Quantum Determinant Estimation of TLS-Sensitive Josephson-Junction Scattering under Persistent Defect Noise

Abstract

This preprint presents a single-author computational proof of concept connecting two-level-system-sensitive Josephson-junction scattering with Quantum Determinant Estimation and device-aware noise modelling. The algorithmic foundation is the Quantum Determinant Estimation protocol of J. Agerskov and K. Splittorff, which uses a completely antisymmetric state to transform the determinant of a unitary matrix into an eigenphase accessible through Quantum Phase Estimation. The physical motivation is the work of J. T. Heath, M. K. Svendsen, and collaborators on localized Josephson hot spots produced by two-level systems in superconducting Josephson junctions. The calculation constructs a unitary two-channel reference scattering matrix and a TLS-modified response. The relative matrixR(E,ϕ)=STLS(E,ϕ)S0†(E,ϕ)R(E,\phi)=S_{\mathrm{TLS}}(E,\phi)S_0^\dagger(E,\phi)R(E,ϕ)=STLS(E,ϕ)S0†(E,ϕ)defines a defect-sensitive determinant phase that is estimated using the antisymmetric-state determinant-QPE protocol. The study includes effective Al, Ta, and Nb interface/bulk configurations, determinant-phase convergence, controlled device-level proxy mappings, finite-register and finite-shot validation, explicit qubit–TLS dynamics, and comparisons between persistent TLS noise and a matched Markovian relaxation model. The original contribution is the computational bridge between a TLS-sensitive scattering observable, determinant-phase estimation, and algorithm-level reliability under structured defect noise. The current scattering matrices, material mappings, linewidths, energy calibration, operation durations, and dynamical coupling strengths are transparent proof-of-concept assumptions. The work does not claim experimentally calibrated material predictions, quantum advantage, uncertainty-robust material identification, or a rigorous non-Markovianity witness. A planned microscopic extension will implement the published Josephson-hot-spot relations, reproduce their spatial and material trends, and use source-derived observables to calibrate the effective determinant and noise models. Preprint status: This manuscript has not undergone peer review. The associated source code and reproducibility package are deposited separately on Zenodo.