Session S48: Superconducting Circuits: Amplifiers

Hybrid-free Josephson Parametric Converter

A necessary component for any quantum computation architecture is the ability to perform efficient quantum operations. In the microwave regime of superconducting qubits, these quantum-limited operations can be realized with a non-degenerate Josephson junction based three-wave mixer, the Josephson Parametric Converter (JPC). Currently, the quantum signal of interest must pass through a lossy 180 degree hybrid to be presented as a differential drive to the JPC. This hybrid therefore places a limit on the quantum efficiency of the system and also increases the device footprint. We present a new design for the JPC eliminating the need for any external hybrid. We also show that this design has nominally identical performance to the conventional JPC.   

Simplifying the circuit of Josephson parametric converters

Josephson parametric converters (JPCs) are quantum-limited three-wave mixing devices that can play various important roles in quantum information processing in the microwave domain, including amplification of quantum signals, transduction of quantum information, remote entanglement of qubits, nonreciprocal amplification, and circulation of signals [1-4]. However, the input-output and biasing circuit of a state-of-the-art JPC consists of bulky components, i.e. two commercial off-chip broadband 180-degree hybrids, four phase-matched short coax cables, and one superconducting magnetic coil. Such bulky hardware significantly hinders the integration of JPCs in scalable quantum computing architectures. In my talk, I will present ideas on how to simplify the JPC circuit and show preliminary experimental results. [1] B. Abdo et al., PRB 87, 014508. [2] M. Silveri et al., arxiv:1507.00732. [3] B. Abdo et al., PRL 112, 167701. [4] K. Sliwa et al., arxiv:1503.00209.   

Phase-sensitive, through-amplification with a double-pumped JPC.

The Josephson Parametric Converter (JPC) is now routinely used as a quantum-limited signal processing device for superconducting qubit experiments. The JPC consists of two modes, the signal and the idler, that are coupled by a ring of Josephson junctions that implements a non-degenerate, three-wave mixing process. This device is conventionally operated as either a phase-preserving parametric amplifier, or a coherent frequency converter, by pumping it at the sum or difference of the signal and idler frequencies, respectively. Here we present a novel double-pumping scheme based on theory by Metelmann and Clerk where a coherent conversion process and a gain process are simultaneously imposed between the signal and idler modes. The interference of these two processes results in a phase-sensitive amplifier with only forward gain, and which breaks the traditional gain-bandwidth limit of parametric amplification. We present results on phase-sensitive amplification with increased bandwidth, and on noise performance and dynamic range that are comparable to the traditional mode of operation.   

Traveling-Wave Parametric Amplifier Based on a Chain of Coupled Asymmetric SQUIDs

A traveling-wave parametric amplifier (TWPA) composed of a transmission line made up of a chain of coupled asymmetric superconducting quantum interference devices (SQUIDs) is proposed. The unique nature of this transmission line is that its nonlinearity can be tuned with an external magnetic flux and can even change sign. This feature of the transmission line can be used to perform phase matching in a degenerate four-wave mixing process which can be utilized for the parametric amplification of a weak signal in the presence of a strong pump. Numerical simulations of the TWPA design show that, with tuning, phase matching can be achieved and an exponential gain as a function of the transmission-line length can be realized. The flexibility of the proposed design can realize: compact TWPAs with fewer than 211 unit cells, signal gains greater than 20 dB, 3-dB bandwidth greater than 5.4 GHz, and saturation powers up to -98 dBm. This amplifier design is well suited for the multiplexed readout of quantum circuits or astronomical detectors in a compact configuration which can foster on-chip implementations. Phys. Rev. Applied 4, 024014 (2015).   

Strong field dynamics and quantum noise in Josephson traveling wave parametric amplifiers (JTWPAs)

Josephson traveling wave parametric amplifiers (JTWPAs) with resonant phase matching have demonstrated high gain over a broad bandwidth with near quantum-limited noise performance. Several amplifier non-idealities were observed in experiments, including a rapid drop in gain at a certain pump power and a near, but non-unity intrinsic quantum efficiency. To understand these non-idealities, we solve the full nonlinear wave equation for the JTWPA for a sinusoidal drive, finding higher harmonic generation and observing a blow-up at an input pump current below the junction critical current. We find analytic traveling wave solutions in the form of snoidal waves which propagate without distortion. A snoidal drive scheme may increase the drive power at which the blow-up occurs. The quantum noise properties of JTWPAs are critically important for their role as low noise amplifiers. We calculate the noise figure and find that coupling to higher order sidebands imposes an upper limit for the quantum efficiency, in good agreement with empirical results. We further show that this limit can be increased by modest changes to the phase matching of the pump and the dispersion relation.   

Broadband Josephson parametric amplifiers: Beyond the standard gain-bandwidth product

Recent development of multiplexed qubit measurement schemes demand broadband quantum-limited amplifiers to enable high fidelity readout with minimal resources. We present a simple technique to enhance the bandwidth of a resonator based Josephson Parametric Amplifier (JPA) beyond the standard gain-bandwidth product. This is achieved by introducing a positive linear slope in the imaginary component of the input impedance seen by the JPA using a $\lambda/2$ transformer. Our theoretical model predicts an extremely flat gain profile with a bandwidth enhancement proportional to the square root of the amplitude gain. Experimentally, we achieved a nearly flat 20 dB gain profile over a 640 MHz band, with a mean 1-dB compression point of -110 dBm along with nearly quantum-limited noise performance. The results are in excellent agreement with our theoretical model. We will then discuss strategies to further enhance the performance in terms of bandwidth and dynamic range of the JPA. Finally, we will consider the applicability of our technique to different parametric pumping methods and other parametric amplifier designs as well.   

Microwave design optimization for broadband Josephson parametric amplifiers

Broadband Josephson parametric amplifiers are crucial components of a scalable superconducting quantum computing architecture. Recently, the bandwidth of a resonator-based Josephson parametric amplifier was significantly enhanced by introducing a controlled reactance in the signal chain. The design was based on a $\lambda$/2 section fabricated on an RF circuit board. We present the design of an on-chip version that will improve robustness and minimize performance variability from one device to another. Further, we will discuss microwave design optimization for flux pumping mechanism to minimize cross-talk between different input-output ports of the device. Finally, we will discuss design goals for further improvement of amplifier performance.   

High dynamic range Josephson parametric amplifiers

Josephson parametric amplifiers (JPAs) have become the technology of choice to amplify small amplitude microwave signals since they show noise performances close to the quantum limit of amplification. An important challenge that faces this technology is the low dynamic range of current devices, which limits the number of measurements that can be performed concurrently and the rate of information acquisition for single measurements. We have fabricated and tested novel parametric amplifiers based on arrays of up to 100 SQUIDS. The amplifiers produce gain in excess of 20 dB over a large bandwidth and match the dynamic range achieved with traveling wave devices. Compared to the latter devices they are fabricated in a single lithography step and we will show that their bandwidth performance can be further extended using a recently developed impedance matching technique.   

Microwave response and photon emission of a voltage baised Josephson junction

The readout of superconducting qubits requires amplifiers combining noise close to the quantum limit, high gain, large bandwidth, and sufficient dynamic range. Josephson parametric amplifiers using Josephson junctions in the 0-voltage state, driven by a large microwave signals, begin to perform sufficiently well in all 4 of these aspects to be of practical use, but remain difficult to optimize and use. Recent experiments with superconducting circuits consisting of a DC voltage-biased Josephson junction in series with a resonator, showed that a tunneling Cooper pair can emit one or several photons with a total energy of 2e times the applied voltage. We present microwave reflection measurements on this device indicating that amplification is possible with a simple DC voltage-biased Josephson junction. We compare these measurements with the noise power emitted by the junction and show that, for low Josephson energy, transmission and noise emission can be explained within the framework of P(E) theory of inelastic Cooper pair tunneling. Combined with a theoretical model, our results indicate that voltage-biased Josephson junctions might be useful for amplification near the quantum limit, offering simpler design and a different trade-off between gain, bandwidth and dynamic range.   

Estimation of the projection error of a qubit readout by quantum Zeno effect

In a quantum system, frequent projection operations can suppress a specific kind of time evolutions that show quadratic behavior in a time domain. This phenomenon is known as quantum Zeno effect (QZE). Normally, projection operations freeze the qubit state so that the qubit remains in the initially prepared state such as a ground state or an excited state. However, if a projection error occurs, qubit state is flipped. In this case, frequent projection operations do not keep qubit state. This means that, by investigating the efficiency of the QZE, we can in principle estimate the projection error rate of the qubit readout system. A Josephson bifurcation amplifier (JBA) readout method provides us a way to perform fast and low back-action superconducting qubit readout. We fabricate a sample that has a JBA resonator coupled to the superconducting flux qubit. By using this sample, we demonstrated QZE by applying multiple readout pulses during Rabi oscillations. Because of the multiple readout pulses, Rabi oscillation was suppressed and the qubit was kept in its initial state. From the holding time of the state via the QZE, we concluded that the projection error of the JBA readout is less than 2{\%}.   

SLUG Microwave Amplifier as a Nonreciprocal Gain Element for Scalable Qubit Readout

Josephson parametric amplifiers for superconducting qubits require several stages of cryogenic isolation to protect the qubit from strong microwave pump tones and downstream noise. But isolators and circulators are large, expensive and magnetic, so they are an obstacle to scaling up a superconducting quantum computer. In contrast, the SLUG (Superconducting Low-inductance Undulatory Galvanometer) is a high gain, broadband, low noise microwave amplifier that provides built-in reverse isolation. Here, we describe the dependence of the SLUG reverse isolation on signal frequency and device operating point. We show that the reverse isolation of the SLUG can be as large as or larger than that of a bulk commercial isolator. Finally, we discuss the use of the SLUG to read out a transmon qubit without isolators or circulators.   

Noise Charactoristics of the Josephson Amplifiers by Stochastic Calulus

We present theoretical studies of the noise performance of non-reciprocal gain elements based on Josephson junctions including the SQUID and the SLUG. We develop a perturbative approach by means of stochastic calculus which combines both analytical and numerical methods, and calculate the noise characteristics of the amplifiers in the thermal regime. We show that noise in the amplifiers originates mainly from the diffusive behavior of phase slips. This new method could help with the optimization of Josephson amplifiers for high-fidelity multiplexed qubit readout.   

Qubit Readout with the Josephson Photomultiplier

The realization of a large-scale fault-tolerant quantum processor will require scalable high-fidelity readout of multiqubit parity operators. Here we describe development of a scalable qubit measurement approach based on microwave photon counting. The measurement protocol involves mapping the qubit state to photon occupation of bright and dark cavity pointer states, followed by photodetection using the Josephson photomultiplier (JPM). We discuss use of the qubit as a calibrated source of photons to measure JPM quantum efficiency, and we describe global optimization of the measurement protocol. Finally, we discuss prospects for interfacing the JPM output to single flux quantum circuits to allow low-latency classical postprocessing of the qubit measurement result.   

Multi-qubit measurements with a Josephson Photomultiplier

The ability to measure multi-qubit parity is critical for the realization of a fault-tolerant quantum information processor. For a system of transmon qubits coupled to a superconducting cavity, a threshold photon detector can provide an efficient path towards the digital readout of qubit parity after the parity information is mapped onto the cavity photon occupation. We will describe progress towards the implementation of such a scheme for measuring the parity of two transmon qubits. On-chip flux bias lines allow us to tune the dispersive cavity shifts related to the state of the two qubits and an appropriately shaped pulse driven to the cavity results in a bright state for one parity but not the other. A Josephson Photomultiplier then serves as a phase-insensitive digital detector of the microwave photons that leak out of the cavity. Future improvements and various technical difficulties will be discussed.