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

Arjun Anand

Published Aug 1, 2026• 0 citations
Publisher

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.

DOI
10.5281/zenodo.21733791

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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.
[EN] Two-level system (TLS) defects constitute a major source of noise and decoherence in superconducting qubits, particularly due to microscopic defects located in Josephson junctions and their surrounding materials, limiting coherence times and the performance of quantum information devices. While extensive experimental evidence of TLS-induced noise exists, establishing a microscopic theoretical description that consistently connects quantum defect dynamics, open-system theory, and experimental observations remains an open challenge. The objective of this Master s thesis is to study the impact of TLS defects on superconducting qubits using a fully quantum, open-system framework. Starting from a microscopic Hamiltonian description of a qubit coupled to TLS defects in Josephson junctions, the project aims to derive and analyze a Bloch-Redfield master equation that captures the correlated dynamics between a qubit, a quantum TLS, and a dissipative environment. This approach enables the investigation of coherence decay, population dynamics, and qubit-TLS correlations beyond phenomenological Lindblad models. The work will combine analytical methods with numerical simulations implemented in the Julia programming language. In addition to master-equation techniques, tensor-network methods based on Matrix Product States (MPS) will be employed as a scalable framework to extend the analysis to multiple interacting TLS, allowing the explicit treatment of quantum correlations and non-Markovian effects in many-body defect environments. Simple effective noise models, such as random telegraph noise, will be considered for comparison in order to assess their range of validity relative to microscopic descriptions. The theoretical analysis will be discussed in connection with recent experimental observations in superconducting circuits, particularly those reported in the work of Christopher Eichler and Andreas Wallraff, with the goal of contributing to a unified microscopic understanding of TLS-induced noise in Josephson-junction-based superconducting qubits.
Superconducting qubits are often adversely affected by two-level systems (TLSs) within the Josephson junction, which contribute to decoherence and subsequently limit the performance of the qubit. By treating the TLS as a soft (i.e., low-frequency) bosonic mode localized in real space, we find that a single TLS in either the amorphous-oxide surface or the superconducting bulk may result in a localized “hot spot” of amplified Josephson energy. Such amplification is shown to have a non-negligible effect on the T 1 time of a simple phase qubit, regardless of whether or not the TLS is on resonance with the qubit frequency. With this study, we identify unique fingerprints of TLS defects in the Josephson current and qubit decoherence time.
Materials defects in Josephson junctions (JJs), often referred to as two-level systems (TLS), couple to superconducting qubits and are a critical bottleneck for scalable quantum processors. Despite their importance, understanding the microscopic sources of TLS and how to mitigate them has remained a major challenge. Here, we demonstrate a high-throughput, correlated approach to trace the microstructural origins of strongly-coupled TLS in Josephson circuits. We assembled a massive dataset of TLS across 6,000 Al/AlOx/Al JJs and more than 600 atomic resolution transmission electron microscopy images. We statistically link fabrication, microstructure, and TLS occurrence, revealing a strong correlation between Al electrode thickness, Al grain size, and TLS density. Correspondingly, we find a two-thirds reduction in TLS prompted by a change in electrode fabrication parameters. These results demonstrate a robust, data-driven methodology to understand and control defects in quantum circuits and pave the way for significantly reducing TLS density.
Abstract Material defects fundamentally limit the coherence times of superconducting qubits, and manufacturing completely defect-free devices is not yet possible. Therefore, understanding the interactions between defects and a qubit in a real quantum processor design is essential. We build a model that incorporates the standard tunneling model, the electric field distributions in the qubit, and open quantum system dynamics, and draws from the current understanding of two-level system (TLS) theory. Specifically, we start with one million TLSs distributed on the surface of a qubit and pick the 200 systems that are most strongly coupled to the qubit. We then perform a full Lindbladian simulation that explicitly includes the coherent coupling between the qubit and the TLS bath to model the time dependent density matrix of resonant TLS defects and the qubit. We find that the 200 most strongly coupled TLSs can accurately describe the qubit energy relaxation time. This work confirms that resonant TLSs located in areas where the electric field is strong can significantly affect the qubit relaxation time, even if they are located far from the Josephson junction (JJ). Similarly, a strongly-coupled resonant TLS located in the JJ does not guarantee a reduced qubit relaxation time if a more strongly coupled TLS is far from the JJ. In addition to the coupling strengths between TLSs and the qubit, the model predicts that the geometry of the device and the TLS relaxation time play a significant role in qubit dynamics. Our work can provide guidance for future quantum processor designs with improved qubit coherence times.
Quantum sensing and computation can be realized with superconducting microwave circuits. Qubits are engineered quantum systems of capacitors and inductors with non-linear Josephson junctions. They operate in the single-excitation quantum regime, photons of 27μ27 μ27μeV at 6.5 GHz. Quantum coherence is fundamentally limited by materials defects, in particular atomic-scale parasitic two-level systems (TLS) in amorphous dielectrics at circuit interfaces.[1] The electric fields driving oscillating charges in quantum circuits resonantly couple to TLS, producing phase noise and dissipation. We use coplanar niobium-on-silicon superconducting resonators to probe decoherence in quantum circuits. By selectively modifying interface dielectrics, we show that most TLS losses come from the silicon surface oxide, and most non-TLS losses are distributed throughout the niobium surface oxide. Through post-fabrication interface modification we reduced TLS losses by 85% and non-TLS losses by 72%, obtaining record single-photon resonator quality factors above 5 million and approaching a regime where non-TLS losses are dominant. [1]Müller, C., Cole, J. H. & Lisenfeld, J. Towards understanding two-level-systems in amorphous solids: insights from quantum circuits. Rep. Prog. Phys. 82, 124501 (2019)
Non-Markovian noise can be a significant source of errors in superconducting qubits. We develop gate sequences utilising mirrored pseudoidentities that allow us to characterise and model the effects of non-Markovian noise on both idle and driven qubits. We compare three approaches to modelling the observed noise: (i) a Markovian noise model, (ii) a model including interactions with a two-level system (TLS), (iii) a model utilising the post Markovian master equation (PMME), which we show to be equivalent to the qubit-TLS model in certain regimes. When running our noise characterisation circuits on a superconducting qubit device we find that purely Markovian noise models cannot reproduce the experimental data. Our model based on a qubit-TLS interaction, on the other hand, is able to closely capture the observed experimental behaviour for both idle and driven qubits. We investigate the stability of the noise properties of the hardware over time, and find that the parameter governing the qubit-TLS interaction strength fluctuates significantly even over short time-scales of a few minutes. Finally, we evaluate the changes in the noise parameters when increasing the qubit drive pulse amplitude. We find that although the hardware noise parameters fluctuate significantly over different days, their drive pulse induced relative variation is rather well defined within computed uncertainties: both the phase error and the qubit-TLS interaction strength change significantly with the pulse strength, with the phase error changing quadratically with the amplitude of the applied pulse. Since our noise model can closely describe the behaviour of idle and driven qubits, it is ideally suited to be used in the development of quantum error mitigation and correction methods.