. Antonov, S. Kubatkin, and M. Grajcar 2 Department of Experimental Physics, Comenius University, SK-84248 Bratislava, Slovakia Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta, Bratislava, Slovakia Leibniz Institute of Photonic Technology, D-07702 Jena, Germany Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-41296 Goteborg, Sweden Physics Department, Royal Holloway, University of London, Egham TW20 0EX, United Kingdom

В настоящее время в процессуальных кодексах однозначно не разрешена ситуация, когда доказательства лжи появились после вступления решения в законную силу, поскольку они чаще всего отклоняются судами как новые доказательства, которые не могут быть основа нием пересмотра по вновь открывшимся обстоятельствам.Автор анализирует причины возникшей ситуации и рассматривает в качестве решения проблемы возможность пересмотра судебного акта, основанного на ложных данных.Рассмо трены правовые позиции Конституционного Суда Российской Федерации о судебных ошиб ках, практика международных судебных учреждений по разрешению ситуации, связанной с обманом суда.Анализ осуществлялся с целью поиска наиболее простого и эффективного средства защиты от лжи в процессе

The integration, scale-up, and multiplexing arrays of superconducting qubits in quantum circuits are the main challenges of superconducting quantum technology. Here we experimentally investigate the solid-state qubit multiplexing readout scheme, containing coplanar quarter-wavelength resonators coupled with a planar Xmon-type qubit, connected to a common coplanar transmission line. We find that the qubit energy spectrum is modified in the presence of an additional exciting signal at the fundamental frequency of the neighboring resonators. We attribute the origin of this effect to the electromagnetic field propagating through the common ground plane, which changes the qubit's characteristics. Our finding may be useful for the development of scalable superconducting quantum integrated circuits with arrays of multiplexed or coupled qubits for applications in superconducting quantum processing and computing.

We demonstrate that the non-Hermitian Hamiltonian approach can be used as a universal tool to design and describe a performance of single photon quantum electrodynamical circuits (cQED). As an example of the validity of this method, we calculate a novel six port quantum router, constructed from four qubits and three open waveguides. We have obtained analytical expressions, which describe the transmission and reflection coefficients of a single photon in general form taking into account the spread qubit's parameters. We show that, due to naturally derived interferences, in situ tuning the probability of photon detection in desired ports.

Microwave superconducting quantum circuits are strongly affected by various defects that are unavoidable during the production process. This paper presents a new method for measuring losses in an open transmission line. This line interacts through a capacitive coupling with a coplanar quarter-wavelength resonator, which is used to study losses therein. The authors have investigated the dependencies of losses on power and temperature (in the millikelvin range). It has been shown that major losses in a transmission line are due to the interaction of a microwave field with defects which are effectively described by two-level systems.

The probability amplitudes of the processes related to the transfer of the excited state from one qubit to another are calculated using an indirect interaction in an open waveguide. The system consists of two qubits located at an arbitrary distance from each other. The non-Hermitian effective Hamiltonian approach used herein makes it possible to bypass using the Markovchain approximation method. Analytic expressions describing the probability of transfer of the excited state from one qubit to another under different initial states of the system were obtained.

The influence of nonradiative damping of qubits on the microwave transport of photons propagating in a onedimensional microstrip line has been considered. Expressions for the transmission and reflection coefficients for two qubits have been obtained within the non-Hermitian Hamiltonian formalism. The indirect interaction between qubits caused by nonradiative decay into a common channel is explicitly taken into account in these expressions. It has been shown that this interaction leads to results significantly different from known results.

We analyze a photon transport through a one-dimensional open waveguide side coupled to the $N$-photon microwave cavity with embedded an artificial two-level atom (qubit). The qubit state is probed by a weak signal at the fundamental frequency of the waveguide. Within the formalism of projection operators and a non-Hermitian Hamiltonian approach we develop a one-photon approximation scheme to obtain the photon wave function, which allows for the calculation of the probability amplitudes of the spontaneous transitions between the levels of two Rabi doublets in an $N$-photon cavity. We obtain analytic expressions for the transmission and reflection factors of the microwave signal through a waveguide which contains the information of the qubit parameters. We show that for a small number of cavity photons the Mollow spectrum consists of four spectral lines, which is a direct manifestation of the quantum nature of light. The results obtained in the paper are of a general nature and can be applied to any type of qubits. The specific properties of the qubit are only encoded in the two parameters: the energy $\mathrm{\ensuremath{\Omega}}$ of the qubit and its coupling $\ensuremath{\lambda}$ to the cavity photons.

In this paper, the scattering of a single photon in a waveguide–resonator–qubit system is studied. An open waveguide is connected to two resonators, located at an arbitrary distance from each other and containing a single qubit each. The scattering of a single photon makes it possible to describe the behavior of the system completely quantum mechanically. We show the existence of Fano resonance, which is a direct manifestation of the interference between the incident photon and virtual photons associated with transitions between the states of the system. The obtained expressions for the transmission coefficients allowed us to take into account the influence of the incident photon frequency on the resonances and their widths.

ПРОЕКТИРОВАНИЕ СВЕРХПРОВОДНИКОВОГО КОПЛАНАРНОГО РЕЗОНАТОРА, НЕПРЯМЫМ ОБРАЗОМ ВЗАИМОДЕЙСТВУЮЩЕГО С

In this work, using the non-Hermitian Hamiltonian method, the transmission of a single photon in a one-dimensional waveguide interacting with the cavity containing an arbitrary number of photons and the two-level artificial atom is studied with allowance for the relaxation of the latter. For transport factors, analytical expressions which explicitly take into account the qubit relaxation parameter have been obtained. The form of the transmission (reflection) coefficient when there is more than one photon in the cavity qualitatively differs from the single-photon cavity and contains the manifestation of the photon blockade effect. The qubit lifetime depends on the number of photons in the cavity.

В работе с помощью метода неэрмитового гамильтониана исследовано прохождение одиночного фотона в одномерном волноводе, взаимодействующем с резонатором, содержащим произвольное число фотонов, и двухуровневый искусственный атом, с учетом релаксации последнего. Получены аналитические выражения для транспортных коэффициентов, в явном виде учитывающие параметр релаксации кубита. Форма коэффициента прохождения (отражения), когда в резонаторе находится более одного фотона, качественно отличается от однофотонного резонатора, и содержит в себе проявление эффекта фотонной блокады. Bремя жизни кубита зависит от числа фотонов в резонаторе. Работа выполнена при финансовой поддержке Российского научного фонда (грант N 16-19-10069.) DOI: 10.21883/FTT.2017.11.45041.08k

The properties of a superconducting flux quantum bit (qubit) in the quasidispersive mode, where the frequency of a probe signal is lower than the qubit excitation frequency but is close to it, have been experimentally studied. It has been shown that all parameters of the qubit inductively coupled to a coplanar resonator can be determined at the single-frequency excitation from the analysis of the frequency responses of the transmission of the probe signal at the output of this resonator. Under the additional excitation of the qubit by the signal at the second harmonic of the cavity, resonance dips have been observed because of resonance between the probe signal and induced Rabi splitting. It has been shown that the positions of these dips are in good agreement with the parameters of the qubit that are obtained by analyzing the amplitude–frequency response within the width of the fundamental resonance frequency.

Cообщается о результатах исследования сверхпроводникового потокового квантового бита (кубита) в квазидисперсионном режиме, когда частота пробного сигнала меньше, но тем не менее близка к частоте возбуждения кубита. В этом режиме, в отличие от известных экспериментов, взаимодействие кубита с волноводом приводит не только к смещению резонансной частоты, что характерно для дисперсионного режима, но также к заметному уширению резонансной линии, обусловленному спонтанным излучением кубита. Это позволяет на основе анализа амплитудно-частотной характеристики сигнала прохождения определить при одночастотном возбуждении характерные параметры кубита, индуктивно связанного с копланарным резонатором. Работа выполнена при финансовой поддержке Российского научного фонда в рамках проекта N 16-19-10069.

In this paper we show a transport characteristic for a system, containing two distanced resonators with artificial atoms inside. The artificial atoms can be realized as superconducting quantum bits performing two level system properties. A fully quantum-mechanical approach is used. We have numerically simulated a transmission through the system with weak and strong couplings. The criteria to observe wavefunction interferences at amplitude-frequency responses was found.

This paper reports on the results of the investigation of a superconducting flux quantum bit (qubit) in the quasi-dispersive regime, where the frequency of a probe signal even though is lower than, but, nevertheless, close to the excitation frequency of the qubit. In this regime, in contrast to the known experiments, the interaction of the qubit with a waveguide leads not only to a shift of the resonance frequency, which is characteristic of the dispersive regime, but also to a significant broadening of the resonance line due to the spontaneous emission of the qubit. On the basis of the analysis of the amplitude–frequency characteristic of the transmission signal, this makes it possible to determine, under single-frequency excitation, the characteristic parameters of the qubit inductively coupled to the coplanar resonator.