1
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Sivak VV, Eickbusch A, Royer B, Singh S, Tsioutsios I, Ganjam S, Miano A, Brock BL, Ding AZ, Frunzio L, Girvin SM, Schoelkopf RJ, Devoret MH. Real-time quantum error correction beyond break-even. Nature 2023; 616:50-55. [PMID: 36949196 DOI: 10.1038/s41586-023-05782-6] [Citation(s) in RCA: 21] [Impact Index Per Article: 21.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2022] [Accepted: 02/02/2023] [Indexed: 03/24/2023]
Abstract
The ambition of harnessing the quantum for computation is at odds with the fundamental phenomenon of decoherence. The purpose of quantum error correction (QEC) is to counteract the natural tendency of a complex system to decohere. This cooperative process, which requires participation of multiple quantum and classical components, creates a special type of dissipation that removes the entropy caused by the errors faster than the rate at which these errors corrupt the stored quantum information. Previous experimental attempts to engineer such a process1-7 faced the generation of an excessive number of errors that overwhelmed the error-correcting capability of the process itself. Whether it is practically possible to utilize QEC for extending quantum coherence thus remains an open question. Here we answer it by demonstrating a fully stabilized and error-corrected logical qubit whose quantum coherence is substantially longer than that of all the imperfect quantum components involved in the QEC process, beating the best of them with a coherence gain of G = 2.27 ± 0.07. We achieve this performance by combining innovations in several domains including the fabrication of superconducting quantum circuits and model-free reinforcement learning.
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Affiliation(s)
- V V Sivak
- Department of Physics, Yale University, New Haven, CT, USA.
- Department of Applied Physics, Yale University, New Haven, CT, USA.
- Yale Quantum Institute, Yale University, New Haven, CT, USA.
- Google AI Quantum, Santa Barbara, CA, USA.
| | - A Eickbusch
- Department of Physics, Yale University, New Haven, CT, USA
- Department of Applied Physics, Yale University, New Haven, CT, USA
- Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - B Royer
- Department of Physics, Yale University, New Haven, CT, USA
- Department of Applied Physics, Yale University, New Haven, CT, USA
- Yale Quantum Institute, Yale University, New Haven, CT, USA
- Institut Quantique, Université de Sherbrooke, Sherbrooke, Quebec, Canada
- Département de Physique, Université de Sherbrooke, Sherbrooke, Quebec, Canada
| | - S Singh
- Department of Physics, Yale University, New Haven, CT, USA
- Department of Applied Physics, Yale University, New Haven, CT, USA
- Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - I Tsioutsios
- Department of Physics, Yale University, New Haven, CT, USA
- Department of Applied Physics, Yale University, New Haven, CT, USA
- Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - S Ganjam
- Department of Physics, Yale University, New Haven, CT, USA
- Department of Applied Physics, Yale University, New Haven, CT, USA
- Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - A Miano
- Department of Physics, Yale University, New Haven, CT, USA
- Department of Applied Physics, Yale University, New Haven, CT, USA
- Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - B L Brock
- Department of Physics, Yale University, New Haven, CT, USA
- Department of Applied Physics, Yale University, New Haven, CT, USA
- Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - A Z Ding
- Department of Physics, Yale University, New Haven, CT, USA
- Department of Applied Physics, Yale University, New Haven, CT, USA
- Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - L Frunzio
- Department of Physics, Yale University, New Haven, CT, USA
- Department of Applied Physics, Yale University, New Haven, CT, USA
- Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - S M Girvin
- Department of Physics, Yale University, New Haven, CT, USA
- Department of Applied Physics, Yale University, New Haven, CT, USA
- Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - R J Schoelkopf
- Department of Physics, Yale University, New Haven, CT, USA
- Department of Applied Physics, Yale University, New Haven, CT, USA
- Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - M H Devoret
- Department of Physics, Yale University, New Haven, CT, USA.
- Department of Applied Physics, Yale University, New Haven, CT, USA.
- Yale Quantum Institute, Yale University, New Haven, CT, USA.
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2
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Campagne-Ibarcq P, Eickbusch A, Touzard S, Zalys-Geller E, Frattini NE, Sivak VV, Reinhold P, Puri S, Shankar S, Schoelkopf RJ, Frunzio L, Mirrahimi M, Devoret MH. Quantum error correction of a qubit encoded in grid states of an oscillator. Nature 2020; 584:368-372. [DOI: 10.1038/s41586-020-2603-3] [Citation(s) in RCA: 133] [Impact Index Per Article: 33.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2019] [Accepted: 06/12/2020] [Indexed: 11/09/2022]
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3
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Rosenblum S, Reinhold P, Mirrahimi M, Jiang L, Frunzio L, Schoelkopf RJ. Fault-tolerant detection of a quantum error. Science 2018; 361:266-270. [PMID: 30026224 DOI: 10.1126/science.aat3996] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2018] [Accepted: 05/22/2018] [Indexed: 11/02/2022]
Abstract
A critical component of any quantum error-correcting scheme is detection of errors by using an ancilla system. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information. We demonstrate a fault-tolerant error-detection scheme that suppresses spreading of ancilla errors by a factor of 5, while maintaining the assignment fidelity. The same method is used to prevent propagation of ancilla excitations, increasing the logical qubit dephasing time by an order of magnitude. Our approach is hardware-efficient, as it uses a single multilevel transmon ancilla and a cavity-encoded logical qubit, whose interaction is engineered in situ by using an off-resonant sideband drive. The results demonstrate that hardware-efficient approaches that exploit system-specific error models can yield advances toward fault-tolerant quantum computation.
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Affiliation(s)
- S Rosenblum
- Departments of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA. .,Yale Quantum Institute, Yale University, New Haven, CT 06520, USA
| | - P Reinhold
- Departments of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA.,Yale Quantum Institute, Yale University, New Haven, CT 06520, USA
| | - M Mirrahimi
- Yale Quantum Institute, Yale University, New Haven, CT 06520, USA.,QUANTIC team, INRIA de Paris, 2 Rue Simone Iff, 75012 Paris, France
| | - Liang Jiang
- Departments of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA.,Yale Quantum Institute, Yale University, New Haven, CT 06520, USA
| | - L Frunzio
- Departments of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA.,Yale Quantum Institute, Yale University, New Haven, CT 06520, USA
| | - R J Schoelkopf
- Departments of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA.,Yale Quantum Institute, Yale University, New Haven, CT 06520, USA
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4
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Chou KS, Blumoff JZ, Wang CS, Reinhold PC, Axline CJ, Gao YY, Frunzio L, Devoret MH, Jiang L, Schoelkopf RJ. Deterministic teleportation of a quantum gate between two logical qubits. Nature 2018; 561:368-373. [PMID: 30185908 DOI: 10.1038/s41586-018-0470-y] [Citation(s) in RCA: 107] [Impact Index Per Article: 17.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2018] [Accepted: 06/27/2018] [Indexed: 11/09/2022]
Abstract
A quantum computer has the potential to efficiently solve problems that are intractable for classical computers. However, constructing a large-scale quantum processor is challenging because of the errors and noise that are inherent in real-world quantum systems. One approach to addressing this challenge is to utilize modularity-a strategy used frequently in nature and engineering to build complex systems robustly. Such an approach manages complexity and uncertainty by assembling small, specialized components into a larger architecture. These considerations have motivated the development of a quantum modular architecture, in which separate quantum systems are connected into a quantum network via communication channels1,2. In this architecture, an essential tool for universal quantum computation is the teleportation of an entangling quantum gate3-5, but such teleportation has hitherto not been realized as a deterministic operation. Here we experimentally demonstrate the teleportation of a controlled-NOT (CNOT) gate, which we make deterministic by using real-time adaptive control. In addition, we take a crucial step towards implementing robust, error-correctable modules by enacting the gate between two logical qubits, encoding quantum information redundantly in the states of superconducting cavities6. By using such an error-correctable encoding, our teleported gate achieves a process fidelity of 79 per cent. Teleported gates have implications for fault-tolerant quantum computation3, and when realized within a network can have broad applications in quantum communication, metrology and simulations1,2,7. Our results illustrate a compelling approach for implementing multi-qubit operations on logical qubits and, if integrated with quantum error-correction protocols, indicate a promising path towards fault-tolerant quantum computation using a modular architecture.
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Affiliation(s)
- Kevin S Chou
- Department of Applied Physics and Physics, Yale University, New Haven, CT, USA. .,Yale Quantum Institute, Yale University, New Haven, CT, USA.
| | - Jacob Z Blumoff
- Department of Applied Physics and Physics, Yale University, New Haven, CT, USA.,Yale Quantum Institute, Yale University, New Haven, CT, USA.,HRL Laboratories, Malibu, CA, USA
| | - Christopher S Wang
- Department of Applied Physics and Physics, Yale University, New Haven, CT, USA.,Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - Philip C Reinhold
- Department of Applied Physics and Physics, Yale University, New Haven, CT, USA.,Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - Christopher J Axline
- Department of Applied Physics and Physics, Yale University, New Haven, CT, USA.,Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - Yvonne Y Gao
- Department of Applied Physics and Physics, Yale University, New Haven, CT, USA.,Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - L Frunzio
- Department of Applied Physics and Physics, Yale University, New Haven, CT, USA.,Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - M H Devoret
- Department of Applied Physics and Physics, Yale University, New Haven, CT, USA.,Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - Liang Jiang
- Department of Applied Physics and Physics, Yale University, New Haven, CT, USA.,Yale Quantum Institute, Yale University, New Haven, CT, USA
| | - R J Schoelkopf
- Department of Applied Physics and Physics, Yale University, New Haven, CT, USA. .,Yale Quantum Institute, Yale University, New Haven, CT, USA.
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5
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Campagne-Ibarcq P, Zalys-Geller E, Narla A, Shankar S, Reinhold P, Burkhart L, Axline C, Pfaff W, Frunzio L, Schoelkopf RJ, Devoret MH. Deterministic Remote Entanglement of Superconducting Circuits through Microwave Two-Photon Transitions. Phys Rev Lett 2018; 120:200501. [PMID: 29864347 DOI: 10.1103/physrevlett.120.200501] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Indexed: 05/26/2023]
Abstract
Large-scale quantum information processing networks will most probably require the entanglement of distant systems that do not interact directly. This can be done by performing entangling gates between standing information carriers, used as memories or local computational resources, and flying ones, acting as quantum buses. We report the deterministic entanglement of two remote transmon qubits by Raman stimulated emission and absorption of a traveling photon wave packet. We achieve a Bell state fidelity of 73%, well explained by losses in the transmission line and decoherence of each qubit.
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Affiliation(s)
- P Campagne-Ibarcq
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - E Zalys-Geller
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - A Narla
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - S Shankar
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - P Reinhold
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - L Burkhart
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - C Axline
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - W Pfaff
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - L Frunzio
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - R J Schoelkopf
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - M H Devoret
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
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6
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Vool U, Shankar S, Mundhada SO, Ofek N, Narla A, Sliwa K, Zalys-Geller E, Liu Y, Frunzio L, Schoelkopf RJ, Girvin SM, Devoret MH. Continuous Quantum Nondemolition Measurement of the Transverse Component of a Qubit. Phys Rev Lett 2016; 117:133601. [PMID: 27715126 DOI: 10.1103/physrevlett.117.133601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2016] [Indexed: 06/06/2023]
Abstract
Quantum jumps of a qubit are usually observed between its energy eigenstates, also known as its longitudinal pseudospin component. Is it possible, instead, to observe quantum jumps between the transverse superpositions of these eigenstates? We answer positively by presenting the first continuous quantum nondemolition measurement of the transverse component of an individual qubit. In a circuit QED system irradiated by two pump tones, we engineer an effective Hamiltonian whose eigenstates are the transverse qubit states, and a dispersive measurement of the corresponding operator. Such transverse component measurements are a useful tool in the driven-dissipative operation engineering toolbox, which is central to quantum simulation and quantum error correction.
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Affiliation(s)
- U Vool
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - S Shankar
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - S O Mundhada
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - N Ofek
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - A Narla
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - K Sliwa
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - E Zalys-Geller
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Y Liu
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - L Frunzio
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - R J Schoelkopf
- 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
| | - M H Devoret
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
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7
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Ofek N, Petrenko A, Heeres R, Reinhold P, Leghtas Z, Vlastakis B, Liu Y, Frunzio L, Girvin SM, Jiang L, Mirrahimi M, Devoret MH, Schoelkopf RJ. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 2016; 536:441-5. [DOI: 10.1038/nature18949] [Citation(s) in RCA: 469] [Impact Index Per Article: 58.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2016] [Accepted: 06/08/2016] [Indexed: 12/18/2022]
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8
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Wang C, Gao YY, Reinhold P, Heeres RW, Ofek N, Chou K, Axline C, Reagor M, Blumoff J, Sliwa KM, Frunzio L, Girvin SM, Jiang L, Mirrahimi M, Devoret MH, Schoelkopf RJ. A Schrödinger cat living in two boxes. Science 2016; 352:1087-91. [DOI: 10.1126/science.aaf2941] [Citation(s) in RCA: 189] [Impact Index Per Article: 23.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2016] [Accepted: 04/14/2016] [Indexed: 11/02/2022]
Affiliation(s)
- Chen Wang
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Yvonne Y. Gao
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Philip Reinhold
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - R. W. Heeres
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Nissim Ofek
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Kevin Chou
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Christopher Axline
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Matthew Reagor
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Jacob Blumoff
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - K. M. Sliwa
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - L. Frunzio
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - S. M. Girvin
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Liang Jiang
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - M. Mirrahimi
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
- INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
| | - M. H. Devoret
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - R. J. Schoelkopf
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
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9
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Vlastakis B, Petrenko A, Ofek N, Sun L, Leghtas Z, Sliwa K, Liu Y, Hatridge M, Blumoff J, Frunzio L, Mirrahimi M, Jiang L, Devoret MH, Schoelkopf RJ. Characterizing entanglement of an artificial atom and a cavity cat state with Bell's inequality. Nat Commun 2015; 6:8970. [PMID: 26611724 PMCID: PMC4674825 DOI: 10.1038/ncomms9970] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2015] [Accepted: 10/22/2015] [Indexed: 11/12/2022] Open
Abstract
The Schrodinger's cat thought experiment highlights the counterintuitive concept of entanglement in macroscopically distinguishable systems. The hallmark of entanglement is the detection of strong correlations between systems, most starkly demonstrated by the violation of a Bell inequality. No violation of a Bell inequality has been observed for a system entangled with a superposition of coherent states, known as a cat state. Here we use the Clauser–Horne–Shimony–Holt formulation of a Bell test to characterize entanglement between an artificial atom and a cat state, or a Bell-cat. Using superconducting circuits with high-fidelity measurements and real-time feedback, we detect correlations that surpass the classical maximum of the Bell inequality. We investigate the influence of decoherence with states up to 16 photons in size and characterize the system by introducing joint Wigner tomography. Such techniques demonstrate that information stored in superpositions of coherent states can be extracted efficiently, a crucial requirement for quantum computing with resonators. Qubit-cavity entanglement can be used for quantum information processing and for investigating the quantum-to-classical transition with high control. Here, the authors characterize the entanglement between an artificial atom and a cat state and its susceptibility to decoherence through Bell test witnesses.
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Affiliation(s)
- Brian Vlastakis
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
| | - Andrei Petrenko
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
| | - Nissim Ofek
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
| | - Luyan Sun
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
| | - Zaki Leghtas
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
| | - Katrina Sliwa
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
| | - Yehan Liu
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
| | - Michael Hatridge
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
| | - Jacob Blumoff
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
| | - Luigi Frunzio
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
| | - Mazyar Mirrahimi
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA.,INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
| | - Liang Jiang
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
| | - M H Devoret
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
| | - R J Schoelkopf
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06510, USA
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10
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Holland ET, Vlastakis B, Heeres RW, Reagor MJ, Vool U, Leghtas Z, Frunzio L, Kirchmair G, Devoret MH, Mirrahimi M, Schoelkopf RJ. Single-Photon-Resolved Cross-Kerr Interaction for Autonomous Stabilization of Photon-Number States. Phys Rev Lett 2015; 115:180501. [PMID: 26565448 DOI: 10.1103/physrevlett.115.180501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2015] [Indexed: 06/05/2023]
Abstract
Quantum states can be stabilized in the presence of intrinsic and environmental losses by either applying an active feedback condition on an ancillary system or through reservoir engineering. Reservoir engineering maintains a desired quantum state through a combination of drives and designed entropy evacuation. We propose and implement a quantum-reservoir engineering protocol that stabilizes Fock states in a microwave cavity. This protocol is realized with a circuit quantum electrodynamics platform where a Josephson junction provides direct, nonlinear coupling between two superconducting waveguide cavities. The nonlinear coupling results in a single-photon-resolved cross-Kerr effect between the two cavities enabling a photon-number-dependent coupling to a lossy environment. The quantum state of the microwave cavity is discussed in terms of a net polarization and is analyzed by a measurement of its steady state Wigner function.
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Affiliation(s)
- E T Holland
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - B Vlastakis
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - R W Heeres
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - M J Reagor
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - U Vool
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Z Leghtas
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - L Frunzio
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - G Kirchmair
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
- 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
| | - M H Devoret
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - M Mirrahimi
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
- INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
| | - R J Schoelkopf
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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11
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Leghtas Z, Touzard S, Pop IM, Kou A, Vlastakis B, Petrenko A, Sliwa KM, Narla A, Shankar S, Hatridge MJ, Reagor M, Frunzio L, Schoelkopf RJ, Mirrahimi M, Devoret MH. Confining the state of light to a quantum manifold by engineered two-photon loss. Science 2015; 347:853-7. [DOI: 10.1126/science.aaa2085] [Citation(s) in RCA: 262] [Impact Index Per Article: 29.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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12
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Vool U, Pop IM, Sliwa K, Abdo B, Wang C, Brecht T, Gao YY, Shankar S, Hatridge M, Catelani G, Mirrahimi M, Frunzio L, Schoelkopf RJ, Glazman LI, Devoret MH. Non-Poissonian quantum jumps of a fluxonium qubit due to quasiparticle excitations. Phys Rev Lett 2014; 113:247001. [PMID: 25541795 DOI: 10.1103/physrevlett.113.247001] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2014] [Indexed: 06/04/2023]
Abstract
As the energy relaxation time of superconducting qubits steadily improves, nonequilibrium quasiparticle excitations above the superconducting gap emerge as an increasingly relevant limit for qubit coherence. We measure fluctuations in the number of quasiparticle excitations by continuously monitoring the spontaneous quantum jumps between the states of a fluxonium qubit, in conditions where relaxation is dominated by quasiparticle loss. Resolution on the scale of a single quasiparticle is obtained by performing quantum nondemolition projective measurements within a time interval much shorter than T₁, using a quantum-limited amplifier (Josephson parametric converter). The quantum jump statistics switches between the expected Poisson distribution and a non-Poissonian one, indicating large relative fluctuations in the quasiparticle population, on time scales varying from seconds to hours. This dynamics can be modified controllably by injecting quasiparticles or by seeding quasiparticle-trapping vortices by cooling down in a magnetic field.
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Affiliation(s)
- U Vool
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - I M Pop
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - K Sliwa
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - B Abdo
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - C Wang
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - T Brecht
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Y Y Gao
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - S Shankar
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - M Hatridge
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - G Catelani
- Peter Grünberg Institut (PGI-2), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - M Mirrahimi
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA and INRIA Paris-Rocquencourt, Domaine de Voluceau, BP105, 78153 Le Chesnay cedex, France
| | - L Frunzio
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - R J Schoelkopf
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - L I Glazman
- 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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13
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Sun L, Petrenko A, Leghtas Z, Vlastakis B, Kirchmair G, Sliwa KM, Narla A, Hatridge M, Shankar S, Blumoff J, Frunzio L, Mirrahimi M, Devoret MH, Schoelkopf RJ. Tracking photon jumps with repeated quantum non-demolition parity measurements. Nature 2014; 511:444-8. [DOI: 10.1038/nature13436] [Citation(s) in RCA: 169] [Impact Index Per Article: 16.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2013] [Accepted: 05/06/2014] [Indexed: 12/26/2022]
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14
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Vlastakis B, Kirchmair G, Leghtas Z, Nigg SE, Frunzio L, Girvin SM, Mirrahimi M, Devoret MH, Schoelkopf RJ. Deterministically encoding quantum information using 100-photon Schrödinger cat states. Science 2013; 342:607-10. [PMID: 24072821 DOI: 10.1126/science.1243289] [Citation(s) in RCA: 126] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
In contrast to a single quantum bit, an oscillator can store multiple excitations and coherences provided one has the ability to generate and manipulate complex multiphoton states. We demonstrate multiphoton control by using a superconducting transmon qubit coupled to a waveguide cavity resonator with a highly ideal off-resonant coupling. This dispersive interaction is much greater than decoherence rates and higher-order nonlinearities to allow simultaneous manipulation of hundreds of photons. With a tool set of conditional qubit-photon logic, we mapped an arbitrary qubit state to a superposition of coherent states, known as a "cat state." We created cat states as large as 111 photons and extended this protocol to create superpositions of up to four coherent states. This control creates a powerful interface between discrete and continuous variable quantum computation and could enable applications in metrology and quantum information processing.
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Affiliation(s)
- Brian Vlastakis
- Department of Physics and Department of Applied Physics, Yale University, New Haven, CT 06511, USA
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15
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Geerlings K, Leghtas Z, Pop IM, Shankar S, Frunzio L, Schoelkopf RJ, Mirrahimi M, Devoret MH. Demonstrating a driven reset protocol for a superconducting qubit. Phys Rev Lett 2013; 110:120501. [PMID: 25166782 DOI: 10.1103/physrevlett.110.120501] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2012] [Indexed: 06/03/2023]
Abstract
Qubit reset is crucial at the start of and during quantum information algorithms. We present the experimental demonstration of a practical method to force qubits into their ground state, based on driving appropriate qubit and cavity transitions. Our protocol, called the double drive reset of population, is tested on a superconducting transmon qubit in a three-dimensional cavity. Using a new method for measuring population, we show that we can prepare the ground state with a fidelity of at least 99.5% in less than 3 μs; faster times and higher fidelity are predicted upon parameter optimization.
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Affiliation(s)
- K Geerlings
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8284, USA
| | - Z Leghtas
- INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay cedex, France
| | - I M Pop
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8284, USA
| | - S Shankar
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8284, USA
| | - L Frunzio
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8284, USA
| | - R J Schoelkopf
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8284, USA
| | - M Mirrahimi
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8284, USA and INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay cedex, France
| | - M H Devoret
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8284, USA
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16
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Kirchmair G, Vlastakis B, Leghtas Z, Nigg SE, Paik H, Ginossar E, Mirrahimi M, Frunzio L, Girvin SM, Schoelkopf RJ. Observation of quantum state collapse and revival due to the single-photon Kerr effect. Nature 2013; 495:205-9. [DOI: 10.1038/nature11902] [Citation(s) in RCA: 338] [Impact Index Per Article: 30.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2012] [Accepted: 01/11/2013] [Indexed: 11/09/2022]
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17
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18
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Hatridge M, Shankar S, Mirrahimi M, Schackert F, Geerlings K, Brecht T, Sliwa KM, Abdo B, Frunzio L, Girvin SM, Schoelkopf RJ, Devoret MH. Quantum back-action of an individual variable-strength measurement. Science 2013; 339:178-81. [PMID: 23307736 DOI: 10.1126/science.1226897] [Citation(s) in RCA: 191] [Impact Index Per Article: 17.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depend on the quantity that is measured. In a partial measurement performed by an ideal apparatus, quantum physics predicts that the system remains in a pure state whose evolution can be tracked perfectly from the measurement record. We demonstrated this property using a superconducting qubit dispersively coupled to a cavity traversed by a microwave signal. The back-action on the qubit state of a single measurement of both signal quadratures was observed and shown to produce a stochastic operation whose action is determined by the measurement result. This accurate monitoring of a qubit state is an essential prerequisite for measurement-based feedback control of quantum systems.
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Affiliation(s)
- M Hatridge
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06520, USA.
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19
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Nigg SE, Paik H, Vlastakis B, Kirchmair G, Shankar S, Frunzio L, Devoret MH, Schoelkopf RJ, Girvin SM. Black-box superconducting circuit quantization. Phys Rev Lett 2012; 108:240502. [PMID: 23004246 DOI: 10.1103/physrevlett.108.240502] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2012] [Indexed: 06/01/2023]
Abstract
We present a semiclassical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions coupled to electromagnetic environments made of an arbitrary combination of distributed and lumped elements. A convenient basis, capturing the multimode physics, is given by the quantized eigenmodes of the linearized circuit and is fully determined by a classical linear response function. The method is used to calculate numerically the low-energy spectrum of a 3D transmon system, and quantitative agreement with measurements is found.
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Affiliation(s)
- Simon E Nigg
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
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20
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Sun L, DiCarlo L, Reed MD, Catelani G, Bishop LS, Schuster DI, Johnson BR, Yang GA, Frunzio L, Glazman L, Devoret MH, Schoelkopf RJ. Measurements of quasiparticle tunneling dynamics in a band-gap-engineered transmon qubit. Phys Rev Lett 2012; 108:230509. [PMID: 23003936 DOI: 10.1103/physrevlett.108.230509] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2011] [Indexed: 06/01/2023]
Abstract
We have engineered the band gap profile of transmon qubits by combining oxygen-doped Al for tunnel junction electrodes and clean Al as quasiparticle traps to investigate energy relaxation due to quasiparticle tunneling. The relaxation time T1 of the qubits is shown to be insensitive to this band gap engineering. Operating at relatively low-E(J)/E(C) makes the transmon transition frequency distinctly dependent on the charge parity, allowing us to detect the quasiparticles tunneling across the qubit junction. Quasiparticle kinetics have been studied by monitoring the frequency switching due to even-odd parity change in real time. It shows the switching time is faster than 10 μs, indicating quasiparticle-induced relaxation has to be reduced to achieve T1 much longer than 100 μs.
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Affiliation(s)
- L Sun
- Department of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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21
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Paik H, Schuster DI, Bishop LS, Kirchmair G, Catelani G, Sears AP, Johnson BR, Reagor MJ, Frunzio L, Glazman LI, Girvin SM, Devoret MH, Schoelkopf RJ. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Phys Rev Lett 2011; 107:240501. [PMID: 22242979 DOI: 10.1103/physrevlett.107.240501] [Citation(s) in RCA: 85] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2011] [Revised: 09/15/2011] [Indexed: 05/27/2023]
Abstract
Superconducting quantum circuits based on Josephson junctions have made rapid progress in demonstrating quantum behavior and scalability. However, the future prospects ultimately depend upon the intrinsic coherence of Josephson junctions, and whether superconducting qubits can be adequately isolated from their environment. We introduce a new architecture for superconducting quantum circuits employing a three-dimensional resonator that suppresses qubit decoherence while maintaining sufficient coupling to the control signal. With the new architecture, we demonstrate that Josephson junction qubits are highly coherent, with T2 ∼ 10 to 20 μs without the use of spin echo, and highly stable, showing no evidence for 1/f critical current noise. These results suggest that the overall quality of Josephson junctions in these qubits will allow error rates of a few 10(-4), approaching the error correction threshold.
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Affiliation(s)
- Hanhee Paik
- Department of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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22
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Catelani G, Koch J, Frunzio L, Schoelkopf RJ, Devoret MH, Glazman LI. Quasiparticle relaxation of superconducting qubits in the presence of flux. Phys Rev Lett 2011; 106:077002. [PMID: 21405533 DOI: 10.1103/physrevlett.106.077002] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2010] [Indexed: 05/30/2023]
Abstract
Quasiparticle tunneling across a Josephson junction sets a limit for the lifetime of a superconducting qubit state. We develop a general theory of the corresponding decay rate in a qubit controlled by a magnetic flux. The flux affects quasiparticles tunneling amplitudes, thus making the decay rate flux-dependent. The theory is applicable for an arbitrary quasiparticle distribution. It provides estimates for the rates in practically important quantum circuits and also offers a new way of measuring the phase-dependent admittance of a Josephson junction.
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Affiliation(s)
- G Catelani
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
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23
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Dicarlo L, Reed MD, Sun L, Johnson BR, Chow JM, Gambetta JM, Frunzio L, Girvin SM, Devoret MH, Schoelkopf RJ. Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature 2010; 467:574-8. [PMID: 20882013 DOI: 10.1038/nature09416] [Citation(s) in RCA: 443] [Impact Index Per Article: 31.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2010] [Accepted: 08/09/2010] [Indexed: 11/09/2022]
Abstract
Traditionally, quantum entanglement has been central to foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can have results at odds with classical behaviour. These discrepancies grow exponentially with the number of entangled particles. With the ample experimental confirmation of quantum mechanical predictions, entanglement has evolved from a philosophical conundrum into a key resource for technologies such as quantum communication and computation. Although entanglement in superconducting circuits has been limited so far to two qubits, the extension of entanglement to three, eight and ten qubits has been achieved among spins, ions and photons, respectively. A key question for solid-state quantum information processing is whether an engineered system could display the multi-qubit entanglement necessary for quantum error correction, which starts with tripartite entanglement. Here, using a circuit quantum electrodynamics architecture, we demonstrate deterministic production of three-qubit Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88 per cent, measured with quantum state tomography. Several entanglement witnesses detect genuine three-qubit entanglement by violating biseparable bounds by 830 ± 80 per cent. We demonstrate the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code. The integration of this encoding with decoding and error-correcting steps in a feedback loop will be the next step for quantum computing with integrated circuits.
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Affiliation(s)
- L Dicarlo
- Department of Physics, Yale University, New Haven, Connecticut 06511, USA.
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24
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Reed MD, DiCarlo L, Johnson BR, Sun L, Schuster DI, Frunzio L, Schoelkopf RJ. High-fidelity readout in circuit quantum electrodynamics using the Jaynes-Cummings nonlinearity. Phys Rev Lett 2010; 105:173601. [PMID: 21231043 DOI: 10.1103/physrevlett.105.173601] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2010] [Indexed: 05/30/2023]
Abstract
We demonstrate a qubit readout scheme that exploits the Jaynes-Cummings nonlinearity of a superconducting cavity coupled to transmon qubits. We find that, in the strongly driven dispersive regime of this system, there is the unexpected onset of a high-transmission "bright" state at a critical power which depends sensitively on the initial qubit state. A simple and robust measurement protocol exploiting this effect achieves a single-shot fidelity of 87% using a conventional sample design and experimental setup, and at least 61% fidelity to joint correlations of three qubits.
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Affiliation(s)
- M D Reed
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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25
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Schuster DI, Sears AP, Ginossar E, DiCarlo L, Frunzio L, Morton JJL, Wu H, Briggs GAD, Buckley BB, Awschalom DD, Schoelkopf RJ. High-cooperativity coupling of electron-spin ensembles to superconducting cavities. Phys Rev Lett 2010; 105:140501. [PMID: 21230817 DOI: 10.1103/physrevlett.105.140501] [Citation(s) in RCA: 112] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2010] [Revised: 08/11/2010] [Indexed: 05/30/2023]
Abstract
Electron spins in solids are promising candidates for quantum memories for superconducting qubits because they can have long coherence times, large collective couplings, and many qubits could be encoded into spin waves of a single ensemble. We demonstrate the coupling of electron-spin ensembles to a superconducting transmission-line cavity at strengths greatly exceeding the cavity decay rates and comparable to the spin linewidths. We also perform broadband spectroscopy of ruby (Al₂O₃:Cr(3+)) at millikelvin temperatures and low powers, using an on-chip feedline. In addition, we observe hyperfine structure in diamond P1 centers.
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Affiliation(s)
- D I Schuster
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06511, USA
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26
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Schuster DI, Fragner A, Dykman MI, Lyon SA, Schoelkopf RJ. Proposal for manipulating and detecting spin and orbital States of trapped electrons on helium using cavity quantum electrodynamics. Phys Rev Lett 2010; 105:040503. [PMID: 20867827 DOI: 10.1103/physrevlett.105.040503] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2009] [Revised: 04/30/2010] [Indexed: 05/29/2023]
Abstract
We propose a hybrid architecture in which an on-chip high finesse superconducting cavity is coupled to the lateral motion and spin state of a single electron trapped on the surface of superfluid helium. We estimate the motional coherence times to exceed 15 μs, while energy will be coherently exchanged with the cavity photons in less than 10 ns for charge states and faster than 1 μs for spin states, making the system attractive for quantum information processing and strong coupling cavity quantum electrodynamics experiments. The cavity is used for nondestructive readout and as a quantum bus mediating interactions between distant electrons or an electron and a superconducting qubit.
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Affiliation(s)
- D I Schuster
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06511, USA
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27
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Wesenberg JH, Ardavan A, Briggs GAD, Morton JJL, Schoelkopf RJ, Schuster DI, Mølmer K. Quantum computing with an electron spin ensemble. Phys Rev Lett 2009; 103:070502. [PMID: 19792625 DOI: 10.1103/physrevlett.103.070502] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2009] [Indexed: 05/28/2023]
Abstract
We propose to encode a register of quantum bits in different collective electron spin wave excitations in a solid medium. Coupling to spins is enabled by locating them in the vicinity of a superconducting transmission line cavity, and making use of their strong collective coupling to the quantized radiation field. The transformation between different spin waves is achieved by applying gradient magnetic fields across the sample, while a Cooper pair box, resonant with the cavity field, may be used to carry out one- and two-qubit gate operations.
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Affiliation(s)
- J H Wesenberg
- Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom
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28
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Chow JM, Gambetta JM, Tornberg L, Koch J, Bishop LS, Houck AA, Johnson BR, Frunzio L, Girvin SM, Schoelkopf RJ. Randomized benchmarking and process tomography for gate errors in a solid-state qubit. Phys Rev Lett 2009; 102:090502. [PMID: 19392502 DOI: 10.1103/physrevlett.102.090502] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2008] [Indexed: 05/27/2023]
Abstract
We present measurements of single-qubit gate errors for a superconducting qubit. Results from quantum process tomography and randomized benchmarking are compared with gate errors obtained from a double pi pulse experiment. Randomized benchmarking reveals a minimum average gate error of 1.1+/-0.3% and a simple exponential dependence of fidelity on the number of gates. It shows that the limits on gate fidelity are primarily imposed by qubit decoherence, in agreement with theory.
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Affiliation(s)
- J M Chow
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
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29
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Houck AA, Schreier JA, Johnson BR, Chow JM, Koch J, Gambetta JM, Schuster DI, Frunzio L, Devoret MH, Girvin SM, Schoelkopf RJ. Controlling the spontaneous emission of a superconducting transmon qubit. Phys Rev Lett 2008; 101:080502. [PMID: 18764596 DOI: 10.1103/physrevlett.101.080502] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2008] [Indexed: 05/26/2023]
Abstract
We present a detailed characterization of coherence in seven transmon qubits in a circuit QED architecture. We find that spontaneous emission rates are strongly influenced by far off-resonant modes of the cavity and can be understood within a semiclassical circuit model. A careful analysis of the spontaneous qubit decay into a microwave transmission-line cavity can accurately predict the qubit lifetimes over 2 orders of magnitude in time and more than an octave in frequency. Coherence times T1 and T_{2};{*} of more than a microsecond are reproducibly demonstrated.
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Affiliation(s)
- A A Houck
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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31
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Leek PJ, Fink JM, Blais A, Bianchetti R, Goppl M, Gambetta JM, Schuster DI, Frunzio L, Schoelkopf RJ, Wallraff A. Observation of Berry's Phase in a Solid-State Qubit. Science 2007; 318:1889-92. [DOI: 10.1126/science.1149858] [Citation(s) in RCA: 292] [Impact Index Per Article: 17.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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32
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Majer J, Chow JM, Gambetta JM, Koch J, Johnson BR, Schreier JA, Frunzio L, Schuster DI, Houck AA, Wallraff A, Blais A, Devoret MH, Girvin SM, Schoelkopf RJ. Coupling superconducting qubits via a cavity bus. Nature 2007; 449:443-7. [PMID: 17898763 DOI: 10.1038/nature06184] [Citation(s) in RCA: 221] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2007] [Accepted: 08/16/2007] [Indexed: 11/09/2022]
Abstract
Superconducting circuits are promising candidates for constructing quantum bits (qubits) in a quantum computer; single-qubit operations are now routine, and several examples of two-qubit interactions and gates have been demonstrated. These experiments show that two nearby qubits can be readily coupled with local interactions. Performing gate operations between an arbitrary pair of distant qubits is highly desirable for any quantum computer architecture, but has not yet been demonstrated. An efficient way to achieve this goal is to couple the qubits to a 'quantum bus', which distributes quantum information among the qubits. Here we show the implementation of such a quantum bus, using microwave photons confined in a transmission line cavity, to couple two superconducting qubits on opposite sides of a chip. The interaction is mediated by the exchange of virtual rather than real photons, avoiding cavity-induced loss. Using fast control of the qubits to switch the coupling effectively on and off, we demonstrate coherent transfer of quantum states between the qubits. The cavity is also used to perform multiplexed control and measurement of the qubit states. This approach can be expanded to more than two qubits, and is an attractive architecture for quantum information processing on a chip.
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Affiliation(s)
- J Majer
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA.
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33
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Houck AA, Schuster DI, Gambetta JM, Schreier JA, Johnson BR, Chow JM, Frunzio L, Majer J, Devoret MH, Girvin SM, Schoelkopf RJ. Generating single microwave photons in a circuit. Nature 2007; 449:328-31. [PMID: 17882217 DOI: 10.1038/nature06126] [Citation(s) in RCA: 339] [Impact Index Per Article: 19.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2007] [Accepted: 07/24/2007] [Indexed: 11/08/2022]
Abstract
Microwaves have widespread use in classical communication technologies, from long-distance broadcasts to short-distance signals within a computer chip. Like all forms of light, microwaves, even those guided by the wires of an integrated circuit, consist of discrete photons. To enable quantum communication between distant parts of a quantum computer, the signals must also be quantum, consisting of single photons, for example. However, conventional sources can generate only classical light, not single photons. One way to realize a single-photon source is to collect the fluorescence of a single atom. Early experiments measured the quantum nature of continuous radiation, and further advances allowed triggered sources of photons on demand. To allow efficient photon collection, emitters are typically placed inside optical or microwave cavities, but these sources are difficult to employ for quantum communication on wires within an integrated circuit. Here we demonstrate an on-chip, on-demand single-photon source, where the microwave photons are injected into a wire with high efficiency and spectral purity. This is accomplished in a circuit quantum electrodynamics architecture, with a microwave transmission line cavity that enhances the spontaneous emission of a single superconducting qubit. When the qubit spontaneously emits, the generated photon acts as a flying qubit, transmitting the quantum information across a chip. We perform tomography of both the qubit and the emitted photons, clearly showing that both the quantum phase and amplitude are transferred during the emission. Both the average power and voltage of the photon source are characterized to verify performance of the system. This single-photon source is an important addition to a rapidly growing toolbox for quantum optics on a chip.
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Affiliation(s)
- A A Houck
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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34
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Wallraff A, Schuster DI, Blais A, Gambetta JM, Schreier J, Frunzio L, Devoret MH, Girvin SM, Schoelkopf RJ. Sideband transitions and two-tone spectroscopy of a superconducting qubit strongly coupled to an on-chip cavity. Phys Rev Lett 2007; 99:050501. [PMID: 17930736 DOI: 10.1103/physrevlett.99.050501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2007] [Indexed: 05/25/2023]
Abstract
Sideband transitions are spectroscopically probed in a system consisting of a Cooper pair box strongly but nonresonantly coupled to a superconducting transmission line resonator. When the Cooper pair box is operated at the optimal charge bias point, the symmetry of the Hamiltonian requires a two-photon process to access sidebands. The observed large dispersive ac-Stark shifts in the sideband transitions induced by the strong nonresonant drives agree well with our theoretical predictions. Sideband transitions are important in realizing qubit-photon and qubit-qubit entanglement in the circuit quantum electrodynamics architecture for quantum information processing.
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Affiliation(s)
- A Wallraff
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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35
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Schuster DI, Houck AA, Schreier JA, Wallraff A, Gambetta JM, Blais A, Frunzio L, Majer J, Johnson B, Devoret MH, Girvin SM, Schoelkopf RJ. Resolving photon number states in a superconducting circuit. Nature 2007; 445:515-8. [PMID: 17268464 DOI: 10.1038/nature05461] [Citation(s) in RCA: 157] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2006] [Accepted: 11/20/2006] [Indexed: 11/09/2022]
Abstract
Electromagnetic signals are always composed of photons, although in the circuit domain those signals are carried as voltages and currents on wires, and the discreteness of the photon's energy is usually not evident. However, by coupling a superconducting quantum bit (qubit) to signals on a microwave transmission line, it is possible to construct an integrated circuit in which the presence or absence of even a single photon can have a dramatic effect. Such a system can be described by circuit quantum electrodynamics (QED)-the circuit equivalent of cavity QED, where photons interact with atoms or quantum dots. Previously, circuit QED devices were shown to reach the resonant strong coupling regime, where a single qubit could absorb and re-emit a single photon many times. Here we report a circuit QED experiment in the strong dispersive limit, a new regime where a single photon has a large effect on the qubit without ever being absorbed. The hallmark of this strong dispersive regime is that the qubit transition energy can be resolved into a separate spectral line for each photon number state of the microwave field. The strength of each line is a measure of the probability of finding the corresponding photon number in the cavity. This effect is used to distinguish between coherent and thermal fields, and could be used to create a photon statistics analyser. As no photons are absorbed by this process, it should be possible to generate non-classical states of light by measurement and perform qubit-photon conditional logic, the basis of a logic bus for a quantum computer.
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Affiliation(s)
- D I Schuster
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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36
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Rabl P, DeMille D, Doyle JM, Lukin MD, Schoelkopf RJ, Zoller P. Hybrid quantum processors: molecular ensembles as quantum memory for solid state circuits. Phys Rev Lett 2006; 97:033003. [PMID: 16907499 DOI: 10.1103/physrevlett.97.033003] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2006] [Indexed: 05/11/2023]
Abstract
We investigate a hybrid quantum circuit where ensembles of cold polar molecules serve as long-lived quantum memories and optical interfaces for solid state quantum processors. The quantum memory realized by collective spin states (ensemble qubit) is coupled to a high-Q stripline cavity via microwave Raman processes. We show that, for convenient trap-surface distances of a few microm, strong coupling between the cavity and ensemble qubit can be achieved. We discuss basic quantum information protocols, including a swap from the cavity photon bus to the molecular quantum memory, and a deterministic two qubit gate. Finally, we investigate coherence properties of molecular ensemble quantum bits.
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Affiliation(s)
- P Rabl
- Institute for Theoretical Physics, University of Innsbruck, and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
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37
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Wallraff A, Schuster DI, Blais A, Frunzio L, Majer J, Devoret MH, Girvin SM, Schoelkopf RJ. Approaching unit visibility for control of a superconducting qubit with dispersive readout. Phys Rev Lett 2005; 95:060501. [PMID: 16090931 DOI: 10.1103/physrevlett.95.060501] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2005] [Indexed: 05/03/2023]
Abstract
In a Rabi oscillation experiment with a superconducting qubit we show that a visibility in the qubit excited state population of more than 95% can be attained. We perform a dispersive measurement of the qubit state by coupling the qubit non-resonantly to a transmission line resonator and probing the resonator transmission spectrum. The measurement process is well characterized and quantitatively understood. In a measurement of Ramsey fringes, the qubit coherence time is larger than 500 ns.
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Affiliation(s)
- A Wallraff
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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38
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Schuster DI, Wallraff A, Blais A, Frunzio L, Huang RS, Majer J, Girvin SM, Schoelkopf RJ. ac Stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field. Phys Rev Lett 2005; 94:123602. [PMID: 15903919 DOI: 10.1103/physrevlett.94.123602] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2004] [Indexed: 05/02/2023]
Abstract
We have performed spectroscopy of a superconducting charge qubit coupled nonresonantly to a single mode of an on-chip resonator. The strong coupling induces a large ac Stark shift in the energy levels of both the qubit and the resonator. The dispersive shift of the resonator frequency is used to nondestructively determine the qubit state. Photon shot noise in the measurement field induces qubit level fluctuations leading to dephasing which is characteristic for the measurement backaction. A crossover in line shape with measurement power is observed and theoretically explained. For weak measurement a long intrinsic dephasing time of T2>200 ns of the qubit is found.
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Affiliation(s)
- D I Schuster
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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39
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Siddiqi I, Vijay R, Pierre F, Wilson CM, Frunzio L, Metcalfe M, Rigetti C, Schoelkopf RJ, Devoret MH, Vion D, Esteve D. Direct observation of dynamical bifurcation between two driven oscillation states of a Josephson junction. Phys Rev Lett 2005; 94:027005. [PMID: 15698220 DOI: 10.1103/physrevlett.94.027005] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2003] [Indexed: 05/24/2023]
Abstract
We performed a novel phase-sensitive microwave reflection experiment which directly probes the dynamics of the Josephson plasma resonance in both the linear and the nonlinear regime. When the junction was driven below the plasma frequency into the nonlinear regime, we observed for the first time the transition between two different dynamical states predicted for nonlinear systems. In our experiment, this transition appears as an abrupt change in the reflected signal phase at a critical excitation power. This controlled dynamical switching can form the basis of a sensitive amplifier, in particular, for the readout of superconducting qubits.
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Affiliation(s)
- I Siddiqi
- Departments of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520-8284, USA
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40
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Wallraff A, Schuster DI, Blais A, Frunzio L, Huang RS, Majer J, Kumar S, Girvin SM, Schoelkopf RJ. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 2004; 431:162-7. [PMID: 15356625 DOI: 10.1038/nature02851] [Citation(s) in RCA: 652] [Impact Index Per Article: 32.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2004] [Accepted: 07/12/2004] [Indexed: 11/09/2022]
Abstract
The interaction of matter and light is one of the fundamental processes occurring in nature, and its most elementary form is realized when a single atom interacts with a single photon. Reaching this regime has been a major focus of research in atomic physics and quantum optics for several decades and has generated the field of cavity quantum electrodynamics. Here we perform an experiment in which a superconducting two-level system, playing the role of an artificial atom, is coupled to an on-chip cavity consisting of a superconducting transmission line resonator. We show that the strong coupling regime can be attained in a solid-state system, and we experimentally observe the coherent interaction of a superconducting two-level system with a single microwave photon. The concept of circuit quantum electrodynamics opens many new possibilities for studying the strong interaction of light and matter. This system can also be exploited for quantum information processing and quantum communication and may lead to new approaches for single photon generation and detection.
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Affiliation(s)
- A Wallraff
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA.
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41
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Schmidt DR, Schoelkopf RJ, Cleland AN. Photon-mediated thermal relaxation of electrons in nanostructures. Phys Rev Lett 2004; 93:045901. [PMID: 15323773 DOI: 10.1103/physrevlett.93.045901] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2003] [Indexed: 05/24/2023]
Abstract
Measurements of the thermal properties of nanoscale electron systems have ignored the effect of electrical noise radiated between the electron gas and the environment, through the electrical leads. Here we calculate the effect of this photon-mediated process, and show that the low-temperature thermal conductance is equal to the quantum of thermal conductance, GQ = pi2kB2T/3h, times a coupling coefficient. We find that, at very low temperatures, the photon conductance is the dominant route for thermal equilibration, while at moderate temperatures this relaxation mode adds one quantum of thermal conductance to that due to phonon transport.
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Affiliation(s)
- D R Schmidt
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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42
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Kiselev SI, Sankey JC, Krivorotov IN, Emley NC, Schoelkopf RJ, Buhrman RA, Ralph DC. Microwave oscillations of a nanomagnet driven by a spin-polarized current. Nature 2003; 425:380-3. [PMID: 14508483 DOI: 10.1038/nature01967] [Citation(s) in RCA: 1694] [Impact Index Per Article: 80.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2003] [Accepted: 07/28/2003] [Indexed: 11/09/2022]
Abstract
The recent discovery that a spin-polarized electrical current can apply a large torque to a ferromagnet, through direct transfer of spin angular momentum, offers the possibility of manipulating magnetic-device elements without applying cumbersome magnetic fields. However, a central question remains unresolved: what type of magnetic motions can be generated by this torque? Theory predicts that spin transfer may be able to drive a nanomagnet into types of oscillatory magnetic modes not attainable with magnetic fields alone, but existing measurement techniques have provided only indirect evidence for dynamical states. The nature of the possible motions has not been determined. Here we demonstrate a technique that allows direct electrical measurements of microwave-frequency dynamics in individual nanomagnets, propelled by a d.c. spin-polarized current. We show that spin transfer can produce several different types of magnetic excitation. Although there is no mechanical motion, a simple magnetic-multilayer structure acts like a nanoscale motor; it converts energy from a d.c. electrical current into high-frequency magnetic rotations that might be applied in new devices including microwave sources and resonators.
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Affiliation(s)
- S I Kiselev
- Cornell University, Ithaca, New York 14853, USA
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43
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Lehnert KW, Turek BA, Bladh K, Spietz LF, Gunnarsson D, Delsing P, Schoelkopf RJ. Quantum charge fluctuations and the polarizability of the single-electron box. Phys Rev Lett 2003; 91:106801. [PMID: 14525496 DOI: 10.1103/physrevlett.91.106801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2003] [Indexed: 05/24/2023]
Abstract
We measure the average charge on the island of a single-electron box, with an accuracy of two thousandths of an electron. Thermal fluctuations alone cannot account for the dependence of the average charge on temperature, on external potential, or on the quasiparticle density of states in the metal from which the box is formed. In contrast, we find excellent agreement between these measurements and a theory that treats the quantum fluctuations of charge perturbatively.
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Affiliation(s)
- K W Lehnert
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06511, USA.
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44
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Abstract
We present a thermometer based on the electrical noise from a tunnel junction. In this thermometer, temperature is related to the voltage across the junction by a relative noise measurement with only the use of the electron charge, Boltzmann's constant, and assumption that electrons in a metal obey Fermi-Dirac statistics. We demonstrate proof-of-concept operation of this primary thermometer over four orders of magnitude in temperature, with as high as 0.1% accuracy and 0.02% precision in the range near 1 kelvin. The self-calibrating nature of this sensor allows for a much faster and simpler measurement than traditional Johnson noise thermometry, making it potentially attractive for metrology and for general use in cryogenic systems.
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Affiliation(s)
- Lafe Spietz
- Department of Applied Physics, Department of Physics, Yale University, New Haven, CT 06520, USA.
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45
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Lehnert KW, Bladh K, Spietz LF, Gunnarsson D, Schuster DI, Delsing P, Schoelkopf RJ. Measurement of the excited-state lifetime of a microelectronic circuit. Phys Rev Lett 2003; 90:027002. [PMID: 12570573 DOI: 10.1103/physrevlett.90.027002] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2002] [Indexed: 05/24/2023]
Abstract
We demonstrate that a continuously measured microelectronic circuit, the Cooper-pair box measured by a radio-frequency single-electron transistor, approximates a quantum two-level system. We extract the Hamiltonian of the circuit through resonant spectroscopy and measure the excited-state lifetime. The lifetime is more than 10(5) times longer than the inverse transition frequency of the two-level system, even though the measurement is active. This lifetime is also comparable to an estimate of the known upper limit, set by spontaneous emission, for this circuit.
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Affiliation(s)
- K W Lehnert
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06511, USA.
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46
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Aassime A, Johansson G, Wendin G, Schoelkopf RJ, Delsing P. Radio-frequency single-electron transistor as readout device for qubits: charge sensitivity and backaction. Phys Rev Lett 2001; 86:3376-3379. [PMID: 11327974 DOI: 10.1103/physrevlett.86.3376] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2000] [Indexed: 05/23/2023]
Abstract
We study the radio-frequency single-electron transistor (rf-SET) as a readout device for charge qubits. We measure the charge sensitivity of an rf-SET to be 6.3microe/sqrt[Hz] and evaluate the backaction of the rf-SET on a single Cooper-pair box. This allows us to compare the needed measurement time with the mixing time of the qubit imposed by the measurement. We find that the mixing time can be substantially longer than the measurement time, which would allow readout of the state of the qubit in a single shot measurement.
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Affiliation(s)
- A Aassime
- Microtechnology Center at Chalmers MC2, Department of Microelectronics and Nanoscience, Chalmers University of Technology and Göteborg University, S-412 96, Göteborg, Sweden
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47
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Kozhevnikov AA, Schoelkopf RJ, Prober DE. Observation of photon-assisted noise in a diffusive normal metal-superconductor junction. Phys Rev Lett 2000; 84:3398-3401. [PMID: 11019099 DOI: 10.1103/physrevlett.84.3398] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/1999] [Indexed: 05/23/2023]
Abstract
We report measurements of nonequilibrium noise in a diffusive normal metal-superconductor (N-S) junction in the presence of both dc bias and high-frequency ac excitation. We find that the shot noise of a diffusive N-S junction is doubled compared to a normal diffusive conductor. Under ac excitation of frequency nu the shot noise develops features at bias voltages |V| = hnu/(2e), which bear all the hallmarks of a photon-assisted process. Observation of these features provides clear evidence that the effective charge of the current carriers is 2e, due to Andreev reflection.
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Affiliation(s)
- AA Kozhevnikov
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520-8284, USA
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48
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Schoelkopf RJ, Wahlgren P, Kozhevnikov AA, Delsing P, Prober DE. The radio-frequency single-electron transistor (RF-SET): A fast and ultrasensitive electrometer. Science 1998; 280:1238-42. [PMID: 9596572 DOI: 10.1126/science.280.5367.1238] [Citation(s) in RCA: 598] [Impact Index Per Article: 23.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
A new type of electrometer is described that uses a single-electron transistor (SET) and that allows large operating speeds and extremely high charge sensitivity. The SET readout was accomplished by measuring the damping of a 1.7-gigahertz resonant circuit in which the device is embedded, and in some ways is the electrostatic "dual" of the well-known radio-frequency superconducting quantum interference device. The device is more than two orders of magnitude faster than previous single-electron devices, with a constant gain from dc to greater than 100 megahertz. For a still-unoptimized device, a charge sensitivity of 1.2 x 10(-5) e/hertz was obtained at a frequency of 1.1 megahertz, which is about an order of magnitude better than a typical, 1/f-noise-limited SET, and corresponds to an energy sensitivity (in joules per hertz) of about 41 Planck's over 2pi.
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Affiliation(s)
- RJ Schoelkopf
- R. J. Schoelkopf, A. A. Kozhevnikov, D. E. Prober, Departments of Applied Physics and Physics, Yale University, New Haven, CT 06520-8284, USA. P. Wahlgren and P. Delsing, Department of Microelectronics and Nanoscience, Chalmers Uni
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