1
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Xu W, Guo T, Zhang K, Li Z, Zhou T, Zuo Q, Sheng Y, Jing L, Ma H, Yu M, Zhou S, Li B, Yang S, Yu Y, Zhang J, Zhu J, Cao C, Zhu G, Sun G, Wu P. Manipulations of a transmon qubit with a null-biased electro-optic fiber link. Nat Commun 2025; 16:2629. [PMID: 40097462 PMCID: PMC11914235 DOI: 10.1038/s41467-025-57820-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2024] [Accepted: 02/27/2025] [Indexed: 03/19/2025] Open
Abstract
In recent years, significant progress has been made in the field of superconducting quantum circuits, particularly in improving the complexity of quantum processors for large-scale quantum computing and quantum simulation tasks. To enable the execution of quantum information processing tasks on large-scale quantum circuits containing millions of qubits, it is essential to minimize thermal effects on control and measurement lines, ensuring that circuit components are superconducting and that qubits are not significantly thermally excited. Recent studies have shown that a quadrature-biased electro-optic fiber link can operate qubits with a much reduced thermal load, thereby facilitating the simultaneous operation of a large number of qubits. Expanding on this, here we propose and demonstrate that coherent manipulations of superconducting qubits can also be achieved by setting the bias point of the electro-optic modulator at the null point instead of the quadrature point. Major advantages of our null-point bias method include further reduction of the thermal load and improvement of the signal-to-noise ratio, and relaxed requirement for experimental implementations. Simultaneous control of two qubits is also demonstrated using the proposed null-biased fiber-optic link, which is the first time to the best of our knowledge.
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Affiliation(s)
- Wenqu Xu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Tingting Guo
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Kaixuan Zhang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Zishuo Li
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Tianshi Zhou
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Quan Zuo
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Yifan Sheng
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Lingxiao Jing
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Huashi Ma
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Mingyuan Yu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Shunhong Zhou
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Binglin Li
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Shiyao Yang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Yongyang Yu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Junzhou Zhang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Jiyuan Zhu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Chunhai Cao
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Guanghao Zhu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
- Hefei National Laboratory, Hefei, China.
| | - Guozhu Sun
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
- Purple Mountain Laboratories, Nanjing, China.
- Hefei National Laboratory, Hefei, China.
- Shishan Laboratory, Suzhou Campus of Nanjing University, Suzhou, China.
| | - Peiheng Wu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Hefei National Laboratory, Hefei, China
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2
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Dijkema J, Xue X, Harvey-Collard P, Rimbach-Russ M, de Snoo SL, Zheng G, Sammak A, Scappucci G, Vandersypen LMK. Cavity-mediated iSWAP oscillations between distant spins. NATURE PHYSICS 2024; 21:168-174. [PMID: 39846006 PMCID: PMC11746143 DOI: 10.1038/s41567-024-02694-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/29/2024] [Accepted: 10/07/2024] [Indexed: 01/24/2025]
Abstract
Direct interactions between quantum particles naturally fall off with distance. However, future quantum computing architectures are likely to require interaction mechanisms between qubits across a range of length scales. In this work, we demonstrate a coherent interaction between two semiconductor spin qubits 250 μm apart using a superconducting resonator. This separation is several orders of magnitude larger than for the commonly used direct interaction mechanisms in this platform. We operate the system in a regime in which the resonator mediates a spin-spin coupling through virtual photons. We report the anti-phase oscillations of the populations of the two spins with controllable frequency. The observations are consistent with iSWAP oscillations of the spin qubits, and suggest that entangling operations are possible in 10 ns. These results hold promise for scalable networks of spin qubit modules on a chip.
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Affiliation(s)
- Jurgen Dijkema
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, Netherlands
| | - Xiao Xue
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, Netherlands
| | - Patrick Harvey-Collard
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, Netherlands
| | - Maximilian Rimbach-Russ
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, Netherlands
| | - Sander L. de Snoo
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, Netherlands
| | - Guoji Zheng
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, Netherlands
| | - Amir Sammak
- QuTech and Netherlands Organization for Applied Scientific Research (TNO), Delft, Netherlands
| | - Giordano Scappucci
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, Netherlands
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3
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Linghu K, Qian Y, Wang R, Hu MJ, Li Z, Li X, Xu H, Zhang J, Ma T, Zhao P, Liu DE, Hsieh MH, Wu X, Du Y, Tao D, Jin Y, Yu H. Quantum Circuit Architecture Search on a Superconducting Processor. ENTROPY (BASEL, SWITZERLAND) 2024; 26:1025. [PMID: 39766654 PMCID: PMC11726871 DOI: 10.3390/e26121025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2024] [Revised: 11/21/2024] [Accepted: 11/21/2024] [Indexed: 01/15/2025]
Abstract
Variational quantum algorithms (VQAs) have shown strong evidence to gain provable computational advantages in diverse fields such as finance, machine learning, and chemistry. However, the heuristic ansatz exploited in modern VQAs is incapable of balancing the trade-off between expressivity and trainability, which may lead to degraded performance when executed on noisy intermediate-scale quantum (NISQ) machines. To address this issue, here, we demonstrate the first proof-of-principle experiment of applying an efficient automatic ansatz design technique, i.e., quantum architecture search (QAS), to enhance VQAs on an 8-qubit superconducting quantum processor. In particular, we apply QAS to tailor the hardware-efficient ansatz toward classification tasks. Compared with heuristic ansätze, the ansatz designed by QAS improves the test accuracy from 31% to 98%. We further explain this superior performance by visualizing the loss landscape and analyzing effective parameters of all ansätze. Our work provides concrete guidance for developing variable ansätze to tackle various large-scale quantum learning problems with advantages.
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Affiliation(s)
- Kehuan Linghu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China (X.L.)
| | - Yang Qian
- School of Computer Science, Faculty of Engineering, University of Sydney, Camperdown, NSW 2006, Australia
- JD Explore Academy, Beijing 102628, China
| | - Ruixia Wang
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China (X.L.)
| | - Meng-Jun Hu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China (X.L.)
| | - Zhiyuan Li
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China (X.L.)
| | - Xuegang Li
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China (X.L.)
| | - Huikai Xu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China (X.L.)
| | - Jingning Zhang
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China (X.L.)
| | - Teng Ma
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China (X.L.)
| | - Peng Zhao
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China (X.L.)
| | - Dong E. Liu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China (X.L.)
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Min-Hsiu Hsieh
- Centre for Quantum Software and Information, Faculty of Engineering and Information Technology, University of Technology Sydney, Ultimo, NSW 2007, Australia
| | - Xingyao Wu
- JD Explore Academy, Beijing 102628, China
| | - Yuxuan Du
- JD Explore Academy, Beijing 102628, China
| | | | - Yirong Jin
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China (X.L.)
| | - Haifeng Yu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China (X.L.)
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4
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Ye Y, Kline JB, Chen S, Yen A, O’Brien KP. Ultrafast superconducting qubit readout with the quarton coupler. SCIENCE ADVANCES 2024; 10:eado9094. [PMID: 39383228 PMCID: PMC11642098 DOI: 10.1126/sciadv.ado9094] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Accepted: 09/04/2024] [Indexed: 10/11/2024]
Abstract
Fast, high-fidelity, and quantum nondemolition (QND) qubit readout is an essential element of quantum information processing. For superconducting qubits, state-of-the-art readout is based on a dispersive cross-Kerr coupling between a qubit and its readout resonator. The resulting readout can be high fidelity and QND, but readout times are currently limited to the order of 50 nanoseconds due to the dispersive cross-Kerr of magnitude 10 megahertz. Here, we present a readout scheme that uses the quarton coupler to facilitate a large (greater than 200 megahertz) cross-Kerr between a transmon qubit and its readout resonator. Full master equation simulations of the coupled system show a 5-nanosecond readout time with greater than 99% readout fidelity and greater than 99.9% QND fidelity. The quartonic readout circuit is experimentally feasible and preserves the coherence properties of the qubit. Our work reveals a path for order of magnitude improvements of superconducting qubit readout by engineering nonlinear light-matter couplings in parameter regimes unreachable by existing designs.
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Affiliation(s)
- Yufeng Ye
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Jeremy B. Kline
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Sean Chen
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Alec Yen
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Kevin P. O’Brien
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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5
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Atalaya J, Opremcak A, Nersisyan A, Lee K, Korotkov AN. Measurement of Small Photon Numbers in Circuit QED Resonators. PHYSICAL REVIEW LETTERS 2024; 132:203601. [PMID: 38829075 DOI: 10.1103/physrevlett.132.203601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2023] [Accepted: 04/09/2024] [Indexed: 06/05/2024]
Abstract
Off-resonant interaction of fluctuating photons in a resonator with a qubit increases the qubit dephasing rate. We use this effect to measure a small average number of intracavity photons that are coherently or thermally driven. For spectral resolution, we do this by subjecting the qubit to a Carr-Purcell-Meiboom-Gill sequence and record the qubit dephasing rate for various periods between qubit π pulses. The recorded data is then analyzed with formulas for the photon-induced dephasing rate derived for the non-Gaussian noise regime with an arbitrary ratio of the resonator dispersive shift to decay rate. We show that the presented Carr-Purcell-Meiboom-Gill dephasing rate formulas agree well with experimental results and demonstrate measurement of thermal and coherent photon populations at the level of a few 10^{-4}.
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Affiliation(s)
- Juan Atalaya
- Google Quantum AI, Santa Barbara, California 93111, USA
| | - Alex Opremcak
- Google Quantum AI, Santa Barbara, California 93111, USA
| | - Ani Nersisyan
- Google Quantum AI, Santa Barbara, California 93111, USA
| | - Kenny Lee
- Google Quantum AI, Santa Barbara, California 93111, USA
| | - Alexander N Korotkov
- Google Quantum AI, Santa Barbara, California 93111, USA
- Department of Electrical and Computer Engineering, University of California, Riverside, California 92521, USA
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6
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Zou J, Bosco S, Loss D. Spatially correlated classical and quantum noise in driven qubits. NPJ QUANTUM INFORMATION 2024; 10:46. [PMID: 38706554 PMCID: PMC11062932 DOI: 10.1038/s41534-024-00842-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/27/2023] [Accepted: 04/17/2024] [Indexed: 05/07/2024]
Abstract
Correlated noise across multiple qubits poses a significant challenge for achieving scalable and fault-tolerant quantum processors. Despite recent experimental efforts to quantify this noise in various qubit architectures, a comprehensive understanding of its role in qubit dynamics remains elusive. Here, we present an analytical study of the dynamics of driven qubits under spatially correlated noise, including both Markovian and non-Markovian noise. Surprisingly, we find that by operating the qubit system at low temperatures, where correlated quantum noise plays an important role, significant long-lived entanglement between qubits can be generated. Importantly, this generation process can be controlled on-demand by turning the qubit driving on and off. On the other hand, we demonstrate that by operating the system at a higher temperature, the crosstalk between qubits induced by the correlated noise is unexpectedly suppressed. We finally reveal the impact of spatio-temporally correlated 1/f noise on the decoherence rate, and how its temporal correlations restore lost entanglement. Our findings provide critical insights into not only suppressing crosstalk between qubits caused by correlated noise but also in effectively leveraging such noise as a beneficial resource for controlled entanglement generation.
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Affiliation(s)
- Ji Zou
- Department of Physics, University of Basel, Basel, Switzerland
| | - Stefano Bosco
- Department of Physics, University of Basel, Basel, Switzerland
| | - Daniel Loss
- Department of Physics, University of Basel, Basel, Switzerland
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7
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Somoroff A, Ficheux Q, Mencia RA, Xiong H, Kuzmin R, Manucharyan VE. Millisecond Coherence in a Superconducting Qubit. PHYSICAL REVIEW LETTERS 2023; 130:267001. [PMID: 37450803 DOI: 10.1103/physrevlett.130.267001] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2021] [Revised: 03/24/2023] [Accepted: 05/10/2023] [Indexed: 07/18/2023]
Abstract
Improving control over physical qubits is a crucial component of quantum computing research. Here we report a superconducting fluxonium qubit with uncorrected coherence time T_{2}^{*}=1.48±0.13 ms, exceeding the state of the art for transmons by an order of magnitude. The average gate fidelity was benchmarked at 0.99991(1). Notably, even in the millisecond range, the coherence time is limited by material absorption and could be further improved with a more rigorous fabrication. Our demonstration may be useful for suppressing errors in the next generation quantum processors.
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Affiliation(s)
- Aaron Somoroff
- Department of Physics, Joint Quantum Institute, and Quantum Materials Center, University of Maryland, College Park, Maryland 20742, USA
| | - Quentin Ficheux
- Department of Physics, Joint Quantum Institute, and Quantum Materials Center, University of Maryland, College Park, Maryland 20742, USA
| | - Raymond A Mencia
- Department of Physics, Joint Quantum Institute, and Quantum Materials Center, University of Maryland, College Park, Maryland 20742, USA
| | - Haonan Xiong
- Department of Physics, Joint Quantum Institute, and Quantum Materials Center, University of Maryland, College Park, Maryland 20742, USA
| | - Roman Kuzmin
- Department of Physics, Joint Quantum Institute, and Quantum Materials Center, University of Maryland, College Park, Maryland 20742, USA
| | - Vladimir E Manucharyan
- Department of Physics, Joint Quantum Institute, and Quantum Materials Center, University of Maryland, College Park, Maryland 20742, USA
- École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
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8
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Danilin S, Barbosa J, Farage M, Zhao Z, Shang X, Burnett J, Ridler N, Li C, Weides M. Engineering the microwave to infrared noise photon flux for superconducting quantum systems. EPJ QUANTUM TECHNOLOGY 2022; 9:1. [PMID: 35098151 PMCID: PMC8761155 DOI: 10.1140/epjqt/s40507-022-00121-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Accepted: 01/03/2022] [Indexed: 06/14/2023]
Abstract
Electromagnetic filtering is essential for the coherent control, operation and readout of superconducting quantum circuits at milliKelvin temperatures. The suppression of spurious modes around transition frequencies of a few GHz is well understood and mainly achieved by on-chip and package considerations. Noise photons of higher frequencies - beyond the pair-breaking energies - cause decoherence and require spectral engineering before reaching the packaged quantum chip. The external wires that pass into the refrigerator and go down to the quantum circuit provide a direct path for these photons. This article contains quantitative analysis and experimental data for the noise photon flux through coaxial, filtered wiring. The attenuation of the coaxial cable at room temperature and the noise photon flux estimates for typical wiring configurations are provided. Compact cryogenic microwave low-pass filters with CR-110 and Esorb-230 absorptive dielectric fillings are presented along with experimental data at room and cryogenic temperatures up to 70 GHz. Filter cut-off frequencies between 1 to 10 GHz are set by the filter length, and the roll-off is material dependent. The relative dielectric permittivity and magnetic permeability for the Esorb-230 material in the pair-breaking frequency range of 75 to 110 GHz are measured, and the filter properties in this frequency range are calculated. The estimated dramatic suppression of the noise photon flux due to the filter proves its usefulness for experiments with superconducting quantum systems.
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Affiliation(s)
- Sergey Danilin
- James Watt School of Engineering, University of Glasgow, Glasgow, G12 8QQ UK
| | - João Barbosa
- James Watt School of Engineering, University of Glasgow, Glasgow, G12 8QQ UK
| | - Michael Farage
- James Watt School of Engineering, University of Glasgow, Glasgow, G12 8QQ UK
| | - Zimo Zhao
- James Watt School of Engineering, University of Glasgow, Glasgow, G12 8QQ UK
| | - Xiaobang Shang
- National Physical Laboratory, Hampton Road, Teddington, TW11 0LW UK
| | - Jonathan Burnett
- National Physical Laboratory, Hampton Road, Teddington, TW11 0LW UK
| | - Nick Ridler
- National Physical Laboratory, Hampton Road, Teddington, TW11 0LW UK
| | - Chong Li
- James Watt School of Engineering, University of Glasgow, Glasgow, G12 8QQ UK
| | - Martin Weides
- James Watt School of Engineering, University of Glasgow, Glasgow, G12 8QQ UK
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9
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Intrinsic and induced quantum quenches for enhancing qubit-based quantum noise spectroscopy. Nat Commun 2021; 12:6528. [PMID: 34764276 PMCID: PMC8586144 DOI: 10.1038/s41467-021-26868-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Accepted: 10/26/2021] [Indexed: 11/18/2022] Open
Abstract
Quantum sensing protocols that exploit the dephasing of a probe qubit are powerful and ubiquitous methods for interrogating an unknown environment. They have a variety of applications, ranging from noise mitigation in quantum processors, to the study of correlated electron states. Here, we discuss a simple strategy for enhancing these methods, based on the fact that they often give rise to an inadvertent quench of the probed system: there is an effective sudden change in the environmental Hamiltonian at the start of the sensing protocol. These quenches are extremely sensitive to the initial environmental state, and lead to observable changes in the sensor qubit evolution. We show how these new features give access to environmental response properties. This enables methods for direct measurement of bath temperature, and for detecting non-thermal equilibrium states. We also discuss how to deliberately control and modulate this quench physics, which enables reconstruction of the bath spectral function. Extensions to non-Gaussian quantum baths are also discussed, as is the application of our ideas to a range of sensing platforms (e.g., nitrogen-vacancy (NV) centers in diamond, semiconductor quantum dots, and superconducting circuits).
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10
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Wang Z, Xu M, Han X, Fu W, Puri S, Girvin SM, Tang HX, Shankar S, Devoret MH. Quantum Microwave Radiometry with a Superconducting Qubit. PHYSICAL REVIEW LETTERS 2021; 126:180501. [PMID: 34018799 DOI: 10.1103/physrevlett.126.180501] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2019] [Accepted: 03/29/2021] [Indexed: 06/12/2023]
Abstract
The interaction of photons and coherent quantum systems can be employed to detect electromagnetic radiation with remarkable sensitivity. We introduce a quantum radiometer based on the photon-induced dephasing process of a superconducting qubit for sensing microwave radiation at the subunit photon level. Using this radiometer, we demonstrate the radiative cooling of a 1 K microwave resonator and measure its mode temperature with an uncertainty ∼0.01 K. We thus develop a precise tool for studying the thermodynamics of quantum microwave circuits, which provides new solutions for calibrating hybrid quantum systems and detecting candidate particles for dark matter.
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Affiliation(s)
- Zhixin Wang
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Mingrui Xu
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06520, USA
| | - Xu Han
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06520, USA
| | - Wei Fu
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06520, USA
| | - Shruti Puri
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - S M Girvin
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Hong X Tang
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06520, USA
| | - S Shankar
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - M H Devoret
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
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11
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de Leon NP, Itoh KM, Kim D, Mehta KK, Northup TE, Paik H, Palmer BS, Samarth N, Sangtawesin S, Steuerman DW. Materials challenges and opportunities for quantum computing hardware. Science 2021; 372:372/6539/eabb2823. [PMID: 33859004 DOI: 10.1126/science.abb2823] [Citation(s) in RCA: 98] [Impact Index Per Article: 24.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.
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Affiliation(s)
- Nathalie P de Leon
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Kohei M Itoh
- School of Fundamental Science and Technology, Keio University, Yokohama 223-8522, Japan
| | - Dohun Kim
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
| | - Karan K Mehta
- Department of Physics, Institute for Quantum Electronics, ETH Zürich, 8092 Zürich, Switzerland
| | - Tracy E Northup
- Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria
| | - Hanhee Paik
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA.
| | - B S Palmer
- Laboratory for Physical Sciences, University of Maryland, College Park, MD 20740, USA.,Quantum Materials Center, University of Maryland, College Park, MD 20742, USA
| | - N Samarth
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA
| | - Sorawis Sangtawesin
- School of Physics and Center of Excellence in Advanced Functional Materials, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand
| | - D W Steuerman
- Kavli Foundation, 5715 Mesmer Avenue, Los Angeles, CA 90230, USA
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12
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Rosenthal EI, Schneider CMF, Malnou M, Zhao Z, Leditzky F, Chapman BJ, Wustmann W, Ma X, Palken DA, Zanner MF, Vale LR, Hilton GC, Gao J, Smith G, Kirchmair G, Lehnert KW. Efficient and Low-Backaction Quantum Measurement Using a Chip-Scale Detector. PHYSICAL REVIEW LETTERS 2021; 126:090503. [PMID: 33750151 DOI: 10.1103/physrevlett.126.090503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2020] [Accepted: 01/21/2021] [Indexed: 06/12/2023]
Abstract
Superconducting qubits are a leading platform for scalable quantum computing and quantum error correction. One feature of this platform is the ability to perform projective measurements orders of magnitude more quickly than qubit decoherence times. Such measurements are enabled by the use of quantum-limited parametric amplifiers in conjunction with ferrite circulators-magnetic devices which provide isolation from noise and decoherence due to amplifier backaction. Because these nonreciprocal elements have limited performance and are not easily integrated on chip, it has been a long-standing goal to replace them with a scalable alternative. Here, we demonstrate a solution to this problem by using a superconducting switch to control the coupling between a qubit and amplifier. Doing so, we measure a transmon qubit using a single, chip-scale device to provide both parametric amplification and isolation from the bulk of amplifier backaction. This measurement is also fast, high fidelity, and has 70% efficiency, comparable to the best that has been reported in any superconducting qubit measurement. As such, this work constitutes a high-quality platform for the scalable measurement of superconducting qubits.
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Affiliation(s)
- Eric I Rosenthal
- JILA, University of Colorado, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Christian M F Schneider
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Experimental Physics, University of Innsbruck, A-6020 Innsbruck, Austria
| | - Maxime Malnou
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Ziyi Zhao
- JILA, University of Colorado, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Felix Leditzky
- JILA, University of Colorado, Boulder, Colorado 80309, USA
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
- Department of Mathematics & Illinois Quantum Information Science and Technology Center, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Benjamin J Chapman
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - Waltraut Wustmann
- The Laboratory for Physical Sciences, College Park, Maryland 20740, USA
| | - Xizheng Ma
- JILA, University of Colorado, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Daniel A Palken
- JILA, University of Colorado, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Maximilian F Zanner
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Experimental Physics, University of Innsbruck, A-6020 Innsbruck, Austria
| | - Leila R Vale
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Gene C Hilton
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Jiansong Gao
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Graeme Smith
- JILA, University of Colorado, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Gerhard Kirchmair
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Experimental Physics, University of Innsbruck, A-6020 Innsbruck, Austria
| | - K W Lehnert
- JILA, University of Colorado, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
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13
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Sung Y, Vepsäläinen A, Braumüller J, Yan F, Wang JIJ, Kjaergaard M, Winik R, Krantz P, Bengtsson A, Melville AJ, Niedzielski BM, Schwartz ME, Kim DK, Yoder JL, Orlando TP, Gustavsson S, Oliver WD. Multi-level quantum noise spectroscopy. Nat Commun 2021; 12:967. [PMID: 33574240 PMCID: PMC7878521 DOI: 10.1038/s41467-021-21098-3] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2020] [Accepted: 01/13/2021] [Indexed: 11/08/2022] Open
Abstract
System noise identification is crucial to the engineering of robust quantum systems. Although existing quantum noise spectroscopy (QNS) protocols measure an aggregate amount of noise affecting a quantum system, they generally cannot distinguish between the underlying processes that contribute to it. Here, we propose and experimentally validate a spin-locking-based QNS protocol that exploits the multi-level energy structure of a superconducting qubit to achieve two notable advances. First, our protocol extends the spectral range of weakly anharmonic qubit spectrometers beyond the present limitations set by their lack of strong anharmonicity. Second, the additional information gained from probing the higher-excited levels enables us to identify and distinguish contributions from different underlying noise mechanisms.
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Affiliation(s)
- Youngkyu Sung
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA.
| | - Antti Vepsäläinen
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Jochen Braumüller
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Fei Yan
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, China
| | - Joel I-Jan Wang
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Morten Kjaergaard
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Niels Bohr Institute, University of Copenhagen, 2100, Copenhagen, Denmark
| | - Roni Winik
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Philip Krantz
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Andreas Bengtsson
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | | | | | | | | | | | - Terry P Orlando
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Simon Gustavsson
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - William D Oliver
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA.
- MIT Lincoln Laboratory, Lexington, MA, USA.
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
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14
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Hauke P, Katzgraber HG, Lechner W, Nishimori H, Oliver WD. Perspectives of quantum annealing: methods and implementations. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2020; 83:054401. [PMID: 32235066 DOI: 10.1088/1361-6633/ab85b8] [Citation(s) in RCA: 60] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
Quantum annealing is a computing paradigm that has the ambitious goal of efficiently solving large-scale combinatorial optimization problems of practical importance. However, many challenges have yet to be overcome before this goal can be reached. This perspectives article first gives a brief introduction to the concept of quantum annealing, and then highlights new pathways that may clear the way towards feasible and large scale quantum annealing. Moreover, since this field of research is to a strong degree driven by a synergy between experiment and theory, we discuss both in this work. An important focus in this article is on future perspectives, which complements other review articles, and which we hope will motivate further research.
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Affiliation(s)
- Philipp Hauke
- INO-CNR BEC Center and Department of Physics, University of Trento, 38123Povo (TN), Italy. Kirchhoff-Institute for Physics, Heidelberg University, 69120 Heidelberg, Germany. Institute for Theoretical Physics, Heidelberg University, 69120 Heidelberg, Germany
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15
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Layden D, Chen M, Cappellaro P. Efficient Quantum Error Correction of Dephasing Induced by a Common Fluctuator. PHYSICAL REVIEW LETTERS 2020; 124:020504. [PMID: 32004019 DOI: 10.1103/physrevlett.124.020504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2019] [Indexed: 06/10/2023]
Abstract
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new family of special-purpose quantum error-correcting codes that offer an exponential reduction in overhead compared to the usual repetition code. They are tailored for a common and important source of decoherence in current experiments, whereby a register of qubits is subject to phase noise through coupling to a common fluctuator, such as a resonator or a spin defect. The smallest instance encodes one logical qubit into two physical qubits, and corrects decoherence to leading-order using a constant number of one- and two-qubit operations. More generally, while the repetition code on n qubits corrects errors to order t^{O(n)}, with t the time between recoveries, our codes correct to order t^{O(2^{n})}. Moreover, they are robust to model imperfections in small- and intermediate-scale devices, where they already provide substantial gains in error suppression. As a result, these hardware-efficient codes open a potential avenue for useful quantum error correction in near-term, pre-fault tolerant devices.
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Affiliation(s)
- David Layden
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Mo Chen
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Paola Cappellaro
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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16
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Wen PY, Lin KT, Kockum AF, Suri B, Ian H, Chen JC, Mao SY, Chiu CC, Delsing P, Nori F, Lin GD, Hoi IC. Large Collective Lamb Shift of Two Distant Superconducting Artificial Atoms. PHYSICAL REVIEW LETTERS 2019; 123:233602. [PMID: 31868475 DOI: 10.1103/physrevlett.123.233602] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2019] [Indexed: 06/10/2023]
Abstract
Virtual photons can mediate interaction between atoms, resulting in an energy shift known as a collective Lamb shift. Observing the collective Lamb shift is challenging, since it can be obscured by radiative decay and direct atom-atom interactions. Here, we place two superconducting qubits in a transmission line terminated by a mirror, which suppresses decay. We measure a collective Lamb shift reaching 0.8% of the qubit transition frequency and twice the transition linewidth. We also show that the qubits can interact via the transmission line even if one of them does not decay into it.
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Affiliation(s)
- P Y Wen
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
- Center for Quantum Technology, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - K-T Lin
- CQSE, Department of Physics, National Taiwan University, Taipei 10617, Taiwan
| | - A F Kockum
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - B Suri
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
- Department of Instrumentation and Applied Physics, Indian Institute of Science, Bengaluru 560012, India
| | - H Ian
- Institute of Applied Physics and Materials Engineering, University of Macau, Macau, China
- UMacau Zhuhai Research Institute, Zhuhai, Guangdong 519031, China
| | - J C Chen
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
- Center for Quantum Technology, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - S Y Mao
- Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu 30013, Taiwan
| | - C C Chiu
- Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - P Delsing
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - F Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - G-D Lin
- CQSE, Department of Physics, National Taiwan University, Taipei 10617, Taiwan
| | - I-C Hoi
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
- Center for Quantum Technology, National Tsing Hua University, Hsinchu 30013, Taiwan
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17
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Sung Y, Beaudoin F, Norris LM, Yan F, Kim DK, Qiu JY, von Lüpke U, Yoder JL, Orlando TP, Gustavsson S, Viola L, Oliver WD. Non-Gaussian noise spectroscopy with a superconducting qubit sensor. Nat Commun 2019; 10:3715. [PMID: 31527608 PMCID: PMC6746758 DOI: 10.1038/s41467-019-11699-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2019] [Accepted: 07/30/2019] [Indexed: 11/17/2022] Open
Abstract
Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the Gaussian assumption and capture distinctive non-Gaussian signatures, a tool for characterizing non-Gaussian noise is essential. Here, we experimentally validate a quantum control protocol which, in addition to the spectrum, reconstructs the leading higher-order spectrum of engineered non-Gaussian dephasing noise using a superconducting qubit as a sensor. This first experimental demonstration of non-Gaussian noise spectroscopy represents a major step toward demonstrating a complete spectral estimation toolbox for quantum devices.
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Affiliation(s)
- Youngkyu Sung
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Félix Beaudoin
- Department of Physics and Astronomy, Dartmouth College, Hanover, NH, 03755, USA
- NanoAcademic Technologies, 666 rue Sherbrooke Ouest, Suite 802, Montreal, Quebec, H3A 1E7, Canada
| | - Leigh M Norris
- Department of Physics and Astronomy, Dartmouth College, Hanover, NH, 03755, USA
| | - Fei Yan
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - David K Kim
- MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA, 02421, USA
| | - Jack Y Qiu
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Uwe von Lüpke
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Jonilyn L Yoder
- MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA, 02421, USA
| | - Terry P Orlando
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Simon Gustavsson
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Lorenza Viola
- Department of Physics and Astronomy, Dartmouth College, Hanover, NH, 03755, USA.
| | - William D Oliver
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
- MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA, 02421, USA.
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
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