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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. Phys Rev Lett 2019; 123:233602. [PMID: 31868475 DOI: 10.1103/physrevlett.123.233602] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [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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Wen PY, Kockum AF, Ian H, Chen JC, Nori F, Hoi IC. Reflective Amplification without Population Inversion from a Strongly Driven Superconducting Qubit. Phys Rev Lett 2018; 120:063603. [PMID: 29481213 DOI: 10.1103/physrevlett.120.063603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2017] [Revised: 12/14/2017] [Indexed: 06/08/2023]
Abstract
Amplification of optical or microwave fields is often achieved by strongly driving a medium to induce population inversion such that a weak probe can be amplified through stimulated emission. Here we strongly couple a superconducting qubit, an artificial atom, to the field in a semi-infinite waveguide. When driving the qubit strongly on resonance such that a Mollow triplet appears, we observe a 7% amplitude gain for a weak probe at frequencies in between the triplet. This amplification is not due to population inversion, neither in the bare qubit basis nor in the dressed-state basis, but instead results from a four-photon process that converts energy from the strong drive to the weak probe. We find excellent agreement between the experimental results and numerical simulations without any free fitting parameters. Since our device consists of a single two-level artificial atom, the simplest possible quantum system, it can be viewed as the most fundamental version of a four-wave-mixing parametric amplifier.
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Affiliation(s)
- P Y Wen
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - A F Kockum
- Center for Emergent Matter Science, RIKEN, Saitama 351-0198, Japan
| | - H Ian
- Institute of Applied Physics and Materials Engineering, University of Macau, Macau
- UMacau Zhuhai Research Institute, Zhuhai, Guangdong 519031, China
| | - J C Chen
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - F Nori
- Center for Emergent Matter Science, RIKEN, Saitama 351-0198, Japan
- Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - I-C Hoi
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
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Barends R, Lamata L, Kelly J, García-Álvarez L, Fowler AG, Megrant A, Jeffrey E, White TC, Sank D, Mutus JY, Campbell B, Chen Y, Chen Z, Chiaro B, Dunsworth A, Hoi IC, Neill C, O'Malley PJJ, Quintana C, Roushan P, Vainsencher A, Wenner J, Solano E, Martinis JM. Digital quantum simulation of fermionic models with a superconducting circuit. Nat Commun 2015; 6:7654. [PMID: 26153660 PMCID: PMC4510643 DOI: 10.1038/ncomms8654] [Citation(s) in RCA: 214] [Impact Index Per Article: 23.8] [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: 03/16/2015] [Accepted: 05/24/2015] [Indexed: 12/20/2022] Open
Abstract
One of the key applications of quantum information is simulating nature. Fermions are ubiquitous in nature, appearing in condensed matter systems, chemistry and high energy physics. However, universally simulating their interactions is arguably one of the largest challenges, because of the difficulties arising from anticommutativity. Here we use digital methods to construct the required arbitrary interactions, and perform quantum simulation of up to four fermionic modes with a superconducting quantum circuit. We employ in excess of 300 quantum logic gates, and reach fidelities that are consistent with a simple model of uncorrelated errors. The presented approach is in principle scalable to a larger number of modes, and arbitrary spatial dimensions.
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Affiliation(s)
- R Barends
- Google Inc., Santa Barbara, California 93117, USA
| | - L Lamata
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, Bilbao E-48080, Spain
| | - J Kelly
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - L García-Álvarez
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, Bilbao E-48080, Spain
| | - A G Fowler
- Google Inc., Santa Barbara, California 93117, USA
| | - A Megrant
- 1] Department of Physics, University of California, Santa Barbara, California 93106, USA. [2] Department of Materials, University of California, Santa Barbara, California 93106, USA
| | - E Jeffrey
- Google Inc., Santa Barbara, California 93117, USA
| | - T C White
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - D Sank
- Google Inc., Santa Barbara, California 93117, USA
| | - J Y Mutus
- Google Inc., Santa Barbara, California 93117, USA
| | - B Campbell
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Yu Chen
- Google Inc., Santa Barbara, California 93117, USA
| | - Z Chen
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - B Chiaro
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - A Dunsworth
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - I-C Hoi
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - C Neill
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - P J J O'Malley
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - C Quintana
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - P Roushan
- Google Inc., Santa Barbara, California 93117, USA
| | - A Vainsencher
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - J Wenner
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - E Solano
- 1] Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, Bilbao E-48080, Spain. [2] IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, Bilbao 48013, Spain
| | - John M Martinis
- 1] Google Inc., Santa Barbara, California 93117, USA. [2] Department of Physics, University of California, Santa Barbara, California 93106, USA
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Kelly J, Barends R, Fowler AG, Megrant A, Jeffrey E, White TC, Sank D, Mutus JY, Campbell B, Chen Y, Chen Z, Chiaro B, Dunsworth A, Hoi IC, Neill C, O'Malley PJJ, Quintana C, Roushan P, Vainsencher A, Wenner J, Cleland AN, Martinis JM. State preservation by repetitive error detection in a superconducting quantum circuit. Nature 2015; 519:66-9. [PMID: 25739628 DOI: 10.1038/nature14270] [Citation(s) in RCA: 130] [Impact Index Per Article: 14.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2014] [Accepted: 01/27/2015] [Indexed: 12/19/2022]
Abstract
Quantum computing becomes viable when a quantum state can be protected from environment-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) is capable of identifying and correcting them. Adding more qubits improves the preservation of states by guaranteeing that increasingly larger clusters of errors will not cause logical failure-a key requirement for large-scale systems. Using QEC to extend the qubit lifetime remains one of the outstanding experimental challenges in quantum computing. Here we report the protection of classical states from environmental bit-flip errors and demonstrate the suppression of these errors with increasing system size. We use a linear array of nine qubits, which is a natural step towards the two-dimensional surface code QEC scheme, and track errors as they occur by repeatedly performing projective quantum non-demolition parity measurements. Relative to a single physical qubit, we reduce the failure rate in retrieving an input state by a factor of 2.7 when using five of our nine qubits and by a factor of 8.5 when using all nine qubits after eight cycles. Additionally, we tomographically verify preservation of the non-classical Greenberger-Horne-Zeilinger state. The successful suppression of environment-induced errors will motivate further research into the many challenges associated with building a large-scale superconducting quantum computer.
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Affiliation(s)
- J Kelly
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - R Barends
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - A G Fowler
- 1] Department of Physics, University of California, Santa Barbara, California 93106, USA [2] Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Victoria 3010, Australia
| | - A Megrant
- 1] Department of Physics, University of California, Santa Barbara, California 93106, USA [2] Department of Materials, University of California, Santa Barbara, California 93106, USA
| | - E Jeffrey
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - T C White
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - D Sank
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - J Y Mutus
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - B Campbell
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Yu Chen
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Z Chen
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - B Chiaro
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - A Dunsworth
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - I-C Hoi
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - C Neill
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - P J J O'Malley
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - C Quintana
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - P Roushan
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - A Vainsencher
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - J Wenner
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - A N Cleland
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - John M Martinis
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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Kelly J, Barends R, Campbell B, Chen Y, Chen Z, Chiaro B, Dunsworth A, Fowler AG, Hoi IC, Jeffrey E, Megrant A, Mutus J, Neill C, O'Malley PJJ, Quintana C, Roushan P, Sank D, Vainsencher A, Wenner J, White TC, Cleland AN, Martinis JM. Optimal quantum control using randomized benchmarking. Phys Rev Lett 2014; 112:240504. [PMID: 24996075 DOI: 10.1103/physrevlett.112.240504] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2014] [Indexed: 06/03/2023]
Abstract
We present a method for optimizing quantum control in experimental systems, using a subset of randomized benchmarking measurements to rapidly infer error. This is demonstrated to improve single- and two-qubit gates, minimize gate bleedthrough, where a gate mechanism can cause errors on subsequent gates, and identify control crosstalk in superconducting qubits. This method is able to correct parameters so that control errors no longer dominate and is suitable for automated and closed-loop optimization of experimental systems.
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Affiliation(s)
- J Kelly
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - R Barends
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - B Campbell
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Y Chen
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Z Chen
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - B Chiaro
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - A Dunsworth
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - A G Fowler
- Department of Physics, University of California, Santa Barbara, California 93106, USA and Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Victoria 3010, Australia
| | - I-C Hoi
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - E Jeffrey
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - A Megrant
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - J Mutus
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - C Neill
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - P J J O'Malley
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - C Quintana
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - P Roushan
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - D Sank
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - A Vainsencher
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - J Wenner
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - T C White
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - A N Cleland
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - John M Martinis
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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