Nondegenerate Parametric Amplifiers Based on Dispersion-Engineered Josephson-Junction Arrays
Patrick Winkel, Ivan Takmakov, Dennis Rieger, Luca Planat, Wiebke Guichard, Lukas Grünhaupt, Nataliya Maleeva, Farshad Foroughi, Fabio Henriques, Kiril Borisov, Julian Ferrero, Alexey Vladimirovich Ustinov, Wolfgang Wernsdorfer, Nicolas Roch, Ioan M. Pop
Determining the state of a qubit on a time scale much shorter than its relaxation time is an essential requirement for quantum information processing. With the aid of a nondegenerate parametric amplifier, we demonstrate the continuous detection of quantum jumps of a transmon qubit with $90\mathrm{%}$ fidelity of state discrimination. Entirely fabricated by standard two-step optical-lithography techniques, this type of parametric amplifier consists of a dispersion-engineered Josephson-junction (JJ) array. By using long arrays, containing ${10}^{3}\phantom{\rule{0.2em}{0ex}}\mathrm{JJs}$, we can obtain amplification in multiple eigenmodes with frequencies below $10\phantom{\rule{0.2em}{0ex}}\mathrm{GHz}$, which is the typical range for qubit readout. Moreover, if a moderate flux tunability of each mode is introduced, employing superconducting-quantum-interference-device junctions, a single amplifier device could potentially cover the entire frequency band between 1 and 10 GHz.
Determining the state of a qubit on a time scale much shorter than its relaxation time is an essential requirement for quantum information processing. With the aid of a nondegenerate parametric amplifier, we demonstrate the continuous detection of quantum jumps of a transmon qubit with 90\mathrm{%} fidelity of state discrimination. Entirely fabricated by standard two-step optical-lithography techniques, this type of parametric amplifier consists of a dispersion-engineered Josephson-junction (JJ) array. By using long arrays, containing 103JJs, we can obtain amplification in multiple eigenmodes with frequencies below 10GHz, which is the typical range for qubit readout. Moreover, if a moderate flux tunability of each mode is introduced, employing superconducting-quantum-interference-device junctions, a single amplifier device could potentially cover the entire frequency band between 1 and 10 GHz.
We introduce a near-quantum-limited amplifier with a large tunable bandwidth and high dynamic range---the Josephson array-mode parametric amplifier (JAMPA). The signal and idler modes involved in the amplification process are realized by the array modes of a chain of 1000 flux-tunable Josephson-junction-based nonlinear elements. The frequency spacing between the array modes is comparable to the flux tunability of the modes, ensuring that any desired frequency can be occupied by a resonant mode, which can further be pumped to produce high gain. We experimentally demonstrate that the device can be operated as a nearly quantum-limited parametric amplifier with 20 dB of gain at almost any frequency within a 4--12-GHz band. On average, it has a 3-dB bandwidth of 11 MHz and an input 1-dB compression power of $\ensuremath{-}108\phantom{\rule{0.2em}{0ex}}\mathrm{dBm}$, which can go as high as $\ensuremath{-}93\phantom{\rule{0.2em}{0ex}}\mathrm{dBm}$. We envision the application of such a device to the time- and frequency-multiplexed readout of multiple qubits, as well as to the generation of continuous-variable cluster states.
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.
Abstract Over the last two decades, the superconducting qubits have become a promising and rapidly growing area of research. However, there are specific challenges when working with such a delicate system. One of them is the qubit state readout. Since a very small signal (of the order of 1 photon) is used for the readout, its detection is challenging and it requires low-noise cryogenic amplifiers working in the 3–12 GHz frequency range. Josephson parametric amplifiers (JPAs) are one of the most studied and developed candidates. Currently, several JPA designs offer low noise performance and instantaneous bandwidth from tens of MHz to several GHz; they are also becoming an integral part of circuit quantum electrodynamics (cQED) setups. In the current work, results are presented of the measurements of a JPA made of a coplanar waveguide with an array of three SQUIDs. Nondegenerate amplification and an amplifier added noise being close to the quantum limit are demonstrated.
Though superconducting qubits offer the potential for a scalable quantum computing architecture, the high-fidelity readout necessary to execute practical algorithms has thus far remained elusive. Moreover, achievements toward high fidelity have been accompanied by either long measurement times or demolition of the quantum state. In this dissertation, we address these issues with the novel integration of two ultralow-noise, superconducting amplifiers into separate dispersive flux qubit measurements. We first demonstrate a flux qubit inductively coupled to a 1.294-GHz nonlinear oscillator formed by a capacitively shunted DC SQUID. The frequency of the oscillator is modulated by the state of the qubit and is detected via microwave reflectometry. A microstrip SQUID (Superconducting QUantum Interference Device) amplifier (MSA) is used to increase the sensitivity of the measurement over that of a semiconductor amplifier. In the second experiment, we report measurements of a flux qubit coupled via a shared inductance to a quasi-lumped element 5.78-GHz readout resonator formed by the parallel combination of an interdigitated capacitor and a meander line inductor. The system noise is substantially reduced by a near-quantum-limited Josephson parametric amplifier (paramp).We present measurements of increased fidelity and reduced measurement backaction using the MSA at readout excitation levels as low as one hundredth of a photon in the readout resonator, observing a 4.5-fold increase in the readout visibility. Furthermore, at low readout excitation levels below one tenth of a photon in the readout resonator, no reduction in T1 is observed, potentially enabling continuous monitoring of the qubit state. Using the paramp, we demonstrate a continuous, high-fidelity readout with sufficient bandwidth and signal-to-noise ratio to resolve quantum jumps in the flux qubit. This is enabled by a readout which discriminates between the readout pointer state distributions to an error below one part in 1000. This, along with the ability to make many successive readouts in a time T1, permits the use of heralding to ensure initialization to a fiducial state, such as the ground state. This method enables us to eliminate errors due to spurious thermal population, increasing the fidelity to 93.9%. Finally, we use heralding to introduce a simple, fast qubit reset protocol without changing the system parameters to induce Purcell relaxation.
Though superconducting qubits offer the potential for a scalable quantum computing architecture, the high-fidelity readout necessary to execute practical algorithms has thus far remained elusive. Moreover, achievements toward high fidelity have been accompanied by either long measurement times or demolition of the quantum state. In this dissertation, we address these issues with the novel integration of two ultralow-noise, superconducting amplifiers into separate dispersive flux qubit measurements. We first demonstrate a flux qubit inductively coupled to a 1.294-GHz nonlinear oscillator formed by a capacitively shunted DC SQUID. The frequency of the oscillator is modulated by the state of the qubit and is detected via microwave reflectometry. A microstrip SQUID (Superconducting QUantum Interference Device) amplifier (MSA) is used to increase the sensitivity of the measurement over that of a semiconductor amplifier. In the second experiment, we report measurements of a flux qubit coupled via a shared inductance to a quasi-lumped element 5.78-GHz readout resonator formed by the parallel combination of an interdigitated capacitor and a meander line inductor. The system noise is substantially reduced by a near-quantum-limited Josephson parametric amplifier (paramp).We present measurements of increased fidelity and reduced measurement backaction using the MSA at readout excitation levels as low as one hundredth of a photon in the readout resonator, observing a 4.5-fold increase in the readout visibility. Furthermore, at low readout excitation levels below one tenth of a photon in the readout resonator, no reduction in T1 is observed, potentially enabling continuous monitoring of the qubit state. Using the paramp, we demonstrate a continuous, high-fidelity readout with sufficient bandwidth and signal-to-noise ratio to resolve quantum jumps in the flux qubit. This is enabled by a readout which discriminates between the readout pointer state distributions to an error below one part in 1000. This, along with the ability to make many successive readouts in a time T1, permits the use of heralding to ensure initialization to a fiducial state, such as the ground state. This method enables us to eliminate errors due to spurious thermal population, increasing the fidelity to 93.9%. Finally, we use heralding to introduce a simple, fast qubit reset protocol without changing the system parameters to induce Purcell relaxation.
High-fidelity quantum nondemolition qubit measurement is critical to error correction and rapid qubit feedback in large-scale quantum computing. Maximizing high-fidelity dispersive readout in superconducting qubits commonly requires passing a short and strong pulse through the qubit's readout resonator, which is then processed by a sufficiently high bandwidth, high saturation power, and quantum-limited amplifier. We have developed an amplifier design pipeline that combines time-domain simulation of the untruncated device Hamiltonian, fabrication constraints, and maximization of saturation power. We have realized an amplifier based on a modified trilayer (Nb-Al-AlOx-Nb) fabrication suite at NIST, which utilizes an array of 25 rf superconducting quantum interference devices embedded within a low-Q resonator powered by a high-power voltage pump delivered via a diplexer on the signal port. We show that, despite the intensity of the pump, the device is quantum efficient and capable of high-fidelity measurement limited by state transitions in the transmon. We present experimental data demonstrating up to $\ensuremath{-}91.2\phantom{\rule{0.2em}{0ex}}\mathrm{dBm}$ input saturation power with 20-dB gain, up to 28-MHz instantaneous bandwidth, and phase-preserving qubit measurements with $62\mathrm{%}$ quantum efficiency.