Contents I. Introduction
State-of-the-art superconducting quantum computers use dispersive readout to indirectly measure the state of individual qubits. A linear resonator with a few MHz linewidth is reactively coupled to the qubit. Since the qubit impedance is state-dependent, the linear resonator's resonance frequency is pulled up or down based on the state of the qubit. Thus, the qubit state can be read-out by making a reflection or transmission measurement of the linear resonator and observing a state-dependent phase shift [1]–[3]. Due to the fragile nature of the qubit state, microwave photons are pumped into the linear resonator at very low rates (typically < -125 dBm [2]) to avoid inducing qubit state transitions [4]. For a fixed measurement duration, typically , this places an upper limit on the SNR that these systems can attain. High fidelity dispersive readout of a qubit's state (error rates on the order of 1%) has been made possible by Josephson Parametric Amplifiers (JPA), which add a quantum-limited half-photon of input-referred noise per unit Hz ( , where and are the Planck and Boltzmann constant) while boosting the signal by 15–20 dB [5]–[7]. However, these amplifiers have low compared to their semiconductor counterparts (typically < -90 dBm, output-referred [8]), and, as such, cryogenic semiconductor amplification is also required.
