One of the major requirements for superconducting qubit hardware to work efficiently is high-fidelity, quantum non-demolition qubit readout. The qubits and the cavity where the qubits are placed are present in a cryogenic setup at a temperature around 10mK. To read the state of qubit at room temperature, it is necessary to amplify the weak microwave signal without adding much noise. The amplification can be done only by using quantum-limited amplifiers. One example of a superconducting quantum limited amplifier is the SNAIL parametric amplifier (SPA). SNAIL Parametric Amplifier (SPA) is a phase preserving superconducting amplifier. The amplifier has a non-linear element where the signal to be amplified interacts with a strong microwave pump at double the signal frequency. It is necessary to separate the amplified signal tone from the pump tone on the output of the device in order to protect the qubit from the strong microwave pump. In this report, we have studied how to add a diplexer to a SPA circuit to achieve this required separation between signal and pump tones. A diplexer is a device that divides the signal from a common port into different frequencies. It consists of two bandpass filters attached to the common port at one end and to the respective signal port at the other. The diplexer here directs the signal from qubit and pump tone to the amplifier which is connected to the common port. Thus, the diplexer along with a circulator is used to direct the signal from qubit to the amplifier and the amplified signal to the observer at room temperature. In this project, different diplexers with filters of different order were designed. The response (linewidth) of these diplexers was observed both in the absence and presence of the amplifier and they were compared. The report concludes by noting the difficulties in designing the perfect diplexer and presents future design methodologies to obtain a diplexer and amplifier, fulfilling the requirements- wide passband, low insertion loss at passband and high isolation between signal and pump ports.
One of the major requirements for superconducting qubit hardware to work efficiently is high-fidelity, quantum non-demolition qubit readout. The qubits and the cavity where the qubits are placed are present in a cryogenic setup at a temperature around 10mK. To read the state of qubit at room temperature, it is necessary to amplify the weak microwave signal without adding much noise. The amplification can be done only by using quantum-limited amplifiers. One example of a superconducting quantum limited amplifier is the SNAIL parametric amplifier (SPA). SNAIL Parametric Amplifier (SPA) is a phase preserving superconducting amplifier. The amplifier has a non-linear element where the signal to be amplified interacts with a strong microwave pump at double the signal frequency. It is necessary to separate the amplified signal tone from the pump tone on the output of the device in order to protect the qubit from the strong microwave pump. In this report, we have studied how to add a diplexer to a SPA circuit to achieve this required separation between signal and pump tones. A diplexer is a device that divides the signal from a common port into different frequencies. It consists of two bandpass filters attached to the common port at one end and to the respective signal port at the other. The diplexer here directs the signal from qubit and pump tone to the amplifier which is connected to the common port. Thus, the diplexer along with a circulator is used to direct the signal from qubit to the amplifier and the amplified signal to the observer at room temperature. In this project, different diplexers with filters of different order were designed. The response (linewidth) of these diplexers was observed both in the absence and presence of the amplifier and they were compared. The report concludes by noting the difficulties in designing the perfect diplexer and presents future design methodologies to obtain a diplexer and amplifier, fulfilling the requirements- wide passband, low insertion loss at passband and high isolation between signal and pump ports.
Superconducting parametric amplifiers (SPAs) are critical components for ultralow-noise qubit readout in quantum computing, addressing the critical challenge of amplifying weak quantum signals without introducing noise that degrades coherence and computational fidelity. Unlike classical amplifiers, SPAs can achieve or closely approach quantum-limited performance, specifically the Standard Quantum Limit (SQL) of half a photon of added noise for phase-preserving amplification. The core principle of SPAs relies on parametric amplification, where energy is transferred from a strong pump tone to a weak input signal through non-dissipative nonlinear mixing processes. This is enabled by intrinsic nonlinearities in superconducting materials, primarily kinetic inductance in thin films (e.g., NbTiN, Al) and, more significantly, the Josephson effect in Josephson junctions. These nonlinear elements facilitate frequency mixing (three-wave or four-wave mixing) and can operate in phase-preserving or phase-sensitive amplification modes, with the latter allowing for noise squeezing below the SQL. This chapter emphasizes the significant role of resonator design in determining critical SPA performance metrics such as gain, bandwidth, and noise characteristics. It details both lumped-element (LC) and distributed-element (coplanar waveguide, CPW) resonators, discussing their unique properties, suitability for different frequency ranges, and the importance of achieving high-quality factors (Q) for efficient energy storage and minimal loss. A practical design and simulation of a meandered quarterwavelength CPW resonator coupled to a feed line is presented, illustrating how precise control over geometric parameters optimizes resonant frequency, coupling strength, and quality factor for high-fidelity qubit state discrimination.
Traveling-Wave Parametric Amplifiers (TWPAs) are ubiquitous in superconducting circuit readout, providing high gain with near-quantum-limited noise performance across a wide bandwidth. Their operation, however, relies on a strong microwave pump tone that is typically delivered using off-chip passive components, such as directional couplers or diplexers. These external elements add loss, increase system complexity, and limit scalability. Here, we present a traveling-wave parametric amplifier that incorporates on-chip input and output diplexers for pump routing. This co-fabricated architecture offers a compact and scalable solution for superconducting-circuit readout.
High-fidelity qubit measurement is a critical element of all quantum computing architectures. In superconducting systems, qubits are typically measured by probing a readout resonator with a weak microwave tone that must be amplified before reaching the room temperature electronics. Superconducting parametric amplifiers have been widely adopted as the first amplifier in the chain, primarily because of their low noise performance, approaching the quantum limit. However, they require isolators and circulators to route signals up the measurement chain and to protect qubits from amplified noise. While these commercial components are wideband and simple to use, their intrinsic loss, size, and magnetic shielding requirements impact overall measurement efficiency and scalability. Here we report a parametric amplifier that achieves both broadband forward amplification and backward isolation in a single, compact, non-magnetic circuit that could be integrated on chip with superconducting qubits. The approach relies on a nonlinear transmission line that supports traveling-wave parametric amplification of forward propagating signals, and isolation via frequency conversion of backward propagating signals. This traveling-wave parametric amplifier and converter has the potential to reduce the readout hardware overhead when scaling up the size of superconducting quantum computers.
As the need for scaling up quantum computers increases there is also an increased need for more compact adjacent circuitry surrounding the quantum processor. In the amplification of a qubit's readout-signal there is a need for quantum-limited amplifiers achieving a high signal-to-noise ratio. Today, it is common to use traveling-wave parametric amplifiers (TWPAs), which are currently powered by an external microwave pump. To further reduce the circuitry an option is to use an on-chip pump only requiring DC-wires to operate. This is possible due to the AC Josephson effect which can convert a DC voltage to an AC current. By connecting multiple Josephson junctions in series it is possible to increase the output power by utilizing their coherent oscillations. The purpose of this project was to simulate and characterize Josephson voltage controlled oscillators in terms of power and frequency-output, with the goal of providing the pump to a TWPA. This also included bandpass filters utilizing the Josephson inductance, to remove higher order harmonics of the oscillations. These bandpass filters were also characterized both in simulations and in measurements. To evaluate these components, a cryogenic testbed was implemented, and benchmarked, with a capacity of 12 parallel experiments. Simulations showed that it was possible to use Josephson junctions to produce stable oscillations which were filtered to give a pure 5 GHz signal with a -86.78 dBm power. When the corresponding device was measured it was not possible to observe the harmonic spectrum, likely due to noise in the DC-biasing system. The measured bandpass filters exhibited either high insertion loss or limited bandwidth as compared to design-specifications. A power-threshold was identified at approximately -90 dBm at which the bandpass filters showed severe non-linear effects, both in simulations and in measurements.
One of the primary requirements for superconducting quantum information processors is high-fidelity, quantum non-demolition qubit readout. In superconducting circuits, we perform measurements with quantum-limited microwave amplifiers. These amplifiers are based on microwave cavities and powered by Josephson-junction based nonlinearities, which we drive to parametrically modulate the circuit and generate gain. However, cavity-based amplifiers generally suffer from a fixed gain-bandwidth product, a limited dynamic range, and the absence of directionality, and so they must be operated with external lossy microwave commercial components such as circulators. Many of these limitations can be circumvented by combining multiple parametric processes in a few-mode device, in particular by combining parametric drives which produce gain and those which produce gainless photon conversion. By combining balanced gain and conversion processes between a pair of modes, we have demonstrated transmission-only, phase-sensitive, gain-bandwidth-free amplification. We have also used measurements of transmon qubits with this mode of amplification to demonstrate its practical utility. More, by combining multiple instances of imbalanced gain and conversion processes among three modes, we have realized devices with non-reciprocal, transmission-only amplification, matched ports, and a large, gain-independent bandwidth. One of the biggest challenges in tuning multiple parametric processes is both inherent and dynamically-generated higher order nonlinearities in the device, which shift mode frequencies and parametric coupling strengths with pump power, preventing accurate balancing of the parametric processes. These can be controlled through engineering the Hamiltonian of the nonlinear element, in this thesis either a linearly-shunted Josephson Ring Modulator or SNAIL (Superconducting Nonlinear Asymmetric Inductive eLements), which for certain applied flux values can minimize or even change the sign of higher-order even nonlinearities. Additionally, we have explored a range of circuit parameters, allowing us to also control the relative size of odd-order nonlinearities. We have developed a series of prototypes which implement these concepts, and have achieved both high-dynamic range singly pumped amplifiers, and a promising platform for multi-parametric devices. We conclude by presenting recent progress towards implementing multiple parametric schemes that generates a practical directional amplifier, and discuss the remaining obstacles to a truly ideal parametric amplifiers.
Superconducting quantum circuits are a leading platform for building a large-scale quantum processor [1]. A crucial component necessary for the high-fidelity readout of qubits in this framework, is an ultra-low-noise microwave amplifier. Thus, over the past two decades, superconducting Josephson parametric amplifiers (JPAs) have been developed that achieve near quantum-limited noise performance, an order of magnitude lower than competing microwave amplifiers based on semiconductor transistors [2]. Nevertheless, JPAs suffer from drawbacks such as limited bandwidth and compression power that makes them difficult to use in an eventual large-scale quantum processor. Thus, an ongoing theme in JPA development is to optimize the circuit to improve these specifications without sacrificing other desirable properties such as the noise performance, ease of construction and operation, etc. Here, we review some results of optimizing a specific JPA circuit called the SNAIL parametric amplifier [3]–[5], shown in Fig. 1, where the acronym SNAIL refers to the Superconducting Nonlinear Asymmetric Inductive eLement. The SNAIL is a composite element made from conventional Al/AlOx/Al Josephson junctions, which has a nonlinear current-phase relation that can be approximated as a nonlinear inductance. By applying a strong microwave frequency pump to modulate the nonlinear inductance, parametric amplification can be realized. By device and circuit engineering we have demonstrated two orders of magnitude improvement in compression power (Fig. 2) in such devices without sacrificing other desirable characteristics.