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Recently, we demonstrated a rapid-single-flux-quantum NOT gate comprising a toggle storage loop. In this paper, we present our design and operation of a NOR gate that is a straightforward extension of the NOT gate by attaching a confluence buffer. Parameter margins wider than ±28% were confirmed in simulation. Functional tests using Nb integrated circuits demonstrated correct NOR operation with a bias margin of ±21%.

Single flux quantum (SFQ) digital circuits have shown the potential for high speed/low power computation applications. Unfortunately, because of the low integration density and low driving capability of SFQ circuits, realizing large-scale memories by using only SFQ circuits is still a challenge. Josephson-CMOS hybrid memory, hybridizing high-speed, low power SFQ circuits, and high-density CMOS memories is already proposed as a solution to the large-scale memory problem in RSFQ digital systems. In this article, an SFQ-based memory controller which works up to 10 GHz clock frequencies is designed for Josephson-CMOS hybrid memory systems. The memory controller acts as a SFQ/CMOS interface between the SFQ circuit and SRAM module and generates the required waveforms for SRAM read and write operations. The circuit which has 4-b data and 2-b address lines is fabricated with AIST 2.5 kA/cm2 STP2 process and operations of the circuits are verified. To demonstrate the scalability of the circuit, memory controller was scaled to 8-b data and 13-b address to control of the 64kb SRAM. Operations of the scaled memory controller are verified with analog simulations. Scaled circuit consumes 0.76 mW power in an area of 1.64 mm × 1.60 mm.

We propose a scalable readout interface for superconducting nanowire single-photon detector (SSPD) arrays, which we call the AQFP/RSFQ interface. This interface is composed of adiabatic quantum-flux-parametron (AQFP) and rapid single-flux-quantum (RSFQ) logic families. The AQFP part reads out the spatial information of an SSPD array via a single cable, and the RSFQ part reads out the temporal information via a single cable. The hybrid interface has high temporal resolution owing to low timing jitter in the operation of the RSFQ part. In addition, the hybrid interface achieves high circuit scalability because of low supply current in the operation of the AQFP part. Therefore, the hybrid interface is suitable for handling many-pixel SSPD arrays. We demonstrate a four-pixel SSPD array using the hybrid interface as proof of concept. The measurement results show that the hybrid interface can read out all of the pixels with a low error rate and low timing jitter., 10 pages, 6 figures

A Josephson junction is a device made of two superconducting electrodes separated by a very thin layer of isolator or normal metal. This relatively simple device has found a variety of technical applications in the form of Superconducting Quantum Interference Devices (SQUIDs) and Single Electron Transistors (SETs). One can expect that in the near future the Josephson junction will find applications in digital electronics technology RSFQ (Rapid Single Flux Quantum) and in the more distant future in construction of quantum computers. Here we concentrate on the relation of the curvature of the Josephson junction with its inductance. We apply a simple Capacitively Shunted Junction (CSJ) model in order to find condition which guarantees consistency of this model with prediction based on the Maxwell and London equations with Landau-Ginzburg current of Cooper pairs. This condition can find direct experimental verification. Keywords: Josephson junction, CSJ model, Fluxon

Bias lines routed over a ground plane naturally form microstrip lines associated with the presence of a capacitance. This can lead to unwanted resonances when coupled to Josephson junctions. This work presents an electrical model of a shunted Josephson junction with its bias lines and pads, fabricated with the 1 kA/cm$^2$ RSFQ niobium process of the FLUXONICS Foundry. A compact LCL T-model is used to simulate the microwave behavior of the bias line, predict resonances and design resonance-free superconducting circuits. The I-V characteristics of three shunted Josephson junctions have been obtained from time-domain simulations done with JSIM and show a good match with the global behavior and experimentally observed resonance at 230 GHz, measured at 4.2 K. The influence of the position and value of a series resistor placed on bias lines is studied to damp unwanted resonances at the junction., Presented at ISEC2019 conference

International audience; Single-flux-quantum (SFQ) digital circuits are mostly based on cells that rely on reliable foundry processes that make use of a superconducting ground plane as a reference for the active elements and the microstrip line interconnects. The quantum of magnetic flux h/2e, associated with the binary information, corresponds to a magnetic field energy density that needs to be localized in space to limit interactions between adjacent cells. In other words, mutual inductances can harm the proper behaviour of circuits unless they are taken carefully into account during the design phase. We studied extensively the Josephson transmission line cell with different geometrical configurations of the ground plane and bias pads. We found with the use of InductEx that the return current sometimes follows paths that are far from what intuition tells, which can lead to nonoptimized designs. In this paper, we emphasize the limitations due to the presence of external or internal magnetic fields. Then, we compare obtained performances with the ones with optimized geometries for which the presence of the magnetic field is taken into account from the design phase.

Two superconductors coupled by a weak link support an equilibrium Josephson electrical current which depends on the phase difference $\varphi$ between the superconducting condensates [1]. Yet, when a temperature gradient is imposed across the junction, the Josephson effect manifests itself through a coherent component of the heat current that flows oppositely to the thermal gradient for $ \varphi, Comment: 10 pages, 9 color figures

An on-chip magnetic shielding technique was characterized on several DC-SQUIDs to prepare the next generation of complex digital RSFQ circuits designed by the FLUXONICS foundry. The maximal frequency of operation of a toggle flip-flop cell was used as a criteria to validate the concept. It goes from a simulated value of 52 GHz (46 $\pm$ 2 GHz experimentally), for a McCumber parameter $\beta_{c}=1$ with $J_{C}=1\ \text{kA}/\text{cm}^{2}$ in the absence of external magnetic field, down to 29 GHz in the presence of an external field of 88 $\mu\text{T}$ . The shielding technique consists of surrounding a circuit by one or several superconducting niobium loops with the same layers as for the SFQ circuit. The loops are connected to the ground plane with vias. It is shown experimentally that the local magnetic field is reduced by a factor of 4 for the best shielded configuration, which limits the reduction of the maximal frequency of operation in presence of external magnetic field.

Considering the two main categories of rapid single flux quantum gates with destructive and nondestructive readout process, we have investigated the effects of readout cell topology and involved critical parameters on the proper functionality and stability of the states of the newly developed bidirectional T flip-flops (TFFs). It is observed that instabilities and fluctuations in the state of the gate (memory of TFF) after each transition determine the minimum time intervals between the clock pulses set by the ac bias current, further limiting the ultimate operation frequency of the circuits. The absolute values of the current levels of the junctions at each state, which play an important role in the behavior of the cell, are studied, and their variations over several consequent pulses are stabilized by optimizing the cell parameters. The appropriate values of the circuit and junction parameters are found, resulting in the optimum operation of the circuit for having the best margins possible. We report on the investigated circuit topology and parameter optimizations of the readout circuit of the considered bidirectional TFF. © 2002-2011 IEEE.

Direct measurements of propagation delay of single-flux-quantum (SFQ) circuits were performed using SFQ double-oscillator time-to-digital converters. The propagation delay of several SFQ logic gates in our cell library named CONNECT were measured in picosecond resolution. Small discrepancy in the propagation delay of picosecond level was observed between measurement and circuit simulation results. The discrepancy is well explained assuming the parasitic inductance around shunt resistors of Josephson junctions.

We develop a theory for the quantum circuit consisting of a superconducting loop interrupted by four Josephson junctions and pierced by a magnetic flux (either static or time-dependent). In addition to the similarity with the typical three-junction flux qubit in the double-well regime, we demonstrate the difference of the four-junction circuit from its three-junction analogue, including its advantages over the latter. Moreover, the four-junction circuit in the single-well regime is also investigated. Our theory provides a tool to explore the physical properties of this four-junction superconducting circuit., 9 pages, 4 figures

Error rates of rapid-single-flux-quantum (RSFQ) shift register memories were investigated using a high-speed error-rate measurement system in order to demonstrate their reliability and stability. We designed and implemented an 8 times 8-bit shift register memory using the CONNECT cell library and the SRL 2.5 kA/cm2 Nb process. The total number of Josephson junctions including the test system is 4184, and the circuit area is 2.1 mm times 3.2 mm. We measured the error rates of every storage node by reading out the data 216 times at the clock frequency of 16 GHz. The measured error rates were lower than 10-10 with DC bias margin better than plusmn5%.

The balanced comparator is an essential part of RSFQ-based readout for superconducting qubits. In this paper we report measurements of the sensitivity of the balanced comparator fabricated in a specialized 30 A/cm2 process with 3.6 muA critical currents and measured at 30-500 mK. At sampling frequency of 3.5 GHz the measured gray zone is DeltaI = 104 nA. Due to electron overheating in the shunt resistors the effective noise temperature is 140 mK. The gray zone has a strong dependence on sampling frequency above 5 GHz due to over-clocking. Related measurements have been reported where cooling fins and reduced critical current density of 10 A/cm2 were used, and a quantum limited gray zone of 40 nA was achieved. This makes single shot readout possible for the phase, RF-SQUID and persistent current qubits. The readout speed is 30-50 ps, which is quite favorable for error correction schemes.

We will propose a new design approach for single-flux-quantum (SFQ) logic circuits based on a binary decision diagram (BDD). The BDD is a way to represent a logical function by using a directed graph, which is composed of nodes having one input (root) and two outputs (branches). The node has binary states internally which can be controlled from outside, and it switches a messenger entering from the root into one of two branches depending on the internal state. It has been proven that any combinational logic can be represented by this basic element. We will show that the BDD is effectively implemented by an SFQ circuit, where the node is replaced with an SFQ D/sub 2/ flip-flop. Important features of the BDD SFQ logic circuit are simplicity of circuit structure, self-timed nature and high modularity. We have designed a BDD SFQ adder and showed that the junction count and latency are smaller than that of the conventional RSFQ adder.

Single-flux quantum logic (SFQ) circuits, in which a flux quantum is used as an information carrier, have the possibility for opening the door to a new digital system operated at over 100-GHz clock frequency at extremely low power dissipation. The SFQ logic system is a so-called pulse logic, which is completely different from the level logic for semiconductors like CMOS, so circuit design technologies for SFQ logic circuits have to be newly developed. Recently, much progress in basic technologies for designing SFQ circuits and operating circuits at high speeds has been made. With advances in these design tools, large-scale circuits including more than several thousand junctions can be easily operated with the clock frequency of more than several tens of gigahertz. High-end routers and high-end computers are possible applications of SFQ logic circuits because of their high throughput nature and the low power dissipation of SFQ logic. In this paper, recent advances of SFQ circuit design technologies and recent developments of switches for high-end routers and microprocessors for high-end computers that are considered possible applications for SFQ logic will be described.

Niobium (Nb) LTS processes are emerging as the technology for future ultra high-speed systems especially in the digital domain. As the number of Josephson Junctions (JJ) per chip has recently increased to around 90000, the quality of the process has to be assured so as to realize these complex circuits. Until now, very little or no information is available in the literature on how to achieve this. In this paper we present an approach and results of a study conducted on an RSFQ process. Measurements and SEM inspection were carried out on sample chips and a list of possible defects has been identified and described in detail. We have also developed test-structures for detection of the top-ranking defects, which will be used for yield analysis and the determination of the probability distribution of faults in the process. A test chip has been designed, based on the results of this study, and certain types of defects were introduced in the design to study the behavior of faulty junctions and interconnections.

International audience; Superconducting correlations may propagate between two superconductors separated by a tiny insulating or metallic barrier, allowing a dissipationless electric current to flow(1,2). In the presence of a magnetic field, the maximum supercurrent oscillates(3) and each oscillation corresponding to the entry of one Josephson vortex into the barrier(4). Josephson vortices are conceptual blocks of advanced quantum devices such as coherent terahertz generators(5) or qubits for quantum computing(6), in which on-demand generation and control is crucial. Here, we map superconducting correlations inside proximity Josephson junctions(7) using scanning tunnelling microscopy. Unexpectedly, we find that such Josephson vortices have real cores, in which the proximity gap is locally suppressed and the normal state recovered. By following the Josephson vortex formation and evolution we demonstrate that they originate from quantum interference of Andreev quasiparticles(8), and that the phase portraits of the two superconducting quantum condensates at edges of the junction decide their generation, shape, spatial extent and arrangement. Our observation opens a pathway towards the generation and control of Josephson vortices by applying supercurrents through the superconducting leads of the junctions, that is, by purely electrical means without any need for a magnetic field, which is a crucial step towards high-density on-chip integration of superconducting quantum devices.

The parallelism between diffraction and interference in optics and quantum interference in Josephson junctions is discussed and studied in details. The interdisciplinary character of the present work is highlighted through specific examples. The Fraunhofer-like pattern of the maximum Josephson current in a single Josephson junction and the periodic field dependence of the critical current in two-junction and in multi-junction quantum interferometers is analyzed and discussed in comparison with the homologous classical optical phenomena.

Bi-directional RSFQ benefits from using both positive and negative SFQ pulses to manipulate and transfer digital data. This allows more flexibility in the design of simpler circuits with enhanced performance. On the other hand, using the AC bias current, one can replace on-chip resistive current distributors with inductors. This resembles RQL logic, but in contrast to RQL, it is possible to use the well-established standard RSFQ cells in bi-directional RSFQ. These two advantages (energy-efficient computation and flexibility in design) make bi-directional RSFQ a powerful tool in next-generation supercomputers and also compatible with ultra-low-temperature quantum computers. In this work, to show the power and simplicity of circuits in bi-directional RSFQ, a fully digital SQUID based on bi-directional RSFQ is designed and optimized. The circuit we show here is a delta modulating ADC with digital integrator. The circuit has fewer Josephson junctions than other reported circuits, which makes the proposed circuit more easily realizable in available LTc and HTc technologies.

We have developed a data-driven self-timed (DDST) rapid-single-flux-quantum (RSFQ) demultiplexer (demux) for the interface between on-chip high-speed RSFQ circuits and off-chip low-speed circuits. In order to eliminate the timing issue in a synchronous clocking system we employed the DDST architecture, where a clock signal is localized within a 2-bit basic demux module and dual rail lines are used to transfer the timing information between the modules. A larger demux can be produced simply by connecting the 2-bit modules in a tree structure. The DDST demux was designed for 10 Gb/s operation with sufficient dc bias margin using HYPRES 1 kA/cm/sup 2/ Nb process. We have successfully tested operation of the 2-bit demux up to 18 GHz using the DDST on-chip high-speed test system which was developed in our group.

The $\varphi$ Josephson junction has a doubly degenerate ground state with the Josephson phases $\pm\varphi$. We demonstrate the use of such a $\varphi$ Josephson junction as a memory cell (classical bit), where writing is done by applying a magnetic field and reading by applying a bias current. In the "store" state, the junction does not require any bias or magnetic field, but just needs to stay cooled for permanent storage of the logical bit. Straightforward integration with Rapid Single Flux Quantum logic is possible., Comment: to be published in APL

An interesting feature of Superconductor–Normal metal–Superconductor Josephson junctions for digital applications is due to their non-hysteretic current–voltage characteristics in a broad temperature range below T c . This allows to design Single-Flux-Quantum (SFQ) cells without the need of external shunts. Two advantages can be drawn from this property: first the SFQ cells can be more compact which leads to a more integrated solution towards nano-devices and more complex circuits; second the absence of electrical parasitic elements associated with the wiring of resistors external to the Josephson junctions increases the performance of SFQ circuits, in particular regarding the ultimate speed of operation. For this purpose Superconductor–Normal metal–Insulator–Superconductor Nb/Al–AlO x /Nb Josephson junctions have been recently developed at INRiM with aluminum layer thicknesses between 30 and 100 nm. They exhibit non-hysteretic current–voltage characteristics with I c R n values higher than 0.5 mV in a broad temperature range and optimal Stewart McCumber parameters at 4.2 K for RSFQ applications. The main features of obtained SNIS junctions regarding digital applications are presented.

It has been suggested that rapid single flux quantum (RSFQ) devices could be used as the classical interface of superconducting qubit systems. One problem is that the interface acts as a dissipative environment for a qubit. Recently, ways to modify the RSFQ damping to reduce the dissipation have been introduced. One of the solutions is to damp the Josephson junctions by a frequency-dependent linear circuit instead of the plain resistor. The approach has previously been experimentally tested with a simple SFQ comparator. In this paper we perform experiments with a full RSFQ circuit, and thus conclude that in terms of stable operation the approach is applicable to scalable RSFQ circuits. Realization and optimization issues are also discussed.

A double SQUID manipulated by fast magnetic flux pulses can be used as a tunable flux qubit. In this paper we study the requirements for the qubit operation and evaluate the dissipation and decoherence due to the manipulation, with particular attention to the contribution related to the applied tuning control, not present in simpler flux qubits. Furthermore, we shortly discuss the possibility to use an integrated Rapid Single Flux Quantum logic for the qubit control.

We report on the development and test of an integrated system composed of a flux qubit and a rapid single- flux quantum ( RSFQ) circuit that allows qubit manipulation. The goal is to demonstrate the feasibility of control electronics integrated on the same chip as the qubit, in view of the application in quantum computation with superconducting devices. RSFQ logic relies on the storage and transmission of magnetic flux quanta and can be profitably used with superconducting qubits because of the speed, scalability, compatibility with the qubit fabrication process and low temperature environment. While standard RSFQ circuitry is well assessed, the application to quantum computing requires a complete rescaling of parameter values, in order to preserve the qubit coherence and reduce the power dissipation. In the system presented in this paper, the qubit role is played by a superconducting loop interrupted by a small dc SQUID, usually called a double SQUID, which behaves as a tunable rf- SQUID. Its energy potential has the shape of a double well, with the barrier between the wells controlled by magnetic flux applied to the inner dc SQUID. Here for the first time we report measurements at a base temperature of 370 mK in which flux control pulses with desired characteristics were supplied by a RSFQ circuit fabricated using non- standard parameters in the same chip as the qubit.

We describe the read-out process of the state of a Josephson flux qubit via solitons in Josephson transmission lines (JTL) as they are in use in the standard rapid single flux quantum (RSFQ) technology. We consider the situation where the information about the state of the qubit is stored in the time delay of the soliton. We analyze dissipative underdamped JTLs, take into account their jitter, and provide estimates of the measuring time and efficiency of the measurement for relevant experimental parameters., 13 pages, 12 figures

We. discuss and demonstrate a prototype of superconducting transformer with a flux transfer function that can be varied in a wide range, by acting on a control parameter. The device is realized by inserting a small hysteretic superconducting quantum interference device (dc-SQUID) with unshunted junctions, working as a Josephson junction with flux-controlled critical current, parallel to a superconducting transformer; by varying the magnetic flux coupled to the dc-SQUID, the transfer function for the flux coupled. to the transformer can be varied. This feature can prove particularly appealing in the field of quantum computing, where it could be exploited to achieve a controllable magnetic coupling among flux-based qubits. Measurements carried out on a prototype at,4.2 K show a reduction factor of about 30 between the "on" and the "off" states. We discuss the system characteristics and the experimental results.

Low-capacitance Josephson junction arrays in the parameter range where single charges can be controlled are suggested as possible physical realizations of the elements which have been considered in the context of quantum computers. We discuss single and multiple quantum bit systems. The systems are controlled by applied gate voltages, which also allow the necessary manipulation of the quantum states. We estimate that the phase coherence time is sufficiently long for experimental demonstration of the principles of quantum computation., RevTex, 15 pages,4 postscript figures, uuencoded, submitted to Phys. Rev. Lett., estimates of the experimental parameters corrected

Superconductive single flux quantum (SFQ) digital circuits can operate at a clock frequency of several tens of gigahertz. However, the operating margin of these circuits decreases with an increase in the operating frequency because a timing error occurs in the low bias region. In this study, a novel design method that enables a wide operating margin at a high operating frequency has been investigated. The proposed circuits incorporate an additional bias feeding line in addition to the conventional bias feeding lines of the conventional Josephson transmission lines (JTLs) and can control the dependence of signal propagation time on the bias voltage. We have shown experimentally that in our proposed JTLs, the signal propagation time becomes more sensitive to the bias voltage. Timing errors can be avoided by inserting proposed JTL cells in the critical data path of the SFQ digital circuits. Circuit simulation results indicate that the operating margin of a bit-serial SFQ full adder, designed assuming the 2.5 kA/cm2 Nb process, can be improved by 15% as compared with the conventional design at a frequency of 20 GHz by employing our novel design method.

Superconducting radiation sensors are of particular interest for imaging applications in the sub-mm wavelength band because of their extraordinary sensitivity. The rising number of sensors integrated in one array entails the requirement of multiplexing techniques in order to reduce the number of wires leading into the cryogenic stage and thus reduce the thermal losses. One kind of promising code division multiplexing technique is based on a current steering switch (CSS), which is composed of two identical superconducting quantum interference devices (SQUIDs) in parallel current paths. One of them is switched from the superconducting into the normal state controlled by the applied magnetic flux. In this way the signal path can be altered and they can act as a polarity switch for analogue signals. We pursue this concept to use rapid single flux quantum (RSFQ) electronics for controlling these switches. As a first step, the SQUIDs of the CSS are inductively coupled to the storing loops of two delay flip flops (DFFs). Thus, one is able to toggle the polarity of the analogue switch by controlling the state of the DFF by RSFQ control signals. The results of simulations and measurements and also margin analyses are discussed.