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arXiv:2211.08535 · Quantum Science and Technology

Simulating noise on a quantum processor: interactions between a qubit and resonant two-level system bath

Yujin Cho, Dipti Jasrasaria, Keith G. Ray, Daniel Tennant, Vincenzo Lordi, Jonathan L. DuBois, Yaniv Jacob Rosen

Published Sep 4, 2023• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/2058-9565/acf685

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[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.

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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.
Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.
Materials improvements in transmon qubits have yielded remarkable advances in qubit lifetimes (T1)and coherence times (T2). However, state-of-the-art superconducting qubits experience temporal fluctuations in their performance, which limit gate fidelities and quantum processor performance. We observe correlated increases in qubit relaxation and dephasing rates that last for minutes to hours, which we call T1 and T2 excursions. Using interleaved lifetime and coherence time measurements, noise spectroscopy, and two-level-system (TLS) spectroscopy, we find that these excursions are caused by single or few strongly-coupled TLS defects that spectrally diffuse into resonance with the qubit frequency. Our measurement protocol provides a powerful tool for understanding the noise sources that cause temporal fluctuations in superconducting qubit performance.
Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.
An outstanding challenge in superconducting quantum circuits is mitigating loss from two-level system (TLS) defects. SWAP spectroscopy with flux-tunable qubits can detect individual TLSs, but the Rabi chevrons that signal coherent exchange have been observed only for the most strongly coupled defects. Here, we introduce a sequence with fast flux pulses only at state preparation and readout, switched off during the energy-relaxation delay for finer frequency resolution and longer interaction times. We detect Rabi chevrons at swap rates as low as 0.1 MHz, an order of magnitude lower than previously reported. In the dressed-state picture, we fit the coherent swap oscillations to extract the TLS energy-relaxation time. These Rabi chevrons reveal coherent TLSs with a median energy-relaxation time of 10 microseconds, at coupling strengths previously associated with incoherent TLSs. The swap coherence times exceed the qubit T2* limited by flux noise, indicating that the dressed gap protects them from low-frequency 1/f noise.
Noise within solid-state systems at low temperatures can typically be traced back to material defects. In amorphous materials, these defects are broadly described by the tunneling two-level systems (TLSs) model. TLS have recently taken on further relevance in quantum computing because they dominate the coherence limit of superconducting quantum circuits. Efforts to mitigate TLS impacts have thus far focused on circuit design, material selection, and surface treatments. Our work takes an approach that directly modifies TLS properties. This is achieved by creating an acoustic bandgap that suppresses all microwave-frequency phonons around the operating frequency of a transmon qubit. For embedded TLS strongly coupled to the transmon qubit, we measure a pronounced increase in relaxation time by two orders of magnitude, with the longestT1time exceeding 5 milliseconds. Our work opens avenues for studying the physics of highly coherent TLS and methods for mitigating noise within solid-state quantum devices.
[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.