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Brand D, Sinayskiy I, Petruccione F. Markovian noise modelling and parameter extraction framework for quantum devices. Sci Rep 2024; 14:4769. [PMID: 38413630 PMCID: PMC10899264 DOI: 10.1038/s41598-024-54598-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2023] [Accepted: 02/14/2024] [Indexed: 02/29/2024] Open
Abstract
In recent years, Noisy Intermediate Scale Quantum (NISQ) computers have been widely used as a test bed for quantum dynamics. This work provides a new hardware-agnostic framework for modelling the Markovian noise and dynamics of quantum systems in benchmark procedures used to evaluate device performance. As an accessible example, the application and performance of this framework is demonstrated on IBM Quantum computers. This framework serves to extract multiple calibration parameters simultaneously through a simplified process which is more reliable than previously studied calibration experiments and tomographic procedures. Additionally, this method allows for real-time calibration of several hardware parameters of a quantum computer within a comprehensive procedure, providing quantitative insight into the performance of each device to be accounted for in future quantum circuits. The framework proposed here has the additional benefit of highlighting the consistency among qubit pairs when extracting parameters, which leads to a less computationally expensive calibration process than evaluating the entire device at once.
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Affiliation(s)
- Dean Brand
- Department of Physics, School of Data Science and Computational Thinking, Stellenbosch University, Stellenbosch, 7604, South Africa.
| | - Ilya Sinayskiy
- School of Chemistry and Physics, University of KwaZulu-Natal, Durban, 4001, South Africa.
- National Institute for Theoretical and Computational Sciences (NITheCS), Stellenbosch, 7604, South Africa.
| | - Francesco Petruccione
- Department of Physics, School of Data Science and Computational Thinking, Stellenbosch University, Stellenbosch, 7604, South Africa
- National Institute for Theoretical and Computational Sciences (NITheCS), Stellenbosch, 7604, South Africa
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2
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Lucas M, Danilov AV, Levitin LV, Jayaraman A, Casey AJ, Faoro L, Tzalenchuk AY, Kubatkin SE, Saunders J, de Graaf SE. Quantum bath suppression in a superconducting circuit by immersion cooling. Nat Commun 2023; 14:3522. [PMID: 37316500 DOI: 10.1038/s41467-023-39249-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Accepted: 06/02/2023] [Indexed: 06/16/2023] Open
Abstract
Quantum circuits interact with the environment via several temperature-dependent degrees of freedom. Multiple experiments to-date have shown that most properties of superconducting devices appear to plateau out at T ≈ 50 mK - far above the refrigerator base temperature. This is for example reflected in the thermal state population of qubits, in excess numbers of quasiparticles, and polarisation of surface spins - factors contributing to reduced coherence. We demonstrate how to remove this thermal constraint by operating a circuit immersed in liquid 3He. This allows to efficiently cool the decohering environment of a superconducting resonator, and we see a continuous change in measured physical quantities down to previously unexplored sub-mK temperatures. The 3He acts as a heat sink which increases the energy relaxation rate of the quantum bath coupled to the circuit a thousand times, yet the suppressed bath does not introduce additional circuit losses or noise. Such quantum bath suppression can reduce decoherence in quantum circuits and opens a route for both thermal and coherence management in quantum processors.
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Affiliation(s)
- M Lucas
- Physics Department, Royal Holloway University of London, Egham, UK
| | - A V Danilov
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96, Göteborg, Sweden
| | - L V Levitin
- Physics Department, Royal Holloway University of London, Egham, UK
| | - A Jayaraman
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96, Göteborg, Sweden
| | - A J Casey
- Physics Department, Royal Holloway University of London, Egham, UK
| | - L Faoro
- Google Quantum AI, Google Research, Mountain View, CA, USA
| | - A Ya Tzalenchuk
- Physics Department, Royal Holloway University of London, Egham, UK
- National Physical Laboratory, Teddington, TW11 0LW, UK
| | - S E Kubatkin
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96, Göteborg, Sweden
| | - J Saunders
- Physics Department, Royal Holloway University of London, Egham, UK
| | - S E de Graaf
- National Physical Laboratory, Teddington, TW11 0LW, UK.
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3
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Rower DA, Ateshian L, Li LH, Hays M, Bluvstein D, Ding L, Kannan B, Almanakly A, Braumüller J, Kim DK, Melville A, Niedzielski BM, Schwartz ME, Yoder JL, Orlando TP, Wang JIJ, Gustavsson S, Grover JA, Serniak K, Comin R, Oliver WD. Evolution of 1/f Flux Noise in Superconducting Qubits with Weak Magnetic Fields. PHYSICAL REVIEW LETTERS 2023; 130:220602. [PMID: 37327421 DOI: 10.1103/physrevlett.130.220602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Accepted: 04/12/2023] [Indexed: 06/18/2023]
Abstract
The microscopic description of 1/f magnetic flux noise in superconducting circuits has remained an open question for several decades despite extensive experimental and theoretical investigation. Recent progress in superconducting devices for quantum information has highlighted the need to mitigate sources of qubit decoherence, driving a renewed interest in understanding the underlying noise mechanism(s). Though a consensus has emerged attributing flux noise to surface spins, their identity and interaction mechanisms remain unclear, prompting further study. Here, we apply weak in-plane magnetic fields to a capacitively shunted flux qubit (where the Zeeman splitting of surface spins lies below the device temperature) and study the flux-noise-limited qubit dephasing, revealing previously unexplored trends that may shed light on the dynamics behind the emergent 1/f noise. Notably, we observe an enhancement (suppression) of the spin-echo (Ramsey) pure-dephasing time in fields up to B=100 G. With direct noise spectroscopy, we further observe a transition from a 1/f to approximately Lorentzian frequency dependence below 10 Hz and a reduction of the noise above 1 MHz with increasing magnetic field. We suggest that these trends are qualitatively consistent with an increase of spin cluster sizes with magnetic field. These results should help to inform a complete microscopic theory of 1/f flux noise in superconducting circuits.
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Affiliation(s)
- David A Rower
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Lamia Ateshian
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Lauren H Li
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Max Hays
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Dolev Bluvstein
- Department of Physics, Harvard University, Cambridge, Massachusetts 02139, USA
| | - Leon Ding
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Bharath Kannan
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Aziza Almanakly
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jochen Braumüller
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - David K Kim
- MIT Lincoln Laboratory, Lexington, Massachusetts 02421, USA
| | | | | | | | | | - Terry P Orlando
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Joel I-Jan Wang
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Simon Gustavsson
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jeffrey A Grover
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Kyle Serniak
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- MIT Lincoln Laboratory, Lexington, Massachusetts 02421, USA
| | - Riccardo Comin
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - William D Oliver
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- MIT Lincoln Laboratory, Lexington, Massachusetts 02421, USA
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4
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Murthy AA, Masih Das P, Ribet SM, Kopas C, Lee J, Reagor MJ, Zhou L, Kramer MJ, Hersam MC, Checchin M, Grassellino A, Reis RD, Dravid VP, Romanenko A. Developing a Chemical and Structural Understanding of the Surface Oxide in a Niobium Superconducting Qubit. ACS NANO 2022; 16:17257-17262. [PMID: 36153944 DOI: 10.1021/acsnano.2c07913] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Superconducting thin films of niobium have been extensively employed in transmon qubit architectures. Although these architectures have demonstrated improvements in recent years, further improvements in performance through materials engineering will aid in large-scale deployment. Here, we use information retrieved from secondary ion mass spectrometry and electron microscopy to conduct a detailed assessment of the surface oxide that forms in ambient conditions for transmon test qubit devices patterned from a niobium film. We observe that this oxide exhibits a varying stoichiometry with NbO and NbO2 found closer to the niobium film/oxide interface and Nb2O5 found closer to the surface. In terms of structural analysis, we find that the Nb2O5 region is semicrystalline in nature and exhibits randomly oriented grains on the order of 1-3 nm corresponding to monoclinic N-Nb2O5 that are dispersed throughout an amorphous matrix. Using fluctuation electron microscopy, we are able to map the relative crystallinity in the Nb2O5 region with nanometer spatial resolution. Through this correlative method, we observe that the highly disordered regions are more likely to contain oxygen vacancies and exhibit weaker bonds between the niobium and oxygen atoms. Based on these findings, we expect that oxygen vacancies likely serve as a decoherence mechanism in quantum systems.
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Affiliation(s)
- Akshay A Murthy
- Superconducting Quantum Materials and Systems Division, Fermi National Accelerator Laboratory (FNAL), Batavia, Illinois 60510, United States
| | - Paul Masih Das
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Stephanie M Ribet
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
- International Institute of Nanotechnology, Northwestern University, Evanston, Illinois 60208, United States
| | - Cameron Kopas
- Rigetti Computing, Berkeley, California 94710, United States
| | - Jaeyel Lee
- Superconducting Quantum Materials and Systems Division, Fermi National Accelerator Laboratory (FNAL), Batavia, Illinois 60510, United States
| | | | - Lin Zhou
- Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011, United States
| | - Matthew J Kramer
- Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011, United States
| | - Mark C Hersam
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
- Department of Electrical and Computer Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Mattia Checchin
- Superconducting Quantum Materials and Systems Division, Fermi National Accelerator Laboratory (FNAL), Batavia, Illinois 60510, United States
| | - Anna Grassellino
- Superconducting Quantum Materials and Systems Division, Fermi National Accelerator Laboratory (FNAL), Batavia, Illinois 60510, United States
| | - Roberto Dos Reis
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
- The NUANCE Center, Northwestern University, Evanston, Illinois 60208, United States
| | - Vinayak P Dravid
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
- International Institute of Nanotechnology, Northwestern University, Evanston, Illinois 60208, United States
- The NUANCE Center, Northwestern University, Evanston, Illinois 60208, United States
| | - Alexander Romanenko
- Superconducting Quantum Materials and Systems Division, Fermi National Accelerator Laboratory (FNAL), Batavia, Illinois 60510, United States
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5
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Gao R, Ku HS, Deng H, Yu W, Xia T, Wu F, Song Z, Wang M, Miao X, Zhang C, Lin Y, Shi Y, Zhao HH, Deng C. Ultrahigh Kinetic Inductance Superconducting Materials from Spinodal Decomposition. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2201268. [PMID: 35678176 DOI: 10.1002/adma.202201268] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2022] [Revised: 04/17/2022] [Indexed: 06/15/2023]
Abstract
Disordered superconducting nitrides with kinetic inductance have long been considered to be leading material candidates for high-inductance quantum-circuit applications. Despite continuing efforts toward reducing material dimensions to increase the kinetic inductance and the corresponding circuit impedance, achieving further improvements without compromising material quality has become a fundamental challenge. To this end, a method to drastically increase the kinetic inductance of superconducting materials via spinodal decomposition while maintaining a low microwave loss is proposed. Epitaxial Ti0.48 Al0.52 N is used as a model system and the utilization of spinodal decomposition to trigger the insulator-to-superconductor transition with a drastically enhanced material disorder is demonstrated. The measured kinetic inductance increases by two to three orders of magnitude compared with the best disordered superconducting nitrides reported to date. This work paves the way for substantially enhancing and deterministically controlling the inductance for advanced superconducting quantum circuits.
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Affiliation(s)
- Ran Gao
- Alibaba Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang, 311121, P. R. China
| | - Hsiang-Sheng Ku
- Alibaba Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang, 311121, P. R. China
| | - Hao Deng
- Alibaba Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang, 311121, P. R. China
| | - Wenlong Yu
- Alibaba Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang, 311121, P. R. China
| | - Tian Xia
- Alibaba Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang, 311121, P. R. China
| | - Feng Wu
- Alibaba Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang, 311121, P. R. China
| | - Zhijun Song
- Alibaba Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang, 311121, P. R. China
| | - Minghua Wang
- Westlake Center for Micro/Nano Fabrication, Westlake University, Hangzhou, Zhejiang, 310024, P. R. China
| | - Xiaohe Miao
- Instrumentation and Service Center for Physical Sciences, Westlake University, Hangzhou, Zhejiang, 310024, P. R. China
| | - Chao Zhang
- Instrumentation and Service Center for Physical Sciences, Westlake University, Hangzhou, Zhejiang, 310024, P. R. China
| | - Yue Lin
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui, 230026, P. R. China
| | - Yaoyun Shi
- Alibaba Quantum Laboratory, Alibaba Group USA, Bellevue, WA, 98004, USA
| | - Hui-Hai Zhao
- Alibaba Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang, 311121, P. R. China
| | - Chunqing Deng
- Alibaba Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang, 311121, P. R. China
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6
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Mutter PM, Burkard G. Fingerprints of Qubit Noise in Transient Cavity Transmission. PHYSICAL REVIEW LETTERS 2022; 128:236801. [PMID: 35749203 DOI: 10.1103/physrevlett.128.236801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 05/10/2022] [Indexed: 06/15/2023]
Abstract
Noise affects the coherence of qubits and thereby places a bound on the performance of quantum computers. We theoretically study a generic two-level system with fluctuating control parameters in a photonic cavity and find that basic features of the noise spectral density are imprinted in the transient transmission through the cavity. We obtain analytical expressions for generic noise and proceed to study the cases of quasistatic, white and 1/f^{α} noise in more detail. Additionally, we propose a way of extracting the noise power spectral density in a frequency band only bounded by the range of the qubit-cavity detuning and with an exponentially decaying error due to finite measurement times. Our results suggest that measurements of the time-dependent transmission probability represent a novel way of extracting noise characteristics.
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Affiliation(s)
- Philipp M Mutter
- Department of Physics, University of Konstanz, D-78457 Konstanz, Germany
| | - Guido Burkard
- Department of Physics, University of Konstanz, D-78457 Konstanz, Germany
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7
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McLauchlan CK, Béri B. Fermion-Parity-Based Computation and Its Majorana-Zero-Mode Implementation. PHYSICAL REVIEW LETTERS 2022; 128:180504. [PMID: 35594115 DOI: 10.1103/physrevlett.128.180504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2021] [Accepted: 03/29/2022] [Indexed: 06/15/2023]
Abstract
Majorana zero modes (MZMs) promise a platform for topologically protected fermionic quantum computation. However, creating multiple MZMs and generating (directly or via measurements) the requisite transformations (e.g., braids) pose significant challenges. We introduce fermion-parity-based computation (FPBC): a measurement-based scheme, modeled on Pauli-based computation, that uses efficient classical processing to virtually increase the number of available MZMs and which, given magic state inputs, operates without transformations. FPBC requires all MZM parities to be measurable, but this conflicts with constraints in proposed MZM hardware. We thus introduce a design in which all parities are directly measurable and which is hence well suited for FPBC. While developing FPBC, we identify the "logical braid group" as the fermionic analog of the Clifford group.
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Affiliation(s)
| | - Benjamin Béri
- DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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8
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Vepsäläinen A, Winik R, Karamlou AH, Braumüller J, Paolo AD, Sung Y, Kannan B, Kjaergaard M, Kim DK, Melville AJ, Niedzielski BM, Yoder JL, Gustavsson S, Oliver WD. Improving qubit coherence using closed-loop feedback. Nat Commun 2022; 13:1932. [PMID: 35410327 PMCID: PMC9001732 DOI: 10.1038/s41467-022-29287-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2021] [Accepted: 02/24/2022] [Indexed: 11/09/2022] Open
Abstract
Superconducting qubits are a promising platform for building a larger-scale quantum processor capable of solving otherwise intractable problems. In order for the processor to reach practical viability, the gate errors need to be further suppressed and remain stable for extended periods of time. With recent advances in qubit control, both single- and two-qubit gate fidelities are now in many cases limited by the coherence times of the qubits. Here we experimentally employ closed-loop feedback to stabilize the frequency fluctuations of a superconducting transmon qubit, thereby increasing its coherence time by 26% and reducing the single-qubit error rate from (8.5 ± 2.1) × 10−4 to (5.9 ± 0.7) × 10−4. Importantly, the resulting high-fidelity operation remains effective even away from the qubit flux-noise insensitive point, significantly increasing the frequency bandwidth over which the qubit can be operated with high fidelity. This approach is helpful in large qubit grids, where frequency crowding and parasitic interactions between the qubits limit their performance. The presence of various noises in the qubit environment is a major limitation on qubit coherence time. Here, the authors demonstrate the use a closed-loop feedback to stabilize frequency noise in a flux-tunable superconducting qubit and suggest this as a scalable approach applicable to other types of noise.
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Niepce D, Burnett JJ, Kudra M, Cole JH, Bylander J. Stability of superconducting resonators: Motional narrowing and the role of Landau-Zener driving of two-level defects. SCIENCE ADVANCES 2021; 7:eabh0462. [PMID: 34559556 PMCID: PMC8462906 DOI: 10.1126/sciadv.abh0462] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/11/2021] [Accepted: 08/05/2021] [Indexed: 06/13/2023]
Abstract
Frequency instability of superconducting resonators and qubits leads to dephasing and time-varying energy loss and hinders quantum processor tune-up. Its main source is dielectric noise originating in surface oxides. Thorough noise studies are needed to develop a comprehensive understanding and mitigation strategy of these fluctuations. We use a frequency-locked loop to track the resonant frequency jitter of three different resonator types—one niobium nitride superinductor, one aluminum coplanar waveguide, and one aluminum cavity—and we observe notably similar random telegraph signal fluctuations. At low microwave drive power, the resonators exhibit multiple, unstable frequency positions, which, for increasing power, coalesce into one frequency due to motional narrowing caused by sympathetic driving of two-level system defects by the resonator. In all three devices, we identify a dominant fluctuator whose switching amplitude (separation between states) saturates with increasing drive power, but whose characteristic switching rate follows the power law dependence of quasi-classical Landau-Zener transitions.
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Affiliation(s)
- David Niepce
- Chalmers University of Technology, Microtechnology, and Nanoscience, SE-41296 Gothenburg, Sweden
| | - Jonathan J. Burnett
- National Physical Laboratory, Hampton Road, Teddington Middlesex TW11 0LW, UK
| | - Marina Kudra
- Chalmers University of Technology, Microtechnology, and Nanoscience, SE-41296 Gothenburg, Sweden
| | - Jared H. Cole
- Chemical and Quantum Physics, School of Science, RMIT University, Melbourne, VIC 3001, Australia
| | - Jonas Bylander
- Chalmers University of Technology, Microtechnology, and Nanoscience, SE-41296 Gothenburg, Sweden
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