Towards metrology for and with superconducting qubits
Mark Bieler, Christoph Kissling, Victor Gaydamachenko, Asen Lyubenov Georgiev, Shekhar Priyadarshi, Michael J. Haas, Abdulrahman H. A. Widaa, Oliver Kieler, Alexander Fernández Scarioni, Thomas Weimann, J. Kohlmann, Lukas Grünhaupt
Superconducting circuits are one of the leading technologies for the realization of quantum computers. However, achieving practical, fault-tolerant quantum computers requires solutions to many technological challenges. Metrology for qubits and their peripherical devices could accelerate this development and help gaining more confidence in scientific achievements. The Quantum Electronics Department of PTB is – together with national and international partners – actively pursuing this metrological support and this poster will highlight some of the corresponding activities at PTB: (i) Concepts of voltage metrology, such as variants of the Josephson arbitrary waveform synthesizer (JAWS), are adopted at PTB for the control of superconducting qubits in order to realize quantum accurate synthesizers with a minimum of amplitude and phase noise. First waveforms at GHz frequencies, that are generated from a JAWS circuit, have been realized. Such devices could help improving qubit operation. (ii) Parametric amplifiers, that do not contain dissipative elements, enable amplification at the quantum limit of added noise. These devices are ideally suited to amplify read out signals of superconducting qubits. PTB is working on travelling-wave parametric amplifiers (TWPAs) and resonant amplifiers. The latest devices of PTB show 20 dB gain over a bandwidth of 4 GHz and, thus, are extremely promising for qubit readout. (iii) Using the properties of a two-level system, superconducting qubits can be employed as quantum-accurate and extremely sensitive power sensors at cryogenic temperatures. So far PTB has fabricated Transmon qubits and employed qubit spectroscopy and the AC Stark shift for the demonstration of power sensing. The ultimate goal will be to have dedicated circuit elements, that can be placed everywhere in a superconducting circuit, enabling quantum-accurate power sensing at this position. (iv) Opto-electronic techniques based on femtosecond lasers allow for quasi non-invasive measurements of high-frequency signals with an unprecedented bandwidth. Based upon these techniques, PTB has constructed a cryogenic sampling oscilloscope with a theoretical bandwidth exceeding 1 THz. This oscilloscope has been used for the characterization of ultrafast photodiodes at 4 K and will be further enhanced for in-situ waveform measurements for the optimization of superconducting circuits. The poster will summarize these topics, showing the latest results and future prospects.
Superconducting circuits are one of the leading technologies for the realization of quantum computers. However, achieving practical, fault-tolerant quantum computers requires solutions to many technological challenges. Metrology for qubits and their peripherical devices could accelerate this development and help gaining more confidence in scientific achievements. The Quantum Electronics Department of PTB is – together with national and international partners – actively pursuing this metrological support and this poster will highlight some of the corresponding activities at PTB: (i) Concepts of voltage metrology, such as variants of the Josephson arbitrary waveform synthesizer (JAWS), are adopted at PTB for the control of superconducting qubits in order to realize quantum accurate synthesizers with a minimum of amplitude and phase noise. First waveforms at GHz frequencies, that are generated from a JAWS circuit, have been realized. Such devices could help improving qubit operation. (ii) Parametric amplifiers, that do not contain dissipative elements, enable amplification at the quantum limit of added noise. These devices are ideally suited to amplify read out signals of superconducting qubits. PTB is working on travelling-wave parametric amplifiers (TWPAs) and resonant amplifiers. The latest devices of PTB show 20 dB gain over a bandwidth of 4 GHz and, thus, are extremely promising for qubit readout. (iii) Using the properties of a two-level system, superconducting qubits can be employed as quantum-accurate and extremely sensitive power sensors at cryogenic temperatures. So far PTB has fabricated Transmon qubits and employed qubit spectroscopy and the AC Stark shift for the demonstration of power sensing. The ultimate goal will be to have dedicated circuit elements, that can be placed everywhere in a superconducting circuit, enabling quantum-accurate power sensing at this position. (iv) Opto-electronic techniques based on femtosecond lasers allow for quasi non-invasive measurements of high-frequency signals with an unprecedented bandwidth. Based upon these techniques, PTB has constructed a cryogenic sampling oscilloscope with a theoretical bandwidth exceeding 1 THz. This oscilloscope has been used for the characterization of ultrafast photodiodes at 4 K and will be further enhanced for in-situ waveform measurements for the optimization of superconducting circuits. The poster will summarize these topics, showing the latest results and future prospects.
Coherent circuits based on superconducting elements hold tremendous promise for the practical implementation of quantum information technology: advanced computation, cryptography, and hardware simulation of complex materials systems are envisioned applications. Such circuits are essentially engineered atoms with level transitions in the 4-8 GHz regime; as such “read” and “write” operations are performed with the aid of fast microwave pulses and low-noise amplifiers, respectively. Recent advances in cavity-based superconducting parametric amplifiers have enabled real-time measurement and feedback in one and two qubits. We demonstrate a novel Josephson junction transmission-line based traveling-wave amplifier which employs sub-wavelength phase matching resonators to achieve high gain, several GHz of bandwidth, and near quantum-noise limited performance. Such devices will enable multiplexed qubit readout in integrated architectures comprised of a variety of microwave frequency analog and digital superconducting technologies: signal sources, multiplexers, ADCs, DACs, mixers, and amplifiers.
Bringing signals from quantum to classical, from few-photon to many-photon levels for further processing, is a common challenge in rising quantum technologies. These include quantum computing, quantum communication, quantum sensing, radio astronomy, and dark matter searches, typically operating at microwave frequencies and millikelvin temperatures. Superconducting parametric amplifiers, as the first piece in the readout chain, have become a cornerstone of these technologies, since they offer unrivaled noise performance near the quantum-mechanical limit and high gain to surpass the noise of subsequent amplifiers. A notable implementation is the Josephson traveling-wave parametric amplifier (TWPA), which stands out due to its bandwidth of several Gigahertz and high saturation power, often larger than -100 dBm. These key properties come at the cost of complexity in design and fabrication: TWPA metamaterials often contain several thousands of Josephson junctions. Designing high-gain TWPAs involves three major challenges: ensuring impedance-matching, phase-matching of parametric amplification, and suppressing unwanted processes, all achievable through sub-wavelength dispersion engineering. This thesis covers the circuit design and analysis, implementation, and experimental characterization of a dispersion-engineered TWPA based on radio-frequency superconducting interference devices (rf-SQUIDs). It focuses on a detailed investigation of dispersion-engineering techniques and their effects on amplifier performance, particularly through the use of time-domain circuit simulations to analyze the multimode dynamics of the circuit. The experimentally realized device features 18 dB of gain, an instantaneous bandwidth spanning from 2.2 to 6.7 GHz, a system noise of 2.5 quanta, and a saturation power of (−86.5 ± 4.0) dBm. With these characteristics, it is suitable for frequency-multiplexed readout of detector arrays or qubits. Its high saturation power, about 10 dB higher than other reported Josephson-junction-based TWPAs, allows increasing the number of qubits per readout line, or decreasing the intermodulation between frequency-multiplexed qubits, both crucial for scaling up quantum computation.
This paper presents the basic principle of the pulse-driven ac Josephson voltage standard, also called “Josephson arbitrary waveform synthesizer” (JAWS). We will mainly focus on activities and developments at the Physikalisch-Technische Bundesanstalt (PTB). The JAWS is suitable to generate high precision quantized waveforms, which can be arbitrarily programmed in the frequency and time domain with extremely high spectral purity (typical signal-to-noise ratios SNR of 120–140 dBc). A brief overview of the fabrication technology for highly integrated JAWS circuits with more than 50 000 junctions per chip will be described. This includes the stacked junction technology with up to 5-stacked junctions. The experimental setup and the key-features of JAWS will be shown too. New approaches designed to further increase the output voltage, to simplify the experimental setup, and to extend the range of applications are the on-chip power dividers, the optical pulse drive, and the RF-JAWS. A selected application of the JAWS is described to demonstrate the usability of sophisticated JAWS waveforms for the complex characterization of electrical devices. The PTB JAWS circuits already have a significant impact on the quantum ac voltage metrology community. JAWS chips made at PTB have been distributed to more than 10 national metrology and other research institutes within the framework of international research projects.
Josephson junction based parametric amplifiers are used to read out the state of superconducting qubits with high fidelity. These amplifiers are themselves superconducting circuits operating at temperatures of tens of millikelvin. A version of this type of amplifier which has exhibited large bandwidth and saturation power is the Josephson traveling wave parametric amplifier (JTWPA). One particular JTWPA topology consists of hundreds to thousands of Josephson junctions in a transmission line configuration along with periodic phase matching resonators to increase gain. Here, we look at using a superconducting qubit fabrication process to realize this circuit To analyze the sensitivity of the JTWPA to fabrication process variation, we discuss a linear model for the circuit which takes into account unit cell to unit cell variation. To extract the measured circuit values, we use in-situ measurements of a JTWPA to compare the designed values to the realized values. Finally we discuss preliminary results realizing an example JTWPA design using a fabrication process designed for superconducting qubits.
The past few decades have witnessed great progress being made from the first voltage standards based on arrays of Josephson junctions. Continuous improvements in the fabrication process have increased the quality and “user-friendliness” of these superconducting circuits. Combined with the improvements in measuring electronics, the range of applications of Josephson-based measurements with unmatched precision has extended from DC into AC voltage metrology for signal frequencies up to 500 kHz. In this poster we will present several Josephson-based measurement systems developed for metrology applications. Two versions of quantum AC standards will be used as Josephson references: Programmable Josephson Voltage Standards (PJVS), which are based on serial arrays with up to 300,000 Josephson junctions, and pulse-driven arrays with more than 50,000 junctions, typically referred to as Josephson Arbitrary Waveform Synthesizers (JAWS). PJVS can reach amplitudes of up to 80 V, while pulse-driven arrays can reach up to 1 V or even 4 V. The advantage of pulse-driven Josephson voltage standards is that they are ideally suited as quantum-based voltage synthesizers for arbitrary waveforms or sine waves with high spectral purity. Therefore, they can be used directly to characterize or calibrate ADCs. In addition, JAWS are particularly useful in Josephson impedance bridges, which perform automated impedance calibrations at the 10-9 uncertainty level over a wide frequency range from 50 Hz to 80 kHz in a single bridge. We will further show how PJVS are used in commercial quantum voltmeters for DC and AC voltages and are typically used as quantum voltage references in measurement systems. Using differential sampling based on PJVS, uncertainties at the level of a few parts in 108 for frequencies up to the kHz range can be achieved. Such quantum-based AC voltage calibrations are at least 30 times faster than conventional AC-DC transfer and offer even better uncertainties. This idea has been quickly adopted by many National Metrology Institutes to establish such systems for AC voltage calibrations. As an example, the BIPM will now start worldwide onsite comparisons to ensure the uniformity of the new method which we introduced in 2006. But developments continue. Recently, a sub-sampling technique was used to extend the frequency range of the AC quantum voltmeter to up to 100 kHz with uncertainties below 5 parts in 106. In addition, a novel method, also for differential sampling, enables the measurement of arbitrary waveforms and the calibration of specific tones. Our poster will provide an overview of these Josephson-based metrological applications and present the latest developments from this fast-developing area.
Feedback control in classical systems is an indispensable, ubiquitous tool. The theoretical basis for achieving optimal classical control is well understood, and crucially relies on a very classical assumption: that measurements of the state of a system under control need not perturb that state. In a quantum context this assumption is fundamentally invalid. Although many aspects of the theory of quantum feedback control are relatively well developed, the technological basis for feedback control of a single quantum system has only very recently matured. We demonstrate the experimental realization of a quantum feedback control protocol, perpetually stabilizing the coherent Rabi oscillations of a superconducting qubit. This is the first utilization of quantum feedback control for stabilizing a dynamical process, and the first application of quantum feedback in a solid-state system of any kind. This demonstration comprises the first half of this thesis. The feedback protocol is predicated on the ability to make high-fidelity quantum measurements, which are enabled by quantum-limited Josephson parametric amplifiers (JPAs). The design and realization of the novel Josephson traveling-wave parametric amplifier (JTWPA) comprises the second half of this thesis. The JTWPA achieves order-of-magnitude improvements over state of the art JPAs in bandwidth and signal power handling while providing quantum-limited noise performance, potentially enabling the simultaneous readout of dozens of superconducting qubits and the generation of broadband multi-mode squeezing in the microwave domain.