[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.
[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.
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.
Microscopic two-level systems (TLS) -- ubiquitous atomic-scale defects in solid-state quantum devices -- are a dominant source of qubit decoherence, yet their role is often considered local and short-memoried. Here, we report the observation of a coherent TLS that couples simultaneously to two spatially distant superconducting qubits. The TLS is identified to reside within the tunable coupler linking the qubits, enabling controllability of the TLS-qubit coupling strength via coupler frequency -- a capability absent in earlier studies. This tunability allows us to systematically probe how TLS distorts qubit dynamics, revisiting the decoherence model in the presence of non-Markovian TLS dephasing noise. This is corroborated by the reconstructed 1/f noise spectrum of TLS frequency fluctuation spanning more than ten orders of magnitude (0.1\,mHz -- 1\,MHz) that reveals discrete fluctuator signatures. Quantum process tomography further unveils TLS-induced correlated qubit dynamics, highlighting the long-lived TLS as an effective source of non-Markovianity. Our findings expose a previously overlooked interaction mechanism in scalable quantum architectures: defects embedded in coupling elements can simultaneously affect multiple qubits with variable impact. Beyond immediate implications for system characterization and calibration, this situation provides a powerful testbed for studying defect-driven quantum dynamics, refining error suppression strategies, and advancing architecture design for scalable quantum technologies.
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.
Recent experimental evidences point to two-level defects, located in the oxides and on the interfaces of the Josephson junctions, as the major constituents of decoherence in superconducting qubits. How these defects affect the qubit evolution with the presence of external driving is less well understood since the semiclassical qubit-field coupling renders the Jaynes–Cummings model for qubit-defect coupling undiagonalizable. We analyze the decoherence dynamics in the continuous coherent state space induced by the driving and solve the master equation endowed with an extra decay-cladded driving term via a Fokker–Planck equation. The solutions for diffusion propagators as Gaussian distributions show four distinct dynamic phases: four types of convergence paths to limit cycles of varying radius by the distribution mean, which are determined by the competing external driving and the defect decays. The qubit trajectory resulted from these solutions is a super-Poissonian over displaced Fock states, which reduces to a Gibbs state of effective temperature decided by the defect at zero driving limit. Furthermore, the Poincare map shows the dependence of the rate of convergence on the initial state. In other words, the qubit evolution can serve as an indicator of the defect coupling strength through the variation of the driving strength as a parameter.
Superconducting quantum circuits rely on compact, low-loss inductive elements, strong anharmonicity, and robust flux biasing to realize coherent and controllable quantum bits. This thesis investigates how vertically stacked Josephson junction arrays can be employed to meet these requirements and enable compact flux qubits operated in the quarton regime. In the first part, stacked Al/AlOx/Al Josephson junctions are established as compact linear inductors. Their three-dimensional geometry reduces parasitic capacitance to ground while allowing multiple junctions to be integrated within a small footprint. A numerical modeling approach is used to quantify stray capacitances, Coulomb screening, and collective modes of extended stacked junction arrays. Cryogenic transport measurements confirm strongly underdamped junction dynamics with uniform junction characteristics, demonstrating their suitability as low-loss inductive elements in superconducting circuits. In the second part, these inductors are integrated into flux qubits operated in the quarton regime. In this regime, the qubit potential becomes nearly quartic around half-flux bias, resulting in positive anharmonicity and first-order insensitivity to flux noise at the operating point. Spectroscopy reveals qubit transition frequencies in the 3–5 GHz range and anharmonicities of 0.5–1.5 GHz, consistent with the expected quartic potential landscape. To distinguish intrinsic from externally induced decoherence, a persistent-current bias scheme is implemented, enabling stable and low-noise flux biasing over time scales of up to one week. A direct comparison between conventionally biased and persistently biased devices rules out external flux noise as the dominant coherence-limiting mechanism. High-resolution spectroscopy identifies avoided level crossings caused by microscopic two-level systems (TLS) in the amorphous tunnel barriers of the stacked junctions. A systematic cumulative analysis of splitting statistics across multiple devices shows that the spectral TLS density scales with the total tunnel-barrier area, while the array length determines the effective qubit–TLS coupling strength. The measured relaxation times follow scaling relations consistent with Fermi’s golden rule for a bath of weakly coupled TLS, demonstrating that TLS in the stacked junction arrays constitute the dominant intrinsic decoherence channel in quarton qubits. These results establish stacked Josephson junction arrays as compact superinductive elements and provide an understanding of coherence limitations in superconducting quantum circuits based on Josephson junction arrays, offering guidance for future device optimization.
Decoherence and parameter fluctuations are two of the mayor obstacles for solid-state quantum computing. In this work, decoherence in superconducting qubits of the transmon type is investigated. For this purpose, a time-multiplexed measurement protocol was developed and applied in long-term measurements. The resulting simultaneous measurement of the qubit's relaxation and dephasing rate, as well as its resonance frequency enables analysis of correlations between these parameters. A spectral noise analysis complements these measurements. Together, the results agree well with the interacting defect model of two-level-systems and yield information about the microscopic origin of the intrinsic decoherence mechanisms in Josephson qubits. Our measurements show inherent correlations between dephasing and fluctuations in qubit frequency on the timescale of seconds to days, which is attributed to the influence of individual defects, located close to conductor edges. Cross-correlation and spectral noise analysis confirm this interpretation and ascribe the source of fluctuation to interactions between thermal fluctuators and surface defects. Single defects reducing the coherence of qubits by up to one order of magnitude are a major challenge for future quantum computers. Non-tunable qubits are intrinsically insensitive to some decoherence channels and thus ideal for this fundamental analysis. However, to widen the focus and contrast the results of different material systems, we pursue the fabrication of voltage controlled gatemon qubits. In the course of this work, the theoretical foundation and technical implementation of transmon qubits based on regular Josephson weak links, and semiconducting nanowires is given. The experimental design and measurement setup are explained in detail. Our findings make continuous re-calibration a necessity in today's solid-state qubits, although new materials or processing techniques might mitigate the problem. However, the results of this work imply that fundamental improvements of qubit parameter stability are necessary in order to realize scalable and coherent qubit circuits.