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Evaluating Machine Learning Approaches for Discovering Optimal Sets of Projection Operators for Quantum State Tomography of Qubit Systems. CYBERNETICS AND INFORMATION TECHNOLOGIES 2020. [DOI: 10.2478/cait-2020-0061] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Abstract
Finding optimal measurement schemes in quantum state tomography is a fundamental problem in quantum computation. It is known that for non-degenerate operators the optimal measurement scheme is based on mutually unbiassed bases. This paper is a follow up from our previous work, where we use standard numerical approaches to look for optimal measurement schemes, where the measurement operators are projections on individual pure quantum states. In this paper we demonstrate the usefulness of several machine learning techniques – reinforcement learning and parallel machine learning approaches, to discover measurement schemes, which are significantly better than the ones discovered by standard numerical methods in our previous work. The high-performing quorums of projection operators we have discovered have complex structure and symmetries, which may imply that the optimal solution will possess such symmetries.
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2
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Müller C, Cole JH, Lisenfeld J. Towards understanding two-level-systems in amorphous solids: insights from quantum circuits. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:124501. [PMID: 31404914 DOI: 10.1088/1361-6633/ab3a7e] [Citation(s) in RCA: 35] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Amorphous solids show surprisingly universal behaviour at low temperatures. The prevailing wisdom is that this can be explained by the existence of two-state defects within the material. The so-called standard tunneling model has become the established framework to explain these results, yet it still leaves the central question essentially unanswered-what are these two-level defects (TLS)? This question has recently taken on a new urgency with the rise of superconducting circuits in quantum computing, circuit quantum electrodynamics, magnetometry, electrometry and metrology. Superconducting circuits made from aluminium or niobium are fundamentally limited by losses due to TLS within the amorphous oxide layers encasing them. On the other hand, these circuits also provide a novel and effective method for studying the very defects which limit their operation. We can now go beyond ensemble measurements and probe individual defects-observing the quantum nature of their dynamics and studying their formation, their behaviour as a function of applied field, strain, temperature and other properties. This article reviews the plethora of recent experimental results in this area and discusses the various theoretical models which have been used to describe the observations. In doing so, it summarises the current approaches to solving this fundamentally important problem in solid-state physics.
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Affiliation(s)
- Clemens Müller
- IBM Research Zurich, 8803 Rüschlikon, Switzerland. Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland. ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland 4072, Australia
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3
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Tan X, Zhang DW, Yang Z, Chu J, Zhu YQ, Li D, Yang X, Song S, Han Z, Li Z, Dong Y, Yu HF, Yan H, Zhu SL, Yu Y. Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit. PHYSICAL REVIEW LETTERS 2019; 122:210401. [PMID: 31283314 DOI: 10.1103/physrevlett.122.210401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Indexed: 06/09/2023]
Abstract
A Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable superconducting circuits, we experimentally demonstrate two methods to directly measure the quantum metric tensor for characterizing the geometry and topology of underlying quantum states in parameter space. The first method is to probe the transition probability after a sudden quench, and the second one is to detect the excitation rate under weak periodic driving. Furthermore, based on quantum metric and Berry-curvature measurements, we explore a topological phase transition in a simulated time-reversal-symmetric system. The work opens up a unique approach to explore the topology of quantum states with the QGT.
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Affiliation(s)
- Xinsheng Tan
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Dan-Wei Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Zhen Yang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Ji Chu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Yan-Qing Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Danyu Li
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Xiaopei Yang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Shuqing Song
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Zhikun Han
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Zhiyuan Li
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Yuqian Dong
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hai-Feng Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hui Yan
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Yang Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
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4
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Tan X, Zhao YX, Liu Q, Xue G, Yu HF, Wang ZD, Yu Y. Simulation and Manipulation of Tunable Weyl-Semimetal Bands Using Superconducting Quantum Circuits. PHYSICAL REVIEW LETTERS 2019; 122:010501. [PMID: 31012718 DOI: 10.1103/physrevlett.122.010501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2018] [Indexed: 05/06/2023]
Abstract
We simulated highly tunable Weyl-semimetal bands using superconducting quantum circuits. Driving the superconducting quantum circuits with microwave fields, we mapped the momentum space of a lattice to the parameter space, realizing the Hamiltonian of a Weyl semimetal. By measuring the energy spectrum, we directly imaged the Weyl points, whose topological winding numbers were further determined from the Berry curvature measurement. In addition, we manipulated the band structure with an additional pump microwave field, producing a momentum-dependent Weyl-point energy together with an artificial magnetic field, which are indispensable for generating chiral magnetic topological currents in some special Weyl semimetals and may have significant impact on topological physics.
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Affiliation(s)
- Xinsheng Tan
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Y X Zhao
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Qiang Liu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Guangming Xue
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hai-Feng Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Z D Wang
- Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Yang Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
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5
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Opremcak A, Pechenezhskiy IV, Howington C, Christensen BG, Beck MA, Leonard E, Suttle J, Wilen C, Nesterov KN, Ribeill GJ, Thorbeck T, Schlenker F, Vavilov MG, Plourde BLT, McDermott R. Measurement of a superconducting qubit with a microwave photon counter. Science 2018; 361:1239-1242. [DOI: 10.1126/science.aat4625] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2018] [Accepted: 07/17/2018] [Indexed: 11/02/2022]
Affiliation(s)
- A. Opremcak
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
| | - I. V. Pechenezhskiy
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
| | - C. Howington
- Department of Physics, Syracuse University, Syracuse, NY 13244, USA
| | - B. G. Christensen
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
| | - M. A. Beck
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
| | - E. Leonard
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
| | - J. Suttle
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
| | - C. Wilen
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
| | - K. N. Nesterov
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
| | - G. J. Ribeill
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
| | - T. Thorbeck
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
| | - F. Schlenker
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
| | - M. G. Vavilov
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
| | - B. L. T. Plourde
- Department of Physics, Syracuse University, Syracuse, NY 13244, USA
| | - R. McDermott
- Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
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Tan X, Zhang DW, Liu Q, Xue G, Yu HF, Zhu YQ, Yan H, Zhu SL, Yu Y. Topological Maxwell Metal Bands in a Superconducting Qutrit. PHYSICAL REVIEW LETTERS 2018; 120:130503. [PMID: 29694203 DOI: 10.1103/physrevlett.120.130503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2017] [Revised: 01/01/2018] [Indexed: 06/08/2023]
Abstract
We experimentally explore the topological Maxwell metal bands by mapping the momentum space of condensed-matter models to the tunable parameter space of superconducting quantum circuits. An exotic band structure that is effectively described by the spin-1 Maxwell equations is imaged. Threefold degenerate points dubbed Maxwell points are observed in the Maxwell metal bands. Moreover, we engineer and observe the topological phase transition from the topological Maxwell metal to a trivial insulator, and report the first experiment to measure the Chern numbers that are higher than one.
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Affiliation(s)
- Xinsheng Tan
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Dan-Wei Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China
| | - Qiang Liu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Guangming Xue
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hai-Feng Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Yan-Qing Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hui Yan
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yang Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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Wendin G. Quantum information processing with superconducting circuits: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:106001. [PMID: 28682303 DOI: 10.1088/1361-6633/aa7e1a] [Citation(s) in RCA: 107] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.
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Affiliation(s)
- G Wendin
- Department of Microtechnology and Nanoscience-MC2, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
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Lisenfeld J, Bilmes A, Matityahu S, Zanker S, Marthaler M, Schechter M, Schön G, Shnirman A, Weiss G, Ustinov AV. Decoherence spectroscopy with individual two-level tunneling defects. Sci Rep 2016; 6:23786. [PMID: 27030167 PMCID: PMC4815015 DOI: 10.1038/srep23786] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2016] [Accepted: 03/14/2016] [Indexed: 12/01/2022] Open
Abstract
Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.
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Affiliation(s)
- Jürgen Lisenfeld
- Physikalisches Institut, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Alexander Bilmes
- Physikalisches Institut, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Shlomi Matityahu
- Department of Physics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
| | - Sebastian Zanker
- Institut für Theoretische Festkörperphysik, KIT, 76131 Karlsruhe, Germany
| | - Michael Marthaler
- Institut für Theoretische Festkörperphysik, KIT, 76131 Karlsruhe, Germany
| | - Moshe Schechter
- Department of Physics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
| | - Gerd Schön
- Institut für Theoretische Festkörperphysik, KIT, 76131 Karlsruhe, Germany
| | - Alexander Shnirman
- Institut für Theorie der Kondensierten Materie, KIT, 76131 Karlsruhe, Germany
- L. D. Landau Institute for Theoretical Physics RAS, Kosygina street 2, 119334 Moscow, Russia
| | - Georg Weiss
- Physikalisches Institut, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Alexey V. Ustinov
- Physikalisches Institut, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
- National University of Science and Technology MISIS, Leninsky prosp. 4, Moscow, 119049, Russia
- Russian Quantum Center, 100 Novaya St., Skolkovo, 143025 Moscow region, Russia
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9
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Parity-dependent State Engineering and Tomography in the ultrastrong coupling regime. Sci Rep 2015; 5:11818. [PMID: 26152809 PMCID: PMC5155612 DOI: 10.1038/srep11818] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2015] [Accepted: 06/08/2015] [Indexed: 11/28/2022] Open
Abstract
Reaching the strong coupling regime of light-matter interaction has led to an impressive development in fundamental quantum physics and applications to quantum information processing. Latests advances in different quantum technologies, like superconducting circuits or semiconductor quantum wells, show that the ultrastrong coupling regime (USC) can also be achieved, where novel physical phenomena and potential computational benefits have been predicted. Nevertheless, the lack of effective decoupling mechanism in this regime has so far hindered control and measurement processes. Here, we propose a method based on parity symmetry conservation that allows for the generation and reconstruction of arbitrary states in the ultrastrong coupling regime of light-matter interactions. Our protocol requires minimal external resources by making use of the coupling between the USC system and an ancillary two-level quantum system.
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10
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Lisenfeld J, Grabovskij GJ, Müller C, Cole JH, Weiss G, Ustinov AV. Observation of directly interacting coherent two-level systems in an amorphous material. Nat Commun 2015; 6:6182. [PMID: 25652611 PMCID: PMC4327544 DOI: 10.1038/ncomms7182] [Citation(s) in RCA: 88] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2014] [Accepted: 12/27/2014] [Indexed: 12/01/2022] Open
Abstract
Parasitic two-level tunnelling systems originating from structural material defects affect the functionality of various microfabricated devices by acting as a source of noise. In particular, superconducting quantum bits may be sensitive to even single defects when these reside in the tunnel barrier of the qubit's Josephson junctions, and this can be exploited to observe and manipulate the quantum states of individual tunnelling systems. Here, we detect and fully characterize a system of two strongly interacting defects using a novel technique for high-resolution spectroscopy. Mutual defect coupling has been conjectured to explain various anomalies of glasses, and was recently suggested as the origin of low-frequency noise in superconducting devices. Our study provides conclusive evidence of defect interactions with full access to the individual constituents, demonstrating the potential of superconducting qubits for studying material defects. All our observations are consistent with the assumption that defects are generated by atomic tunnelling.
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Affiliation(s)
- Jürgen Lisenfeld
- Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
| | | | - Clemens Müller
- Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1
- ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia
| | - Jared H. Cole
- Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne 3001, Australia
| | - Georg Weiss
- Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
| | - Alexey V. Ustinov
- Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
- National University of Science and Technology MISIS, Leninsky prosp. 4, Moscow, 119049, Russia
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11
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Gustavsson S, Zwier O, Bylander J, Yan F, Yoshihara F, Nakamura Y, Orlando TP, Oliver WD. Improving quantum gate fidelities by using a qubit to measure microwave pulse distortions. PHYSICAL REVIEW LETTERS 2013; 110:040502. [PMID: 25166145 DOI: 10.1103/physrevlett.110.040502] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2012] [Indexed: 06/03/2023]
Abstract
We present a new method for determining pulse imperfections and improving the single-gate fidelity in a superconducting qubit. By applying consecutive positive and negative π pulses, we amplify the qubit evolution due to microwave pulse distortions, which causes the qubit state to rotate around an axis perpendicular to the intended rotation axis. Measuring these rotations as a function of pulse period allows us to reconstruct the shape of the microwave pulse arriving at the sample. Using the extracted response to predistort the input signal, we are able to reduce the average error per gate by 37%, which enables us to reach an average single-qubit gate fidelity higher than 0.998.
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Affiliation(s)
- Simon Gustavsson
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Olger Zwier
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA and Zernike Institute for Advanced Materials, University of Groningen, 9747AG Groningen, The Netherlands
| | - Jonas Bylander
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Fei Yan
- Department of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, USA
| | - Fumiki Yoshihara
- The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-0198, Japan
| | - Yasunobu Nakamura
- The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-0198, Japan and Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8904, Japan
| | - Terry P Orlando
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - William D Oliver
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA and MIT Lincoln Laboratory, 244 Wood Street, Lexington, Massachusetts 02420, USA
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12
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Chang YC, Liu GQ, Liu DQ, Fan H, Pan XY. Room-temperature quantum cloning machine with full coherent phase control in nanodiamond. Sci Rep 2013; 3:1498. [PMID: 23511233 PMCID: PMC3603226 DOI: 10.1038/srep01498] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2012] [Accepted: 03/05/2013] [Indexed: 11/16/2022] Open
Abstract
In contrast to the classical world, an unknown quantum state cannot be cloned ideally, as stated by the no-cloning theorem. However, it is expected that approximate or probabilistic quantum cloning will be necessary for different applications, and thus various quantum cloning machines have been designed. Phase quantum cloning is of particular interest because it can be used to attack the Bennett-Brassard 1984 (BB84) states used in quantum key distribution for secure communications. Here, we report the first room-temperature implementation of quantum phase cloning with a controllable phase in a solid-state system: the nitrogen-vacancy centre of a nanodiamond. The phase cloner works well for all qubits located on the equator of the Bloch sphere. The phase is controlled and can be measured with high accuracy, and the experimental results are consistent with theoretical expectations. This experiment provides a basis for phase-controllable quantum information devices.
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Affiliation(s)
- Yan-Chun Chang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Gang-Qin Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Dong-Qi Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Heng Fan
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xin-Yu Pan
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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13
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Grabovskij GJ, Peichl T, Lisenfeld J, Weiss G, Ustinov AV. Strain Tuning of Individual Atomic Tunneling Systems Detected by a Superconducting Qubit. Science 2012; 338:232-4. [DOI: 10.1126/science.1226487] [Citation(s) in RCA: 86] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Grigorij J. Grabovskij
- Physikalisches Institut and Deutsche Forschungsgemeinschaft (DFG) Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
| | - Torben Peichl
- Physikalisches Institut and Deutsche Forschungsgemeinschaft (DFG) Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
| | - Jürgen Lisenfeld
- Physikalisches Institut and Deutsche Forschungsgemeinschaft (DFG) Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
| | - Georg Weiss
- Physikalisches Institut and Deutsche Forschungsgemeinschaft (DFG) Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
| | - Alexey V. Ustinov
- Physikalisches Institut and Deutsche Forschungsgemeinschaft (DFG) Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
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14
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Vijay R, Macklin C, Slichter DH, Weber SJ, Murch KW, Naik R, Korotkov AN, Siddiqi I. Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback. Nature 2012; 490:77-80. [DOI: 10.1038/nature11505] [Citation(s) in RCA: 332] [Impact Index Per Article: 27.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2012] [Accepted: 08/17/2012] [Indexed: 11/10/2022]
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15
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Lecocq F, Pop IM, Matei I, Dumur E, Feofanov AK, Naud C, Guichard W, Buisson O. Coherent frequency conversion in a superconducting artificial atom with two internal degrees of freedom. PHYSICAL REVIEW LETTERS 2012; 108:107001. [PMID: 22463441 DOI: 10.1103/physrevlett.108.107001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2011] [Indexed: 05/31/2023]
Abstract
By adding a large inductance in a dc-SQUID phase qubit loop, one decouples the junctions' dynamics and creates a superconducting artificial atom with two internal degrees of freedom. In addition to the usual symmetric plasma mode (s mode) which gives rise to the phase qubit, an antisymmetric mode (a mode) appears. These two modes can be described by two anharmonic oscillators with eigenstates |ns> and |na> for the s and a mode, respectively. We show that a strong nonlinear coupling between the modes leads to a large energy splitting between states |0s,1a> and |2s,0a>. Finally, coherent frequency conversion is observed via free oscillations between the states |0s,1a> and |2s,0a>.
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Affiliation(s)
- F Lecocq
- Institut Néel, CNRS-Université Joseph Fourier, BP 166, 38042 Grenoble-cedex 9, France
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16
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Lecocq F, Pop IM, Peng Z, Matei I, Crozes T, Fournier T, Naud C, Guichard W, Buisson O. Junction fabrication by shadow evaporation without a suspended bridge. NANOTECHNOLOGY 2011; 22:315302. [PMID: 21737875 DOI: 10.1088/0957-4484/22/31/315302] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We present a novel shadow evaporation technique for the realization of junctions and capacitors. The design by e-beam lithography of strongly asymmetric undercuts on a bilayer resist enables in situ fabrication of junctions and capacitors without the use of the well-known suspended bridge (Dolan 1977 Appl. Phys. Lett. 31 337-9). The absence of bridges increases the mechanical robustness of the resist mask as well as the accessible range of the junction size, from 10(-2) µm(2) to more than 10(4) µm(2). We have fabricated Al/AlO(x)/Al Josephson junctions, phase qubit and capacitors using a 100 kV e-beam writer. Although this high voltage enables a precise control of the undercut, implementation using a conventional 20 kV e-beam is also discussed. The phase qubit coherence times, extracted from spectroscopy resonance width, Rabi and Ramsey oscillation decays and energy relaxation measurements, are longer than the ones obtained in our previous samples realized by standard techniques. These results demonstrate the high quality of the junction obtained by this bridge-free technique.
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Affiliation(s)
- Florent Lecocq
- Institut Néel, CNRS and Université Joseph Fourier, Grenoble, France
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17
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Abdumalikov AA, Astafiev OV, Pashkin YA, Nakamura Y, Tsai JS. Dynamics of coherent and incoherent emission from an artificial atom in a 1D space. PHYSICAL REVIEW LETTERS 2011; 107:043604. [PMID: 21867005 DOI: 10.1103/physrevlett.107.043604] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2011] [Indexed: 05/31/2023]
Abstract
We study dynamics of a two-level superconducting quantum system, analogous to a natural atom in an open space, by measuring the evolution of its coherent and incoherent emission. The emitted waves containing full information about the states of the artificial atom are efficiently collected due to strong atom-transmission-line coupling. This allows us to do simultaneous measurements of all the quantum state projections and perform a full characterization of the system. We derive coherence times and extract the two-time correlation function from the dynamics of the coherent emission.
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Affiliation(s)
- A A Abdumalikov
- RIKEN Advanced Science Institute, Wako, Saitama 351-0198, Japan.
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18
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19
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Lisenfeld J, Müller C, Cole JH, Bushev P, Lukashenko A, Shnirman A, Ustinov AV. Measuring the temperature dependence of individual two-level systems by direct coherent control. PHYSICAL REVIEW LETTERS 2010; 105:230504. [PMID: 21231441 DOI: 10.1103/physrevlett.105.230504] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2010] [Indexed: 05/30/2023]
Abstract
We demonstrate a new method to directly manipulate the state of individual two-level systems (TLSs) in phase qubits. It allows one to characterize the coherence properties of TLSs using standard microwave pulse sequences, while the qubit is used only for state readout. We apply this method to measure the temperature dependence of TLS coherence for the first time. The energy relaxation time T1 is found to decrease quadratically with temperature for the two TLSs studied in this work, while their dephasing time measured in Ramsey and spin-echo experiments is found to be T1 limited at all temperatures.
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Affiliation(s)
- J Lisenfeld
- Physikalisches Institut, Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany
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20
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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. PHYSICAL REVIEW LETTERS 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] [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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21
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Tian L. Circuit QED and sudden phase switching in a superconducting qubit array. PHYSICAL REVIEW LETTERS 2010; 105:167001. [PMID: 21230996 DOI: 10.1103/physrevlett.105.167001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2010] [Indexed: 05/30/2023]
Abstract
Superconducting qubits connected in an array can form quantum many-body systems such as the quantum Ising model. By coupling the qubits to a superconducting resonator, the combined system forms a circuit QED system. Here, we study the nonlinear behavior in the many-body state of the qubit array using a semiclassical approach. We show that sudden switchings as well as a bistable regime between the ferromagnetic phase and the paramagnetic phase can be observed in the qubit array. A superconducting circuit to implement this system is presented with realistic parameters.
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Affiliation(s)
- L Tian
- University of California, Merced, 5200 North Lake Road, Merced, California 95343, USA.
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22
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Savel’ev S, Zagoskin A, Omelyanchouk A, Nori F. Noise-spectroscopy of multiqubit systems: Determining all their parameters by applying an external classical noise. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2010.07.003] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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23
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Quantum ground state and single-phonon control of a mechanical resonator. Nature 2010; 464:697-703. [PMID: 20237473 DOI: 10.1038/nature08967] [Citation(s) in RCA: 436] [Impact Index Per Article: 31.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2009] [Accepted: 03/01/2010] [Indexed: 11/08/2022]
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24
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Steffen M, Brito F, DiVincenzo D, Farinelli M, Keefe G, Ketchen M, Kumar S, Milliken F, Rothwell MB, Rozen J, Koch RH. Quantum information storage using tunable flux qubits. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:053201. [PMID: 21386337 DOI: 10.1088/0953-8984/22/5/053201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We present details and results for a superconducting quantum bit (qubit) design in which a tunable flux qubit is coupled strongly to a transmission line. Quantum information storage in the transmission line is demonstrated with a dephasing time of T(2)∼ 2.5 µs. However, energy lifetimes of the qubit are found to be short (∼ 10 ns) and not consistent with predictions. Several design and material changes do not affect qubit coherence times. In order to determine the cause of these short coherence times, we fabricated standard flux qubits based on a design which was previously successfully used by others. Initial results show significantly improved coherence times, possibly implicating losses associated with the large size of our qubit.
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25
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Neeley M, Ansmann M, Bialczak RC, Hofheinz M, Lucero E, O'Connell AD, Sank D, Wang H, Wenner J, Cleland AN, Geller MR, Martinis JM. Emulation of a Quantum Spin with a Superconducting Phase Qudit. Science 2009; 325:722-5. [DOI: 10.1126/science.1173440] [Citation(s) in RCA: 198] [Impact Index Per Article: 13.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Matthew Neeley
- Department of Physics, University of California at Santa Barbara (UCSB), Santa Barbara, CA 93106, USA
| | - Markus Ansmann
- Department of Physics, University of California at Santa Barbara (UCSB), Santa Barbara, CA 93106, USA
| | - Radoslaw C. Bialczak
- Department of Physics, University of California at Santa Barbara (UCSB), Santa Barbara, CA 93106, USA
| | - Max Hofheinz
- Department of Physics, University of California at Santa Barbara (UCSB), Santa Barbara, CA 93106, USA
| | - Erik Lucero
- Department of Physics, University of California at Santa Barbara (UCSB), Santa Barbara, CA 93106, USA
| | - Aaron D. O'Connell
- Department of Physics, University of California at Santa Barbara (UCSB), Santa Barbara, CA 93106, USA
| | - Daniel Sank
- Department of Physics, University of California at Santa Barbara (UCSB), Santa Barbara, CA 93106, USA
| | - Haohua Wang
- Department of Physics, University of California at Santa Barbara (UCSB), Santa Barbara, CA 93106, USA
| | - James Wenner
- Department of Physics, University of California at Santa Barbara (UCSB), Santa Barbara, CA 93106, USA
| | - Andrew N. Cleland
- Department of Physics, University of California at Santa Barbara (UCSB), Santa Barbara, CA 93106, USA
| | - Michael R. Geller
- Department of Physics and Astronomy, University of Georgia, Athens, GA 30602, USA
| | - John M. Martinis
- Department of Physics, University of California at Santa Barbara (UCSB), Santa Barbara, CA 93106, USA
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26
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Filipp S, Maurer P, Leek PJ, Baur M, Bianchetti R, Fink JM, Göppl M, Steffen L, Gambetta JM, Blais A, Wallraff A. Two-qubit state tomography using a joint dispersive readout. PHYSICAL REVIEW LETTERS 2009; 102:200402. [PMID: 19519010 DOI: 10.1103/physrevlett.102.200402] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2008] [Indexed: 05/27/2023]
Abstract
Quantum state tomography is an important tool in quantum information science for complete characterization of multiqubit states and their correlations. Here we report a method to perform a joint simultaneous readout of two superconducting qubits dispersively coupled to the same mode of a microwave transmission line resonator. The nonlinear dependence of the resonator transmission on the qubit state dependent cavity frequency allows us to extract the full two-qubit correlations without the need for single-shot readout of individual qubits. We employ standard tomographic techniques to reconstruct the density matrix of two-qubit quantum states.
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Affiliation(s)
- S Filipp
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland.
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27
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Synthesizing arbitrary quantum states in a superconducting resonator. Nature 2009; 459:546-9. [DOI: 10.1038/nature08005] [Citation(s) in RCA: 651] [Impact Index Per Article: 43.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2009] [Accepted: 03/19/2009] [Indexed: 11/09/2022]
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28
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Rebentrost P, Serban I, Schulte-Herbrüggen T, Wilhelm FK. Optimal control of a qubit coupled to a non-Markovian environment. PHYSICAL REVIEW LETTERS 2009; 102:090401. [PMID: 19392499 DOI: 10.1103/physrevlett.102.090401] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2007] [Indexed: 05/27/2023]
Abstract
A central challenge for implementing quantum computing in the solid state is decoupling the qubits from the intrinsic noise of the material. We investigate the implementation of quantum gates for a paradigmatic, non-Markovian model: a single-qubit coupled to a two-level system that is exposed to a heat bath. We systematically search for optimal pulses using a generalization of the novel open systems gradient ascent pulse engineering algorithm. Next to the known optimal bias point of this model, there are optimal pulses which lead to high-fidelity quantum operations for a wide range of decoherence parameters.
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Affiliation(s)
- P Rebentrost
- Department Physik, ASC and CeNS, Ludwig-Maximilians-Universität, Theresienstrasse 37, 80333 München, Germany.
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29
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Peng ZH, Chu HF, Wang ZD, Zheng DN. Implementation of adiabatic geometric gates with superconducting phase qubits. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:045701. [PMID: 21715819 DOI: 10.1088/0953-8984/21/4/045701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We present an adiabatic geometric quantum computation strategy based on the non-degenerate energy eigenstates in (but not limited to) superconducting phase qubit systems. The fidelity of the designed quantum gate was evaluated in the presence of simulated thermal fluctuations in a superconducting phase qubits circuit and was found to be quite robust against random errors. In addition, it was elucidated that the Berry phase in the designed adiabatic evolution may be detected directly via the quantum state tomography developed for superconducting qubits. We also analyze the effects of control parameter fluctuations on the experimental detection of the Berry phase.
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Affiliation(s)
- Z H Peng
- National Laboratory for Superconductivity, Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100080, People's Republic of China
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30
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Katz N, Neeley M, Ansmann M, Bialczak RC, Hofheinz M, Lucero E, O'Connell A, Wang H, Cleland AN, Martinis JM, Korotkov AN. Reversal of the weak measurement of a quantum state in a superconducting phase qubit. PHYSICAL REVIEW LETTERS 2008; 101:200401. [PMID: 19113317 DOI: 10.1103/physrevlett.101.200401] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2008] [Indexed: 05/27/2023]
Abstract
We demonstrate in a superconducting qubit the conditional recovery (uncollapsing) of a quantum state after a partial-collapse measurement. A weak measurement extracts information and results in a nonunitary transformation of the qubit state. However, by adding a rotation and a second partial measurement with the same strength, we erase the extracted information, canceling the effect of both measurements. The fidelity of the state recovery is measured using quantum process tomography and found to be above 70% for partial-collapse strength less than 0.6.
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Affiliation(s)
- Nadav Katz
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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31
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Rudner MS, Shytov AV, Levitov LS, Berns DM, Oliver WD, Valenzuela SO, Orlando TP. Quantum phase tomography of a strongly driven qubit. PHYSICAL REVIEW LETTERS 2008; 101:190502. [PMID: 19113251 DOI: 10.1103/physrevlett.101.190502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2008] [Indexed: 05/27/2023]
Abstract
The interference between repeated Landau-Zener transitions in a qubit swept through an avoided level crossing results in Stückelberg oscillations in qubit magnetization, a hallmark of the coherent strongly driven regime in two-level systems. The two-dimensional Fourier transforms of the resulting oscillatory patterns are found to exhibit a family of one-dimensional curves in Fourier space, in agreement with recent observations in a superconducting qubit. We interpret these images in terms of time evolution of the quantum phase of the qubit state and show that they can be used to probe dephasing mechanisms.
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Affiliation(s)
- M S Rudner
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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32
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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. PHYSICAL REVIEW LETTERS 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] [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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33
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Abstract
Superconducting circuits are macroscopic in size but have generic quantum properties such as quantized energy levels, superposition of states, and entanglement, all of which are more commonly associated with atoms. Superconducting quantum bits (qubits) form the key component of these circuits. Their quantum state is manipulated by using electromagnetic pulses to control the magnetic flux, the electric charge or the phase difference across a Josephson junction (a device with nonlinear inductance and no energy dissipation). As such, superconducting qubits are not only of considerable fundamental interest but also might ultimately form the primitive building blocks of quantum computers.
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Affiliation(s)
- John Clarke
- Department of Physics,366 LeConte Hall, University of California, Berkeley, California 94720, USA.
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34
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Hofheinz M, Weig EM, Ansmann M, Bialczak RC, Lucero E, Neeley M, O’Connell AD, Wang H, Martinis JM, Cleland AN. Generation of Fock states in a superconducting quantum circuit. Nature 2008; 454:310-4. [DOI: 10.1038/nature07136] [Citation(s) in RCA: 408] [Impact Index Per Article: 25.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2008] [Accepted: 05/23/2008] [Indexed: 11/09/2022]
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35
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Lucero E, Hofheinz M, Ansmann M, Bialczak RC, Katz N, Neeley M, O'Connell AD, Wang H, Cleland AN, Martinis JM. High-fidelity gates in a single josephson qubit. PHYSICAL REVIEW LETTERS 2008; 100:247001. [PMID: 18643615 DOI: 10.1103/physrevlett.100.247001] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2008] [Indexed: 05/26/2023]
Abstract
We demonstrate new experimental procedures for measuring small errors in a superconducting quantum bit (qubit). By carefully separating out gate and measurement errors, we construct a complete error budget and demonstrate single qubit gate fidelities of 0.98, limited by energy relaxation. We also introduce a new metrology tool-- Ramsey interference error filter-that can measure the occupation probability of the state |2> which is outside the computational basis, down to 10{-4}, thereby confirming that our quantum system stays within the qubit manifold during single qubit logic operations.
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Affiliation(s)
- Erik Lucero
- Department of Physics, University of California at Santa Barbara, Broida Hall, Santa Barbara, California 93106, USA
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36
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Bialczak RC, McDermott R, Ansmann M, Hofheinz M, Katz N, Lucero E, Neeley M, O'Connell AD, Wang H, Cleland AN, Martinis JM. 1/f Flux noise in Josephson phase qubits. PHYSICAL REVIEW LETTERS 2007; 99:187006. [PMID: 17995432 DOI: 10.1103/physrevlett.99.187006] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2007] [Indexed: 05/25/2023]
Abstract
We present a new method to measure 1/f noise in Josephson quantum bits (qubits) that yields low-frequency spectra below 1 Hz. A comparison of the noise taken at positive and negative bias of a phase qubit shows the dominant noise source to be flux noise and not junction critical-current noise, with a magnitude similar to that measured previously in other systems. Theoretical calculations show that the level of flux noise is not compatible with the standard model of noise from two-level state defects in the surface oxides of the films.
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Affiliation(s)
- Radoslaw C Bialczak
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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37
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Sillanpää MA, Park JI, Simmonds RW. Coherent quantum state storage and transfer between two phase qubits via a resonant cavity. Nature 2007; 449:438-42. [PMID: 17898762 DOI: 10.1038/nature06124] [Citation(s) in RCA: 113] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2007] [Accepted: 07/25/2007] [Indexed: 11/09/2022]
Abstract
As with classical information processing, a quantum information processor requires bits (qubits) that can be independently addressed and read out, long-term memory elements to store arbitrary quantum states, and the ability to transfer quantum information through a coherent communication bus accessible to a large number of qubits. Superconducting qubits made with scalable microfabrication techniques are a promising candidate for the realization of a large-scale quantum information processor. Although these systems have successfully passed tests of coherent coupling for up to four qubits, communication of individual quantum states between superconducting qubits via a quantum bus has not yet been realized. Here, we perform an experiment demonstrating the ability to coherently transfer quantum states between two superconducting Josephson phase qubits through a quantum bus. This quantum bus is a resonant cavity formed by an open-ended superconducting transmission line of length 7 mm. After preparing an initial quantum state with the first qubit, this quantum information is transferred and stored as a nonclassical photon state of the resonant cavity, then retrieved later by the second qubit connected to the opposite end of the cavity. Beyond simple state transfer, these results suggest that a high-quality-factor superconducting cavity could also function as a useful short-term memory element. The basic architecture presented here can be expanded, offering the possibility for the coherent interaction of a large number of superconducting qubits.
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Affiliation(s)
- Mika A Sillanpää
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
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38
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Lisenfeld J, Lukashenko A, Ansmann M, Martinis JM, Ustinov AV. Temperature dependence of coherent oscillations in Josephson phase qubits. PHYSICAL REVIEW LETTERS 2007; 99:170504. [PMID: 17995313 DOI: 10.1103/physrevlett.99.170504] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2007] [Indexed: 05/25/2023]
Abstract
We experimentally investigate the temperature dependence of Rabi oscillations and Ramsey fringes in superconducting phase qubits. In a wide range of temperatures, we find that both the decay time and the amplitude of these coherent oscillations remain nearly unaffected by thermal fluctuations. In the two-level limit, coherent qubit response rapidly vanishes as soon as the energy of thermal fluctuations k(B)T becomes larger than the energy level spacing variant Planck's over h omega of the qubit. In contrast, a sample of much shorter coherence times displayed semiclassical oscillations very similar to Rabi oscillation, but showing a qualitatively different temperature dependence. Our observations shed new light on the origin of decoherence in superconducting qubits. The experimental data suggest that, without degrading already achieved coherence times, phase qubits can be operated at temperatures much higher than those reported till now.
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Affiliation(s)
- J Lisenfeld
- Physikalisches Institut III, Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
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39
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Tian L, Simmonds RW. Josephson junction microscope for low-frequency fluctuators. PHYSICAL REVIEW LETTERS 2007; 99:137002. [PMID: 17930626 DOI: 10.1103/physrevlett.99.137002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2007] [Indexed: 05/25/2023]
Abstract
The high-Q harmonic oscillator mode of a Josephson junction can be used as a novel probe of spurious two-level systems (TLSs) inside the amorphous oxide tunnel barrier of the junction. In particular, we show that spectroscopic transmission measurements of the junction resonator mode can reveal how the coupling magnitude between the junction and the TLSs varies with an external magnetic field applied in the plane of the tunnel barrier. The proposed experiments offer the possibility of clearly resolving the underlying coupling mechanism for these spurious TLSs, an important decoherence source limiting the quality of superconducting quantum devices.
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Affiliation(s)
- L Tian
- Department of Applied Physics and E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA.
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40
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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] [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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41
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Steffen M, Ansmann M, Bialczak RC, Katz N, Lucero E, McDermott R, Neeley M, Weig EM, Cleland AN, Martinis JM. Measurement of the Entanglement of Two Superconducting Qubits via State Tomography. Science 2006; 313:1423-5. [PMID: 16960003 DOI: 10.1126/science.1130886] [Citation(s) in RCA: 88] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Demonstration of quantum entanglement, a key resource in quantum computation arising from a nonclassical correlation of states, requires complete measurement of all states in varying bases. By using simultaneous measurement and state tomography, we demonstrated entanglement between two solid-state qubits. Single qubit operations and capacitive coupling between two super-conducting phase qubits were used to generate a Bell-type state. Full two-qubit tomography yielded a density matrix showing an entangled state with fidelity up to 87%. Our results demonstrate a high degree of unitary control of the system, indicating that larger implementations are within reach.
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Affiliation(s)
- Matthias Steffen
- Department of Physics and California Nano Systems Institute, University of California, Santa Barbara, CA 93106, USA
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