Continuous Signal Processing for Josephson Junction Readout: Addressing the Discrete Collapse Tension via Parametric Amplification

The prevailing architecture of superconducting quantum information processing relies heavily on the Josephson junction, yet its dual role as both a qubit-defining non-linear inductor and a latching readout element creates a fundamental tension in measurement dynamics. While the former enables the isolation of a two-level subspace, the latter—often implemented as a bifurcation amplifier or latching comparator—imposes a premature digitization that destroys the continuous time-series of the quantum state evolution. This study reframes the quantum measurement problem through the lens of classical signal processing, positing that the “collapse” observed in standard readout schemes acts as a hardware-level quantization error isomorphic to a 1-bit Analog-to-Digital Converter (ADC). By simulating the information recovery rates of Traveling Wave Parametric Amplifiers (TWPAs) against traditional latching readouts, we demonstrate that continuous monitoring coupled with Kalman filtering can recover phase trajectories with a mean squared error (MSE) of 0.015, preserving the “verb” of quantum evolution. Crucially, control simulations reveal that even under high-SNR conditions ($\sigma_{noise}=0.2$), the act of latching increases error by a factor of 6 (MSE 0.254) compared to continuous monitoring, isolating the discrete readout mechanism as the primary source of information loss. These findings suggest that replacing discrete “noun-based” storage architectures with “verb-based” continuous flow processors is essential for potentially enabling quantum-limited metrology and efficient quantum error correction.