This paper introduces a subharmonic qubit drive technique, intended to provide a method to control higher frequency superconducting qubits. This is achieved by up-converting the frequency of qubit control pulses using a superconducting frequency multiplier device after the pulses have entered the dilution refrigerator. The effectiveness of the subharmonic drive technique was evaluated against the typical direct drive approach (without frequency conversion) using a 4.83 GHz transmon qubit by measuring the error-per-gate in the two cases using randomized benchmarking. The error rates of the subharmonic drive technique and typical direct drive are equivalent when the control pulse is wider than 25 ns; the subharmonic error rate is 2.4x that of the direct drive technique when using the shortest 10 ns control pulses.

Globally over the past decade, significant public and private investment has been made in the research and development of quantum systems based on optical photons, atoms or ions, spins in semiconductors, and superconductor circuits. A key technology hurdle for all these paradigms is scaling to the large number of qubits required to make a quantum computer (QC) capable of solving relevant problems that cannot be efficiently solved using a conventional computer. For example, it is estimated that greater than 1 million physical qubits will be required for a fault-tolerant QC using superconducting qubits with state-of-the-art gate error rates. Scaling superconductor-based QCs to this size from the present $\sim 100$ qubits will require designing, implementing, and testing large, cryogenic microwave systems for initialization, control of gate/entanglement operations, and readout using millions of low-power microwave signals. With the goal of assisting the nascent QC industry in this scaling challenge, NIST is developing the measurement tools, calibration standards, and algorithms for ultrasensitive, calibrated, cryogenic, microwave testing at millikelvin temperatures inside a dilution refrigerator, advances that will be required for fabrication process control, design verification, and accurate modeling and simulation in the development of large-scale QCs.

This article presents a method of frequency multiplication which exploits the kinetic inductance of a superconducting coplanar waveguide (CPW). Both frequency doubling and tripling are examined, with attention paid to conversion efficiency. This approach allows up-conversion to be implemented in a miniaturized packaged and cryogenic environment, which can simplify the design of cryogenic systems. We achieved a conversion efficiency of 12.7% and an output power of -5.0 dBm when up-converting a 10-GHz fundamental tone to the 20-GHz second harmonic, which is an improvement compared to higher power room-temperature commercial offerings. To better understand device behavior, we also develop a measurement-based model using a harmonic balance simulation, and achieved good agreement between measurements and simulations.

Radio frequency cryogenic switches are a critical enabling technology for quantum information science for both calibration and high throughput testing of samples. Traditionally, solenoid-based switches have been used [1,2], but a transition is being made to MEMS-based (Micro Electro Mechanical Systems) switches due to their lower power dissipation and smaller size, and to minimize the risk that solenoid switches tend to produce current pulses that destroy expensive cryogenic amplifiers and can cause electrostatic damage to devices. These MEMS switches require a 90-volt signal to be applied to the control lines to determine the state of the switches. Switches exist that have built-in CMOS-based (Complimentary Metal Oxide Semiconductor) control electronics to drive the 90 V, but these do not work at the cryogenic temperatures used in quantum information science. There is no currently available room temperature control system with direct control of the switches. The instrument presented here is a 19-inch rack-mount controller for a cryogenic MEMS switch network that allows a human operator to see the state of the switch via a row of clearly marked indicator lights and to change the state manually via buttons on an LED-based indicator board or automatically via Python-based serial port commands to the Arduino, an open source microcontroller platform available from multiple vendors. The design can also be modified to control other switches that require either a large voltage or current to switch.

The performance of programmable voltage signals that exploit the quantum behavior of superconducting Josephson junctions continues to improve and enhance measurements in metrology, communications, and quantum control. We review advances in pulse-driven digital synthesis techniques with Josephson-junction-based devices. Quantum-based synthesis of voltage waveforms has been demonstrated at frequencies up to 3 GHz and rms amplitudes up to 4 V. Josephson pulse generators have also been used to control and characterize superconducting qubits.

We present a technique for implementing a frequency-doubler in NbTiN on silicon for operation in a cryogenic environment. The kinetic inductance of a superconducting coplanar waveguide is exploited for efficient frequency conversion, while the fabrication allows for co-location with other cryogenic circuits. A conversion efficiency greater than 10% is demonstrated at a frequency of 9.87 GHz, offering lower input power requirements and competitive conversion efficiencies relative to other state-of-the-art solutions.

In addition to the standard geometric inductance, superconductors have a kinetic inductance that can have a strong quadratic dependence on current. We use this nonlinearity to generate large harmonics of GHz signals by etching a 0.5 m long meandered coplanar waveguide from a 60 nm thick NbTiN sputtered film. After cooling the fabricated chip to 3 K, we measure a maximum on-chip conversion efficiency from 10 GHz to 20 GHz of 14% when applying a 2.5 dBm 10 GHz signal and a 20 rnA dc current bias. The measured powers up to the third harmonic and changes in phase agree with harmonic balance simulations of the nonlinear system. We anticipate that further optimization of the design including frequency dispersion engineering will significantly increase the conversion efficiency. This approach and material, which has a critical temperature above 15K, is also extendable up to THz frequencies; we chose to operate at 10s of GHz based on the available instruments and cabling.

We demonstrate Josephson arbitrary waveform synthesizers (JAWS) with increased operating temperature range for temperatures below 4 K. These JAWS synthesizers were fabricated with externally-shunted Nb/a-Si/Nb junctions whose critical current exhibits improved temperature stability compared to the self-shunted Nb/Nb0.15Si0.85/Nb junctions typically used. Vertical stud resistors made of 230 nm of PdAu were developed to provide the milliohm shunt resistance required for junction overdamping while maintaining a small footprint suitable for high-density series arrays embedded in a coplanar waveguide. We evaluated the performance of these resistors from 3.8 K down to 20 mK. We designed, fabricated and tested a JAWS circuit with 4650 externally shunted Nb/a-Si/Nb JJs with a critical current density (Jc) of 0.12 mA∕μm2 and critical current (Ic) of 3 mA. This circuit was designed to be mounted to the 3 K stage of a dilution refrigerator and used to control and calibrate a qubit mounted at the 10 mK stage. To increase the circuit density of the JAWS circuits we made arrays of two-junction vertical stacks. Current-voltage (I-V) curves of this JAWS circuit with stacked junctions under microwave excitation show Shapiro steps with quantum-locking ranges similar to those of JAWS circuits used for qubit control.

We present electrical characterization data of sputtered Nb/a-Si/Nb Josephson junctions (JJs) for high-speed and high-density superconducting circuits. Junctions were studied with critical current densities (Jc) ranging from 0.01 to 3 mA/μm2 at 4 K. For junctions deposited at room temperature and processed to a maximum temperature of 150 °C, the dependence of Jc on barrier thickness d is exponential, Jc∝exp (−d/d0), with d0 constant over the entire range of Jc values studied. Junctions were annealed at temperatures up to 300 °C to study changes in their electrical properties and possible compatibility with high temperature fabrication processes. Current–voltage characteristics, critical current uniformity, critical current modulation with in-plane magnetic field, and sub-gap resistance behavior of these junctions were measured at 4 K and demonstrate that the junction properties do not degrade with annealing. These data indicate that Nb/a-Si/Nb JJs are a potential candidate for higher speed and higher density superconducting circuits.

We designed, simulated, and experimentally demonstrated components for a microwave-frequency digital-to-analog converter based on single flux quantum (SFQ) circuits and an amplifier based on superconducting-quantum-interference-device (SQUID) stacks. These are key components for a self-calibrated programmable waveform reference for communications metrology capable of synthesizing high-frequency signals with quantumbased output accuracy. The amplifier is an SFQ voltage multiplier circuit that consists of a network of SFQ-splitters and SQUID transformers that provides output signals consisting of quantized pulses. The circuits were fabricated using our Nb/NbxSi1-x/Nb Josephson-junction (JJ) fabrication process, which produces selfshunted JJs with Nb-doped silicon barriers. In order to demonstrate quantum-based reproducibility, stability and performance at 4 K, we synthesized single-tone and multitone waveforms at gigahertz frequencies and demonstrated their operation over a range of synthesizer output and experimental bias parameters. We also propose circuit designs for achieving higher synthesis frequencies and higher output power with improved power accuracy and spectral purity, and discuss the potential limitations of these circuits.

Quantum computers with thousands or millions of qubits will require a scalable solution for qubit control and readout electronics. Colocating these electronics at millikelvin temperatures has been proposed and demonstrated, but there exist significant challenges with power dissipation, reproducibility, fidelity, and scalability. In this article, we experimentally demonstrate the use of a Josephson arbitrary waveform synthesizer (JAWS) to generate control signals at 4 K and perform spectroscopy of two components of a typical superconducting quantum information system: a linear resonator and a (nonlinear) transmon qubit. By locating the JAWS chip at 4 K and a qubit at 0.1 K, the direct path for quasi-particle poisoning from the JAWS chip to the qubit is broken. We demonstrate the stable, self-calibrated, and reproducible output signal of the JAWS when operated in its quantum locking range, a feature that allows these synthesizers to be replicated and scaled in the cryostat, all with identical on-chip, quantized, outputs. This is a proof-of-concept demonstration to generate signals at 4 K using driven superconducting electronics to control qubits at lower temperatures.

Compared to traditional semiconductor control electronics (TSCE) located at room temperature, cryogenic single flux quantum (SFQ) electronics can provide qubit measurement and control alternatives that address critical issues related to scalability of cryogenic quantum processors. Single-qubit control and readout have been demonstrated recently using SFQ circuits coupled to superconducting qubits. Experiments where the SFQ electronics are co-located with the qubit have suffered from excess decoherence and loss due to quasiparticle poisoning of the qubit. A previous experiment by our group showed that moving the control electronics to the 3 K stage of the dilution refrigerator avoided this source of decoherence in a high-coherence three-dimensional transmon geometry. In this paper, we also generate the pulses at the 3 K stage but have optimized the qubit design and control lines for scalable two-dimensional transmon devices. We directly compare the qubit lifetime T1, coherence time T2*, and gate fidelity when the qubit is controlled by the Josephson pulse generator (JPG) circuit vs the TSCE setup. We find agreement within the daily fluctuations for T1 and T2*, and agreement within 10% for randomized benchmarking. We also performed interleaved randomized benchmarking on individual JPG gates demonstrating an average error per gate of 0.46% showing good agreement with what is expected based on the qubit coherence and higher-state leakage. These results are an order of magnitude improvement in gate fidelity over our previous work and demonstrate that a Josephson microwave source operated at 3 K is a promising component for scalable qubit control.

Large-scale integration of single flux quantum (SFQ) circuits requires components as compact as possible. In this paper, we study the feasibility of integrating vertically stacked Josephson inductors (VSJIs) fabricated with self-shunted Josephson junctions into our SFQ-based circuits, and use both dc and RF electrical measurements to verify the performance of these junction stacks as compact inductors. The VSJIs consist of three Josephson junctions stacked vertically and are inserted into test structures to validate their potential as compact alternatives to geometrical inductors. The VSJIs are designed to be non-switching junctions and are combined with smaller area, switching Josephson junctions fabricated with the same junction barrier process. The VSJIs have a designed critical current of approximately 50% greater than that of the switching junctions, and their observed behavior can be modeled correctly by including the known nonlinearity of the Josephson inductance. To confirm that this nonlinearity does not degrade the expected bias margins, we simulate two common types of SFQ cells with the geometrical inductors replaced by VSJIs. The results verify that incorporating VSJIs in SFQ circuits would increase circuit density with minimal impact on circuit margins.

Nonreciprocal transmission and isolation at microwave frequencies are important in many practical applications. In particular, compact isolators are useful in protecting sensitive quantum circuits operating at cryogenic temperatures from amplifier backaction and other environmental noise such as black-body radiation from higher temperature stages. However, the size of commercial cryogenic isolators limits the ability to measure multiple quantum circuits because of space constraints in typical dilution refrigerator systems. Furthermore, isolators usually require the use of ferrite components that cannot be integrated at the chip level and, since they also need large biasing magnetic fields, are incompatible with superconducting quantum circuits. In this work we show one way to accomplish isolation in a superconducting chip-scale device, a traveling-wave unidirectional frequency converter based on a parametrically pumped superconducting Josephson-junction transmission line, demonstrating better than 4.8 dB of inferred signal isolation from 6.6 to 11.4 GHz, with a maximum of 12 dB at 9.5 GHz. By using frequency diplexing techniques a conventional isolator could be implemented over this bandwidth.

In superconducting quantum information, machined aluminum superconducting cavities have proven to be a well-controlled, low-dissipation electromagnetic environment for quantum circuits such as qubits. They can possess large internal quality factors, Qint > 108, and present the possibility of storing quantum information for times far exceeding those of microfabricated circuits. However, in order to be useful as a storage element, these cavities require a fast “read/write” mechanism—in other words, they require tunable coupling between other systems of interest such as other cavity modes and qubits, as well as any associated readout hardware. In this work, we demonstrate these qualities in a simple dual cavity architecture in which a low-Q “readout” mode is parametrically coupled to a high-Q “storage” mode, allowing us to store and retrieve classical information. Specifically, we employ a flux-driven Josephson junction-based coupling scheme to controllably swap coherent states between two cavities, demonstrating full, sequenced control over the coupling rates between modes.