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International Conference on Electromagnetics in Advanced Applications (ICEAA)

A Theoretical Proposal for a Unified Modeling Approach for Superconducting Parametric Amplifiers

Yongjie Yuan, Özüm Emre Aşırım, Michael Haider, Christian Jirauschek

Published Sep 8, 2025• 0 citations
Publisher

Abstract

In this paper, we present a unified theoretical framework for analyzing nonlinear superconducting element-based quantum amplifiers. These amplifiers may be implemented either in nonlinear resonant geometries for reflection-based amplification or transmission lines for traveling-wave, transmission-based amplification. At the core of our approach is a general black-box quantum description of the dynamic system, which incorporates a flexible system-bath coupling formalism to accurately model diverse dissipation mechanisms in superconducting circuits. This framework enables a systematic evaluation of the amplification performance across various device architectures, offering a versatile tool for the design and optimization of quantum amplifiers.

DOI
10.1109/iceaa65662.2025.11305837

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Detecting single-photon level signals—carriers of both classical and quantum information—is particularly challenging for low-energy microwave frequency excitations. Here we introduce a superconducting amplifier based on a Josephson junction transmission line. Unlike current standing-wave parametric amplifiers, this traveling wave architecture robustly achieves high gain over a bandwidth of several gigahertz with sufficient dynamic range to read out 20 superconducting qubits. To achieve this performance, we introduce a subwavelength resonant phase-matching technique that enables the creation of nonlinear microwave devices with unique dispersion relations. We benchmark the amplifier with weak measurements, obtaining a high quantum efficiency of 75% (70% including noise added by amplifiers following the Josephson amplifier). With a flexible design based on compact lumped elements, this Josephson amplifier has broad applicability to microwave metrology and quantum optics.
We present an efficient, accurate, and comprehensive analysis framework for generic, multi-port nonlinear parametric circuits, in the presence of dissipation from lossy circuit components, based on "quantum-adapted" X-parameters. We apply this method to Josephson traveling-wave parametric amplifiers (JTWPAs) – a key component in superconducting and spin qubit quantum computing architectures – which are challenging to model accurately due to their thousands of linear and nonlinear circuit components. X-parameters are generated from a harmonic balance solution of the classical nonlinear circuit and then mapped to the field ladder operator basis, so that the energy associated with each of the multiple interacting modes corresponds to photon occupancy, rather than classical power waves. Explicit relations for the quantum efficiency of a generic, multi-port, multi-frequency parametric circuit are presented and evaluated for two distinct JTWPA designs. The gain and quantum efficiency are consistent with those obtained from Fourier analysis of time-domain solutions, but with enhanced accuracy, speed, and the ability to include real-world impairments, statistical variations, parasitic effects, and impedance mismatches (inand out-of-band) seamlessly. The unified flow is implemented in Keysight’s PathWave Advanced Design System (ADS) and independently in an open-source simulation code, JosephsonCircuits.jl, from the MIT authors.