Superconductor electronics fabrication technology developed at MIT Lincoln Laboratory enables the development of VLSI digital circuits with millions of Josephson junctions per square centimeter. However, conventional DC and multi-phase AC biasing techniques already encounter serious challenges for scaling circuits above several hundred thousand junctions. In this work, we propose a novel AC-based biasing scheme for RSFQ-type logic families requiring DC bias. The major step toward this scheme is a superconducting AC/DC rectifier which we introduced at ASC 2014. Initially, we proposed to connect the rectifiers to 'payload cells' via superconducting inductors with large inductance in order to reduce parasitic effects of flux quantization. Recently, we discovered that this powering scheme works even better at a much lower value of the inductance, when it is just sufficient to hold only one or two flux quanta in the inductive loop between the converter and the payload. In this case, flux quantization in the loop becomes beneficial because the value of current fed into the payload is defined by the value of the coupling inductance. Therefore, our AC/SFQ converter powers the payload cell by a single flux quantum rather than by DC current. Such mode of operation is extremely energy efficient because the energy is used only to recover flux quantum consumed by the cell during the logic operation. We present designs of AC/SFQ converters comprising an AC/DC rectifier and a current conditioning circuit which we termed an SFQ filter. We also present test results and demonstrate AC/SFQ powering a payload circuit using circuits fabricated in a new, 150-nm node of Lincoln Laboratory fabrication technology using self-shunted Nb/AlOx-Al/Nb Josephson junctions with 600 $μ$A/$μ$$m^2$ critical current density and 200 nm minimum linewidth of inductors.
Recent progress of Reciprocal Quantum Logic (RQL) has renewed interest in AC powering of superconductor digital circuits, which had been abandoned since the famous IBM project of 1970s. In this work we propose and demonstrate new AC-biased Single Flux Quantum (SFQ) circuits, and search for synergy of AC and currently dominating DC biasing schemes. As the first step, we suggest an on-chip AC/DC converter capable of feeding a few DC-biased gates surrounded by their AC-biased counterparts. As the second step, we introduce and present the first successful demonstration of a new AC-powered circuit …
We demonstrate the successful operation of a multi-element superconducting nanowire single-photon detector (SSPD) array integrated with a single-flux-quantum (SFQ) readout circuit in a compact 0.1 W Gifford-McMahon cryocooler. A time-resolved readout technique, where output signals from each element enter the SFQ readout circuit with finite time intervals, revealed crosstalk-free operation of the four-element SSPD array connected with the SFQ readout circuit. The timing jitter and the system detection efficiency were measured to be 50 ps and 11.4%, respectively, which were comparable to the pe…
Superconducting single-flux-quantum (SFQ) circuits have so far been developed and optimized for operation at or above helium temperatures. The SFQ approach, however, should also provide potentially viable and scalable control and read-out circuits for Josephson-junction qubits and other applications with much lower, milli-kelvin, operating temperatures. This paper analyzes the overheating problem which becomes important in this new temperature range. We suggest a thermal model of the SFQ circuits at sub-kelvin temperatures and present experimental results on overheating of electrons and silico…
A design of subkelvin single flux quantum (SFQ) circuits with reduced power dissipation and additional cooling of shunt resistors for superconducting qubit control circuits has been developed and characterized. We demonstrate operation of SFQ comparators with current resolution of 40 nA at 2 GHz sampling rate. Due to improved cooling the electron temperature in shunt resistors of a SFQ comparator is below 50 mK when the bath temperature is about 30 mK.
We have developed a fabrication technology for the development of large-scale superconducting integrated circuits with Nb-based Josephson junctions. The standard fabrication process with 10 mask levels uses four metal layers including 3 Nb superconducting layers and a Mo resistor layer. The influence of deposition parameters on film stress, electrical properties, and surface roughness were studied systematically. High quality Nb, Al, Mo, and SiO2 films were successfully deposited for the subsequent fabrication of circuits. The circuit fabrication started with the fabrication of Mo resistors wi…
We propose and demonstrate the functioning of a special Rapid Single Flux Quantum (RSFQ) circuit with frequency-dependent damping. This damping is achieved by shunting individual Josephson junctions by pieces of open-ended RC transmission lines. Our circuit includes a toggle flip-flop cell, Josephson transmission lines transferring single flux quantum pulses to and from this cell, as well as DC/SFQ and SFQ/DC converters. Due to the desired frequency-dispersion in the RC line shunts which ensures sufficiently low noise at low frequencies, such circuits are well-suited for integrating with the f…
We investigate Magnetic Josephson Junction (MJJ) - a superconducting device with ferromagnetic barrier for a scalable high-density cryogenic memory compatible with energy-efficient single flux quantum (SFQ) circuits. The superconductor-insulator-superconductor-ferromagnet-superconductor (SIS'FS) MJJs are analyzed both experimentally and theoretically. We found that the properties of SIS'FS junctions fall into two distinct classes based on the thickness of S' layer. We fabricate Nb-Al/AlOx-Nb-PdFe-Nb SIS'FS MJJs using a co-processing approach with a combination of HYPRES and ISSP fabrication pr…
Quantum computing using superconducting circuits underwent rapid development in the last decade. This field has propelled from quantum manipulation of single two-level systems to complex designs employing multiple coupled qubits allowing one to execute simple quantum algorithms. On the way to a practical quantum computer, a need for scalable interfaces between classical circuits and the quantum counterparts has arisen. Low-temperature superconducting single-flux quantum (SFQ) logic employs magnetic fluxons in Josephson transmission lines (JTLs) as basic bits for classical computation. Here, we…
We develop a fast Magnetic Josephson Junction (MJJ) - a superconducting ferromagnetic device for a scalable high-density cryogenic memory compatible in speed and fabrication with energy-efficient Single Flux Quantum (SFQ) circuits. We present experimental results for Superconductor-Insulator-Ferromagnet-Superconductor (SIFS) MJJs with high characteristic voltage IcRn of >700 uV proving their applicability for superconducting circuits. By applying magnetic field pulses, the device can be switched between MJJ logic states. The MJJ IcRn product is only ~30% lower than that of conventional junctio…
Single flux quantum (SFQ) circuits form a natural neuromorphic technology with SFQ pulses and superconducting transmission lines simulating action potentials and axons, respectively. Here we present a new component, magnetic Josephson junctions, that have a tunablility and re-configurability that was lacking from previous SFQ neuromorphic circuits. The nanoscale magnetic structure acts as a tunable synaptic constituent that modifies the junction critical current. These circuits can operate near the thermal limit where stochastic firing of the neurons is an essential component of the technology…
Superconducting single flux quantum (SFQ) circuits can process information at extremely high speeds, in the range of hundreds of GHz. SFQ circuits are based on Josephson junction cells for switching logic and ballistic transmission for transferring SFQ pulses. Multi-chip modules (MCM) are often used to implement larger complex designs, which cannot be fit onto a single chip. We have optimized the design of wideband interconnects for transferring signals and SFQ pulses between chips in flip-chip MCMs and evaluated the importance of several design parameters such as the geometry of bump pads on …
High-fidelity gate operations are essential to the realization of a fault-tolerant quantum computer. In addition, the physical resources required to implement gates must scale efficiently with system size. A longstanding goal of the superconducting qubit community is the tight integration of a superconducting quantum circuit with a proximal classical cryogenic control system. Here we implement coherent control of a superconducting transmon qubit using a Single Flux Quantum (SFQ) pulse driver cofabricated on the qubit chip. The pulse driver delivers trains of quantized flux pulses to the qubit …
Motivated by recent progress in development of cryogenic memory compatible with single flux quantum (SFQ) circuits we have performed a theoretical study of magnetic SIsFS Josephson junctions, where 'S' is a bulk superconductor, 's' is a thin superconducting film, 'F' is a metallic ferromagnet and 'I' is an insulator. We calculate the Josephson current as a function of s and F layers thickness, temperature and exchange energy of F film. We outline several modes of operation of these junctions and demonstrate their unique ability to have large product of a critical current $I_{C}$ and a normal-s…
Digital-analog concept for superconducting perceptron-like neural networks
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University（莫斯科国立大学索博列夫核物理研究所）；Moscow Technical University of Communications and Informatics (MTUCI)（莫斯科通信与信息技术大学）；Superconducting Quantum Computing Lab, Quantum Center, Skolkovo（斯科尔科沃量子中心超导量子计算实验室）；Kotelnikov Institute of Radioengineering and Electronics（科尔涅利尼科夫无线电工程与电子学研究所）
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 con…
Josephson junction circuits, such as superconducting quantum interference devices (SQUIDs) and single-flux-quantum (SFQ) circuits, have been successfully applied in both analog and digital electronic domains. They are considered to be distinct from the normal resistor-inductor-capacitor (RLC) circuits, due to the superconducting physics. To bridge the gap between Josephson junction circuits and conventional RLC circuits, we introduce a magnetic-flux-generator (MFG) model to unify the definitions of Josephson junctions and normal noninductive components, and transform their circuits uniformly i…
Single flux quantum (SFQ) based circuits are the subject of renewed attention due to their high speed and their very high energy efficiency. However, the need of cryogenic temperature, the complex physics of Josephson junctions and the lack of proper EDA tools causes slow progress in the field of superconducting electronics. In this work we introduce a new open source program named JOsephson INterface Utility Software (JOINUS [1]) that incorporates SPICE-based simulator engines, improved physical models and several powerful built-in routines. JOINUS is based on a user-friendly environment avai…
We investigated current-voltage characteristics of unshunted and externally shunted Josephson junctions (JJs) with high critical current densities, Jc, in order to extract their basic parameters and statistical characteristics for JJ modeling in superconducting integrated circuits and to assess their potential for future technology nodes. Nb/AlOx-Al/Nb JJs with diameters from 0.5 μm to 6 μm were fabricated using a fully planarized process with Mo or MoNx thin-film shunt resistors with sheet resistance Rsq = 2 Ω/sq and Rsq = 6 Ω/sq, respectively. We used our standard MIT LL process SFQ5ee to fa…
We report the first experimental demonstration of recently proposed energy-efficient single flux quantum logic, eSFQ. This logic can represent the next generation of RSFQ logic eliminating dominant static power dissipation associated with a dc bias current distribution and providing over two orders of magnitude efficiency improvement over conventional RSFQ logic. We further demonstrate that the introduction of passive phase shifters allows the reduction of dynamic power dissipation by about 20%, reaching ~0.8 aJ per bit operation. Two types of demonstration eSFQ circuits, shift registers and d…
The difference between the phases of superconducting order parameter plays in superconducting circuits the role similar to that played by the electrostatic potential difference required to drive a current in conventional circuits. This fundamental property can be altered by inserting in a superconducting circuit a particular type of weak link, the so-called Josephson $π$-junction having inverted current-phase relation and enabling a shift of the phase by $π$. We demonstrate the operation of three superconducting circuits -- two of them are classical and one quantum -- which all utilize such $π…
Superconductor digital electronics using Josephson junctions as ultrafast switches and magnetic-flux encoding of information was proposed over 30 years ago as a sub-terahertz clock frequency alternative to semiconductor electronics based on complementary metal-oxide-semiconductor (CMOS) transistors. Recently, interest in developing superconductor electronics has been renewed due to a search for energy saving solutions in applications related to high-performance computing. The current state of superconductor electronics and fabrication processes are reviewed in order to evaluate whether this el…
We develop an ac-biased shift register introduced in our previous work (V.K. Semenov et al., IEEE Trans. Appl. Supercond., vol. 25, no. 3, 1301507, June 2015) into a benchmark circuit for evaluation of superconductor electronics fabrication technology. The developed testing technique allows for extracting margins of all individual cells in the shift register, which in turn makes it possible to estimate statistical distribution of Josephson junctions in the circuit. We applied this approach to successfully test registers having 8, 16, 36, and 202 thousand cells and, respectively, about 33000, 6…
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 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.
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…
Quantum simulations consist in the intentional reproduction of physical or unphysical models into another more controllable quantum system. Beyond establishing communication vessels between unconnected fields, they promise to solve complex problems which may be considered as intractable for classical computers. From a historic perspective, two independent approaches have been pursued, namely, digital and analog quantum simulations. The former usually provide universality and flexibility, while the latter allows for better scalability. Here, we review recent literature merging both paradigms in…
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 …
Simulating quantum physics with a device which itself is quantum mechanical, a notion Richard Feynman originated, would be an unparallelled computational resource. However, the universal quantum simulation of fermionic systems is daunting due to their particle statistics, and Feynman left as an open question whether it could be done, because of the need for non-local control. Here, we implement fermionic interactions with digital techniques in a superconducting circuit. Focusing on the Hubbard model, we perform time evolution with constant interactions as well as a dynamic phase transition wit…
Superconducting digital computing systems, primarily involving Josephson junctions are actively being pursued as high performance and low energy dissipating alternatives to CMOS-based technologies for petascale and exascale computers, although several challenges still exist in overcoming barriers to practically implement these technologies. In this paper, we present an alternative superconducting logic structure: quantized charge-based logic circuits using quantum phase-slip junctions, which have been identified as dual devices to Josephson junctions. Basic principles of logic implementation u…
Superconducting circuits have become a leading quantum technology for testing fundamentals of quantum mechanics and for the implementation of advanced quantum information protocols. In this chapter, we revise the basic concepts of circuit network theory and circuit quantum electrodynamics for the sake of digital and analog quantum simulations of quantum field theories, relativistic quantum mechanics, and many-body physics, involving fermions and bosons. Based on recent improvements in scalability, controllability, and measurement, superconducting circuits can be considered as a promising quant…
