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IEEE International Conference on Computer and Communications (ICCC)

Modeling of Entanglement in a Josephson Traveling-Wave Parametric Amplifier by a Novel Lie Algebra Approach

Yongjie Yuan, Johannes Stowasser, Michael Haider, Christian Jirauschek

Published Dec 12, 2025• 0 citations
Publisher

Abstract

Quantum computers based on superconducting circuits are approaching quantum supremacy, which means they have the potential to perform specific tasks significantly faster than even the most powerful classical supercomputers. As a crucial component in the measurement chain, parametric amplifiers based on Josephson junctions are promising tools for the readout of superconducting qubits in the microwave range. In this contribution, we present a novel Lie algebra approach for modeling a Josephson junction-embedded traveling-wave parametric amplifier, characterized by a lossy dielectric substrate and nonlinear dispersion, and investigate the generation of entangled signal-idler photon pairs in a two-mode squeezed state.

DOI
10.1109/iccc68654.2025.11438166

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Quantum computers based on superconducting circuits are approaching quantum supremacy, which means they have the potential to perform specific tasks significantly faster than even the most powerful classical supercomputers. As a crucial component in the measurement chain, parametric amplifiers based on Josephson junctions are promising tools for the readout of superconducting qubits in the microwave range. In this contribution, we present a novel Lie algebra approach for modeling a Josephson junction-embedded traveling-wave parametric amplifier, characterized by a lossy dielectric substrate and nonlinear dispersion, and investigate the generation of entangled signal-idler photon pairs in a two-mode squeezed state.
Superconducting parametric amplifiers have great promise for quantum-limited readout of superconducting qubits and detectors. Until recently, most superconducting parametric amplifiers had been based on resonant structures, limiting their bandwidth and dynamic range. Broadband traveling-wave parametric amplifiers based both on the nonlinear kinetic inductance of superconducting thin films and on Josephson junctions are in development. By modifying the dispersion property of the amplifier circuit, referred to as dispersion engineering, the gain can be greatly enhanced and the size can be reduced. We present two theoretical frameworks for analyzing and understanding such parametric amplifiers: 1) generalized coupled-mode equations and 2) a finite difference time domain (FDTD) model combined with a small signal analysis. We show how these analytical and numerical tools may be used to understand device performance.
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.
The development of large-scale superconducting quantum computers critically depends on the accurate readout of qubit states. To enable this, cryogenic parametric amplifiers have been proposed and developed, and have since found widespread use in small-signal detection applications. Among various amplifier architectures, Josephson traveling-wave parametric amplifiers (JTWPAs) are widely adopted due to their broad bandwidth, high saturation power, and compatibility with superconducting qubits. In this work, we present a design workflow of JTWPAs based on a co-simulation approach combining electromagnetic (EM) and circuit-level simulation. We apply this method to a uniform JTWPA, comparing our simulation results with experimental data. To mitigate the challenge of constructing lumped element circuit models usually used in conventional simulation method, we directly perform full EM analysis of the device to accurately determine its linear response. The extracted S parameters are then fed into a nonlinear harmonic balance simulator with Josephson junctions modeled as circuit elements. By doing so, the linear and gain properties of the JTWPA are extracted. Different factors that impact device performance including gain compression, phase matching, and fabrication imperfections are further investigated and modeled. A good agreement between simulation and measurements is identified, establishing the effectiveness of our approach in designing quantum parametric amplifiers.
Josephson Traveling Wave Parametric Amplifier (JTWPA) has the potential to offer quantum limited noise and a large bandwidth. This amplifier is based on parametric amplification of microwaves traveling through a transmission line with embedded non-linear elements. In this paper, starting from the fabrication of the JTWPA, based on Quantum Electrodynamics (QEDs), operating as a non-classical quantum source for generating a signal-idler entangled state, its characterization in terms of scattering parameters is presented. The cryogenic and room temperature experimental results are discussed. The good performance of the JTWPA in terms of wide bandwidth and increased transmitted power, makes it an ideal candidate for Microwave Quantum Radar (MQR) applications. Finally, the performance of a MQR based on the JTWPA developed at INRiM are reported, showing a radar maximum range equal to 82.2 m, that represents the greatest value compared to previously published works.
In this paper, we present models for the nonlinearity of different nonlinear elements for superconducting Josephson traveling-wave parametric amplifiers. Such devices are typically used as a first-stage readout amplifier for superconducting qubits in a cryogenic quantum computing environment. The nonlinear coefficients of different designs are evaluated as functions of an externally applied bias field, taking into account direct and external pumping schemes. Finally, we present results of the total gain for two different nonlinear transmission lines, one that is embedded with single Josephson junctions operating in four-wave mixing mode with direct pumping, and an externally pumped SNAIL-based amplifier operating in the three-wave mixing regime with a corresponding constant external flux bias. The gain is evaluated using a quantum circuit model including substrate losses and chromatic dispersion.
In this paper, we present a density operator description for a dissipative-dispersive Josephson traveling-wave parametric amplifier. A quantum master equation has been derived for the description of dissipation and thermal fluctuations that arise from lossy dielectric substrates. The formalism is especially effective in the dispersive case. Based on the equation of motion of the system density operator, we investigate the amplification performance by predicting the signal gain and the total photon number, considering amplifier phase-mismatch present in real devices. In addition to the gain investigation, we perform a two-mode squeezing analysis for such structures.