Impedance matching is a crucial feature of an amplifier used to increase its instantaneous bandwidth and is typically achieved using static LC resonators. Here we show an approach toimpedance matching in parametric amplifiers using arrays of unequal Josephson-junction-based elements (rf/dc SQUIDs, SNAILs, etc). The elements act either as small-footprint flux-tunable inductors forming an impedance-matching circuit, or ‚active‘ amplifier elements which result in amplifier gain. We develop an analytical theory describing these systems, predicting a quasi-non-periodic amplifier frequency and gain modulation with applied flux and the broadening of gain bandwidths. We demonstrate this in devices using arrays of flux-focused SNAILs where flux biasing varies across the array. We find instantaneous bandwidths of 200 MHz with >17 dB of gain centred at ∼5.4 GHz in a device without a static impedance matcher. This broadening of amplifier bandwidth is stable with >100 MHz bandwidth at 17 dB gain across >1.2 GHz tunable bandwidth. Our analytical model captures flux dependence and qualitatively reproduces gain-bandwidths giving confidence in our understanding of these systems and allowing operational figures of merit to be optimised in future devices.
We demonstrate a sapphire machining process integrated with intermediate-scale quantum processors. The process allows through-substrate electrical connections, necessary for low-frequencymode-mitigation, as well as signal-routing, which are vital as quantum computers scale in qubit number, and thus dimension. High-coherence qubits are required to build fault-tolerant quantum computers and so material choices are an important consideration when developing a qubit technology platform. Sapphire, as a low-loss dielectric substrate, has shown to support high-coherence qubits. In addition, recent advances in material choices such as tantalum and titanium-nitride, both deposited on a sapphire substrate, have demonstrated qubit lifetimes exceeding 0.3 ms. However, the lack of any process equivalent of deep-silicon etching to create through-substrate-vias in sapphire, or to inductively shunt large dies, has limited sapphire to small-scale processors, or necessitates the use of chiplet architecture. Here, we present a sapphire machining process that is compatible with high-coherence qubits. This technique immediately provides a means to scale QPUs with integrated mode-mitigation, and provides a route toward the development of through-sapphire-vias, both of which allow the advantages of sapphire to be leveraged as well as facilitating the use of sapphire-compatible materials for large-scale QPUs.
Superconducting qubits are a promising route to achieving large-scale quantum computers. A key challenge in realising large-scale superconducting quantum processors involves mitigatingfrequency collisions. In this paper, we present an approach to tuning fixed-frequency qubits with the use of an electron beam to locally anneal the Josephson junction. We demonstrate the ability to both increase and decrease the junction barrier resistance. The technique shows an improvement in wafer scale frequency targetting by assessing the frequency collisions in our qubit architecture. Coherence measurements are also done to evaluate the performance before and after tuning. The tuning process utilises a standard electron beam lithography system, ensuring reproducibility and implementation by any group capable of fabricating these Josephson junctions. This technique has the potential to significantly improve the performance of large-scale quantum computing systems, thereby paving the way for the future of quantum computing.
We present an analysis of wave-mixing in recently developed Josephson Travelling Wave Parametric Amplifiers (JTWPAs). Circuit simulations performed using WRspice show the full behaviourof the JTWPA allowing propagation of all tones. The Coupled Mode Equations (CMEs) containing only pump, signal, and idler propagation are shown to be insufficient to completely capture complex mixing behaviour in the JTWPA. Extension of the CMEs through additional state vectors in the analytic solutions allows closer agreement with WRspice. We consider an ordered framework for the systematic inclusion of extended eigenmodes and make a qualitative comparison with WRspice at each step. The agreement between the two methods validates both approaches and provides insight into the operation of the JTWPA. We show that care should be taken when using the CMEs and propose that WRspice should be used as a design tool for non-linear superconducting circuits such as the JTWPA.