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Sajid A, Ford MJ, Reimers JR. Single-photon emitters in hexagonal boron nitride: a review of progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2020; 83:044501. [PMID: 31846956 DOI: 10.1088/1361-6633/ab6310] [Citation(s) in RCA: 41] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
This report summarizes progress made in understanding properties such as zero-phonon-line energies, emission and absorption polarizations, electron-phonon couplings, strain tuning and hyperfine coupling of single photon emitters in hexagonal boron nitride. The primary aims of this research are to discover the chemical nature of the emitting centres and to facilitate deployment in device applications. Critical analyses of the experimental literature and data interpretation, as well as theoretical approaches used to predict properties, are made. In particular, computational and theoretical limitations and challenges are discussed, with a range of suggestions made to overcome these limitations, striving to achieve realistic predictions concerning the nature of emitting centers. A symbiotic relationship is required in which calculations focus on properties that can easily be measured, whilst experiments deliver results in a form facilitating mass-produced calculations.
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Affiliation(s)
- A Sajid
- University of Technology Sydney, School of Mathematical and Physical Sciences, Ultimo, New South Wales 2007, Australia. CAMD, Department of Physics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark. Department of Physics, GC University Faisalabad, Allama Iqbal Road, 38000 Faisalabad, Pakistan. Author to whom any correspondence should be addressed
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2
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Liang YC, Yeh YH, Mendonça PEMF, Teh RY, Reid MD, Drummond PD. Quantum fidelity measures for mixed states. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:076001. [PMID: 31022705 DOI: 10.1088/1361-6633/ab1ca4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more subtle for the more general case of mixed quantum states often found in practice. A large number of different proposals exist. In this review, we summarize the required properties of a quantum fidelity measure, and compare them, to determine which properties each of the different measures has. We show that there are large classes of measures that satisfy all the required properties of a fidelity measure, just as there are many norms of Hilbert space operators, and many measures of entropy. We compare these fidelities, with detailed proofs of their properties. We also summarize briefly the applications of these measures in teleportation, quantum memories and quantum computers, quantum communications, and quantum phase-space simulations.
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Affiliation(s)
- Yeong-Cherng Liang
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan. Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan
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3
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Dogra S, Madhok V, Lakshminarayan A. Quantum signatures of chaos, thermalization, and tunneling in the exactly solvable few-body kicked top. Phys Rev E 2019; 99:062217. [PMID: 31330664 DOI: 10.1103/physreve.99.062217] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2018] [Indexed: 06/10/2023]
Abstract
Exactly solvable models that exhibit quantum signatures of classical chaos are both rare as well as important-more so in view of the fact that the mechanisms for ergodic behavior and thermalization in isolated quantum systems and its connections to nonintegrability are under active investigation. In this work, we study quantum systems of few qubits collectively modeled as a kicked top, a textbook example of quantum chaos. In particular, we show that the three- and four-qubit cases are exactly solvable and yet, interestingly, can display signatures of ergodicity and thermalization. Deriving analytical expressions for entanglement entropy and concurrence, we see agreement in certain parameter regimes between long-time average values and ensemble averages of random states with permutation symmetry. Comparing with results using the data of a recent transmons-based experiment realizing the three-qubit case, we find agreement for short times, including a peculiar steplike behavior in correlations of some states. In the case of four qubits we point to a precursor of dynamical tunneling between what in the classical limit would be two stable islands. Numerical results for larger number of qubits show the emergence of the classical limit including signatures of a bifurcation.
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Affiliation(s)
- Shruti Dogra
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Vaibhav Madhok
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Arul Lakshminarayan
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
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4
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Analyzing the Quantum Zeno and anti-Zeno effects using optimal projective measurements. Sci Rep 2017; 7:11766. [PMID: 28924194 PMCID: PMC5603598 DOI: 10.1038/s41598-017-11787-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2017] [Accepted: 08/30/2017] [Indexed: 11/09/2022] Open
Abstract
Measurements in quantum mechanics can not only effectively freeze the quantum system (the quantum Zeno effect) but also accelerate the time evolution of the system (the quantum anti-Zeno effect). In studies of these effects, a quantum state is prepared repeatedly by projecting the quantum state onto the initial state. In this paper, we repeatedly prepare the initial quantum state in a different manner. Instead of only performing projective measurements, we allow unitary operations to be performed, on a very short time-scale, after each measurement. We can then repeatedly prepare the initial state by performing some projective measurement and then, after each measurement, we perform a suitable unitary operation to end up with the same initial state as before. Our objective is to find the projective measurements that minimize the effective decay rate of the quantum state. We find such optimal measurements and the corresponding decay rates for a variety of system-environment models such as the pure dephasing model and the spin-boson model. We find that there can be considerable differences between this optimized effective decay rate and the usual decay rate obtained by repeatedly projecting onto the initial state. In particular, the Zeno and anti-Zeno regimes can be considerably modified.
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5
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Zhong YP, Xu D, Wang P, Song C, Guo QJ, Liu WX, Xu K, Xia BX, Lu CY, Han S, Pan JW, Wang H. Emulating Anyonic Fractional Statistical Behavior in a Superconducting Quantum Circuit. PHYSICAL REVIEW LETTERS 2016; 117:110501. [PMID: 27661671 DOI: 10.1103/physrevlett.117.110501] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2016] [Indexed: 05/06/2023]
Abstract
Anyons are exotic quasiparticles obeying fractional statistics, whose behavior can be emulated in artificially designed spin systems. Here we present an experimental emulation of creating anyonic excitations in a superconducting circuit that consists of four qubits, achieved by dynamically generating the ground and excited states of the toric code model, i.e., four-qubit Greenberger-Horne-Zeilinger states. The anyonic braiding is implemented via single-qubit rotations: a phase shift of π related to braiding, the hallmark of Abelian 1/2 anyons, has been observed through a Ramsey-type interference measurement.
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Affiliation(s)
- Y P Zhong
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
- CAS Center for Excellence and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - D Xu
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - P Wang
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - C Song
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Q J Guo
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - W X Liu
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - K Xu
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - B X Xia
- CAS Center for Excellence and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - C-Y Lu
- CAS Center for Excellence and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS-Alibaba Quantum Computing Laboratory, Shanghai 201315, China
| | - Siyuan Han
- Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA
| | - Jian-Wei Pan
- CAS Center for Excellence and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS-Alibaba Quantum Computing Laboratory, Shanghai 201315, China
| | - H Wang
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
- CAS Center for Excellence and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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6
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Casparis L, Larsen TW, Olsen MS, Kuemmeth F, Krogstrup P, Nygård J, Petersson KD, Marcus CM. Gatemon Benchmarking and Two-Qubit Operations. PHYSICAL REVIEW LETTERS 2016; 116:150505. [PMID: 27127949 DOI: 10.1103/physrevlett.116.150505] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2015] [Indexed: 06/05/2023]
Abstract
Recent experiments have demonstrated superconducting transmon qubits with semiconductor nanowire Josephson junctions. These hybrid gatemon qubits utilize field effect tunability characteristic of semiconductors to allow complete qubit control using gate voltages, potentially a technological advantage over conventional flux-controlled transmons. Here, we present experiments with a two-qubit gatemon circuit. We characterize qubit coherence and stability and use randomized benchmarking to demonstrate single-qubit gate errors below 0.7% for all gates, including voltage-controlled Z rotations. We show coherent capacitive coupling between two gatemons and coherent swap operations. Finally, we perform a two-qubit controlled-phase gate with an estimated fidelity of 91%, demonstrating the potential of gatemon qubits for building scalable quantum processors.
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Affiliation(s)
- L Casparis
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - T W Larsen
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - M S Olsen
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - F Kuemmeth
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - P Krogstrup
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - J Nygård
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
- Nano-Science Center, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - K D Petersson
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - C M Marcus
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
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7
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Chen Z, Kelly J, Quintana C, Barends R, Campbell B, Chen Y, Chiaro B, Dunsworth A, Fowler AG, Lucero E, Jeffrey E, Megrant A, Mutus J, Neeley M, Neill C, O'Malley PJJ, Roushan P, Sank D, Vainsencher A, Wenner J, White TC, Korotkov AN, Martinis JM. Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit. PHYSICAL REVIEW LETTERS 2016; 116:020501. [PMID: 26824531 DOI: 10.1103/physrevlett.116.020501] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2015] [Indexed: 06/05/2023]
Abstract
Leakage errors occur when a quantum system leaves the two-level qubit subspace. Reducing these errors is critically important for quantum error correction to be viable. To quantify leakage errors, we use randomized benchmarking in conjunction with measurement of the leakage population. We characterize single qubit gates in a superconducting qubit, and by refining our use of derivative reduction by adiabatic gate pulse shaping along with detuning of the pulses, we obtain gate errors consistently below 10^{-3} and leakage rates at the 10^{-5} level. With the control optimized, we find that a significant portion of the remaining leakage is due to incoherent heating of the qubit.
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Affiliation(s)
- Zijun Chen
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - Julian Kelly
- Google Inc., Santa Barbara, California 93117, USA
| | - Chris Quintana
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - R Barends
- Google Inc., Santa Barbara, California 93117, USA
| | - B Campbell
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - Yu Chen
- Google Inc., Santa Barbara, California 93117, USA
| | - B Chiaro
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - A Dunsworth
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - A G Fowler
- Google Inc., Santa Barbara, California 93117, USA
| | - E Lucero
- Google Inc., Santa Barbara, California 93117, USA
| | - E Jeffrey
- Google Inc., Santa Barbara, California 93117, USA
| | - A Megrant
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
- Department of Materials, University of California, Santa Barbara, California 93106, USA
| | - J Mutus
- Google Inc., Santa Barbara, California 93117, USA
| | - M Neeley
- Google Inc., Santa Barbara, California 93117, USA
| | - C Neill
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - P J J O'Malley
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - P Roushan
- Google Inc., Santa Barbara, California 93117, USA
| | - D Sank
- Google Inc., Santa Barbara, California 93117, USA
| | - A Vainsencher
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - J Wenner
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - T C White
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - A N Korotkov
- Department of Electrical and Computer Engineering, University of California, Riverside, California 92521, USA
| | - John M Martinis
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
- Google Inc., Santa Barbara, California 93117, USA
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8
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Chen Y, Neill C, Roushan P, Leung N, Fang M, Barends R, Kelly J, Campbell B, Chen Z, Chiaro B, Dunsworth A, Jeffrey E, Megrant A, Mutus JY, O'Malley PJJ, Quintana CM, Sank D, Vainsencher A, Wenner J, White TC, Geller MR, Cleland AN, Martinis JM. Qubit Architecture with High Coherence and Fast Tunable Coupling. PHYSICAL REVIEW LETTERS 2014; 113:220502. [PMID: 25494061 DOI: 10.1103/physrevlett.113.220502] [Citation(s) in RCA: 73] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2014] [Indexed: 06/04/2023]
Abstract
We introduce a superconducting qubit architecture that combines high-coherence qubits and tunable qubit-qubit coupling. With the ability to set the coupling to zero, we demonstrate that this architecture is protected from the frequency crowding problems that arise from fixed coupling. More importantly, the coupling can be tuned dynamically with nanosecond resolution, making this architecture a versatile platform with applications ranging from quantum logic gates to quantum simulation. We illustrate the advantages of dynamical coupling by implementing a novel adiabatic controlled-z gate, with a speed approaching that of single-qubit gates. Integrating coherence and scalable control, the introduced qubit architecture provides a promising path towards large-scale quantum computation and simulation.
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Affiliation(s)
- Yu Chen
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - C Neill
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - P Roushan
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - N Leung
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - M Fang
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - R Barends
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - J Kelly
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - B Campbell
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - Z Chen
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - B Chiaro
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - A Dunsworth
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - E Jeffrey
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - A Megrant
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA and Department of Materials, University of California, Santa Barbara, California 93106-5050, USA
| | - J Y Mutus
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - P J J O'Malley
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - C M Quintana
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - D Sank
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - A Vainsencher
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - J Wenner
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - T C White
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - Michael R Geller
- Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602, USA
| | - A N Cleland
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
| | - John M Martinis
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
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9
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Salmilehto J, Solinas P, Möttönen M. Quantum driving and work. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:052128. [PMID: 25353760 DOI: 10.1103/physreve.89.052128] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2014] [Indexed: 06/04/2023]
Abstract
As quantum systems become more experimentally accessible, we are forced to reconsider the notions of control and work to fully account for quantum effects. To this end, we identify the work injected into a quantum system during a general quantum-mechanical driving protocol and quantify the relevant heat flows. The known results that are applicable in the limit of a classical drive are shown to emerge from our equations as a special case. Using the established framework, we show that the Bochkov-Kuzovlev identity for the exclusive work distribution is modified in a nontrivial way by the accumulation of system-drive correlations resulting from quantum back action. Our results accentuate the conceptual and discernible differences between a fully quantum-mechanical and classical driving protocols of quantum systems.
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Affiliation(s)
- J Salmilehto
- QCD Labs, COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 13500, FI-00076 Aalto, Finland
| | - P Solinas
- SPIN-CNR, Via Dodecaneso 33, I-16146 Genova, Italy
| | - M Möttönen
- QCD Labs, COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 13500, FI-00076 Aalto, Finland and Low Temperature Laboratory (OVLL), Aalto University, P.O. Box 13500, FI-00076 Aalto, Finland
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10
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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. PHYSICAL REVIEW LETTERS 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] [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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11
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Devoret MH, Schoelkopf RJ. Superconducting Circuits for Quantum Information: An Outlook. Science 2013; 339:1169-74. [DOI: 10.1126/science.1231930] [Citation(s) in RCA: 1301] [Impact Index Per Article: 118.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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12
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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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13
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Peano V, Marthaler M, Dykman MI. Sharp tunneling peaks in a parametric oscillator: quantum resonances missing in the rotating wave approximation. PHYSICAL REVIEW LETTERS 2012; 109:090401. [PMID: 23002813 DOI: 10.1103/physrevlett.109.090401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2012] [Indexed: 06/01/2023]
Abstract
We describe a new mechanism of tunneling between period-two vibrational states of a weakly nonlinear, parametrically modulated oscillator. The tunneling results from resonant transitions induced by the fast oscillating terms conventionally disregarded in the rotating wave approximation (RWA). The tunneling amplitude displays resonant peaks as a function of the modulation frequency; near the maxima it is exponentially larger than the RWA tunneling amplitude.
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Affiliation(s)
- V Peano
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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14
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Sank D, Barends R, Bialczak RC, Chen Y, Kelly J, Lenander M, Lucero E, Mariantoni M, Megrant A, Neeley M, O'Malley PJJ, Vainsencher A, Wang H, Wenner J, White TC, Yamamoto T, Yin Y, Cleland AN, Martinis JM. Flux noise probed with real time qubit tomography in a Josephson phase qubit. PHYSICAL REVIEW LETTERS 2012; 109:067001. [PMID: 23006294 DOI: 10.1103/physrevlett.109.067001] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2011] [Indexed: 06/01/2023]
Abstract
We measure the dependence of qubit phase coherence and flux noise on inductor loop geometry. While wider inductor traces change neither the flux noise power spectrum nor the qubit dephasing time, increased inductance leads to a simultaneous increase in both. Using our new tomographic protocol for measuring low frequency flux noise, we make a direct comparison between the flux noise spectrum and qubit phase decay, finding agreement within 10% of theory.
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Affiliation(s)
- Daniel Sank
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
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15
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Gustavsson S, Yan F, Bylander J, Yoshihara F, Nakamura Y, Orlando TP, Oliver WD. Dynamical decoupling and dephasing in interacting two-level systems. PHYSICAL REVIEW LETTERS 2012; 109:010502. [PMID: 23031094 DOI: 10.1103/physrevlett.109.010502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2012] [Indexed: 06/01/2023]
Abstract
We implement dynamical decoupling techniques to mitigate noise and enhance the lifetime of an entangled state that is formed in a superconducting flux qubit coupled to a microscopic two-level system. By rapidly changing the qubit's transition frequency relative to the two-level system, we realize a refocusing pulse that reduces dephasing due to fluctuations in the transition frequencies, thereby improving the coherence time of the entangled state. The coupling coherence is further enhanced when applying multiple refocusing pulses, in agreement with our 1/f noise model. The results are applicable to any two-qubit system with transverse coupling and they highlight the potential of decoupling techniques for improving two-qubit gate fidelities, an essential prerequisite for implementing fault-tolerant quantum computing.
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Affiliation(s)
- Simon Gustavsson
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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16
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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. PHYSICAL REVIEW LETTERS 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] [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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17
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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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18
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Shalibo Y, Rofe Y, Barth I, Friedland L, Bialczack R, Martinis JM, Katz N. Quantum and classical chirps in an anharmonic oscillator. PHYSICAL REVIEW LETTERS 2012; 108:037701. [PMID: 22400784 DOI: 10.1103/physrevlett.108.037701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2011] [Indexed: 05/31/2023]
Abstract
We measure the state dynamics of a tunable anharmonic quantum system, the Josephson phase circuit, under the excitation of a frequency-chirped drive. At small anharmonicity, the state evolves like a wave packet-a characteristic response in classical oscillators; in this regime, we report exponentially enhanced lifetimes of highly excited states, held by the drive. At large anharmonicity, we observe sharp steps, corresponding to the excitation of discrete energy levels. The continuous transition between the two regimes is mapped by measuring the threshold of these two effects.
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Affiliation(s)
- Yoni Shalibo
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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19
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Lecocq F, Claudon J, Buisson O, Milman P. Nonlinear coupling between the two oscillation modes of a dc SQUID. PHYSICAL REVIEW LETTERS 2011; 107:197002. [PMID: 22181637 DOI: 10.1103/physrevlett.107.197002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2011] [Indexed: 05/31/2023]
Abstract
We make a detailed theoretical description of the two-dimensional nature of a dc SQUID, analyzing the coupling between its two orthogonal phase oscillation modes. While it has been shown that the mode defined as "longitudinal" can be initialized, manipulated, and measured, so as to encode a quantum bit of information, the mode defined as "transverse" is usually repelled at high frequency and does not interfere in the dynamics. We show that, using typical parameters of existing devices, the transverse mode energy can be made of the order of the longitudinal one. In this regime, we can observe a strong coupling between these modes, described by a Hamiltonian providing a wide range of interesting effects, such as conditional quantum operations and entanglement. This coupling also creates an atomiclike structure for the combined two mode states, with a V-like scheme.
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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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20
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Chow JM, Córcoles AD, Gambetta JM, Rigetti C, Johnson BR, Smolin JA, Rozen JR, Keefe GA, Rothwell MB, Ketchen MB, Steffen M. Simple all-microwave entangling gate for fixed-frequency superconducting qubits. PHYSICAL REVIEW LETTERS 2011; 107:080502. [PMID: 21929152 DOI: 10.1103/physrevlett.107.080502] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2011] [Indexed: 05/31/2023]
Abstract
We demonstrate an all-microwave two-qubit gate on superconducting qubits which are fixed in frequency at optimal bias points. The gate requires no additional subcircuitry and is tunable via the amplitude of microwave irradiation on one qubit at the transition frequency of the other. We use the gate to generate entangled states with a maximal extracted concurrence of 0.88, and quantum process tomography reveals a gate fidelity of 81%.
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Affiliation(s)
- Jerry M Chow
- IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
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21
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Bianchetti R, Filipp S, Baur M, Fink JM, Lang C, Steffen L, Boissonneault M, Blais A, Wallraff A. Control and tomography of a three level superconducting artificial atom. PHYSICAL REVIEW LETTERS 2010; 105:223601. [PMID: 21231385 DOI: 10.1103/physrevlett.105.223601] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2010] [Indexed: 05/30/2023]
Abstract
A number of superconducting qubits, such as the transmon or the phase qubit, have an energy level structure with small anharmonicity. This allows for convenient access of higher excited states with similar frequencies. However, special care has to be taken to avoid unwanted higher-level populations when using short control pulses. Here we demonstrate the preparation of arbitrary three level superposition states using optimal control techniques in a transmon. Performing dispersive readout, we extract the populations of all three levels of the qutrit and study the coherence of its excited states. Finally we demonstrate full quantum state tomography of the prepared qutrit states and evaluate the fidelities of a set of states, finding on average 95%.
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Affiliation(s)
- R Bianchetti
- Department of Physics, ETH Zurich, CH-8093 Zürich, Switzerland
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22
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Neeley M, Bialczak RC, Lenander M, Lucero E, Mariantoni M, O'Connell AD, Sank D, Wang H, Weides M, Wenner J, Yin Y, Yamamoto T, Cleland AN, Martinis JM. Generation of three-qubit entangled states using superconducting phase qubits. Nature 2010; 467:570-3. [PMID: 20882012 DOI: 10.1038/nature09418] [Citation(s) in RCA: 311] [Impact Index Per Article: 22.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2010] [Accepted: 08/11/2010] [Indexed: 11/09/2022]
Abstract
Entanglement is one of the key resources required for quantum computation, so the experimental creation and measurement of entangled states is of crucial importance for various physical implementations of quantum computers. In superconducting devices, two-qubit entangled states have been demonstrated and used to show violations of Bell's inequality and to implement simple quantum algorithms. Unlike the two-qubit case, where all maximally entangled two-qubit states are equivalent up to local changes of basis, three qubits can be entangled in two fundamentally different ways. These are typified by the states |GHZ>= (|000+ |111>)/ sqrt [2] and |W>= (|001> + |010> + |100>)/ sqrt [3]. Here we demonstrate the operation of three coupled superconducting phase qubits and use them to create and measure |GHZ> and |W>states. The states are fully characterized using quantum state tomography and are shown to satisfy entanglement witnesses, confirming that they are indeed examples of three-qubit entanglement and are not separable into mixtures of two-qubit entanglement.
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Affiliation(s)
- Matthew Neeley
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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23
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Shalibo Y, Rofe Y, Shwa D, Zeides F, Neeley M, Martinis JM, Katz N. Lifetime and coherence of two-level defects in a Josephson junction. PHYSICAL REVIEW LETTERS 2010; 105:177001. [PMID: 21231072 DOI: 10.1103/physrevlett.105.177001] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2010] [Indexed: 05/30/2023]
Abstract
We measure the lifetime (T₁) and coherence (T₂) of two-level defect states (TLSs) in the insulating barrier of a Josephson phase qubit and compare to the interaction strength between the two systems. We find for the average decay times a power-law dependence on the corresponding interaction strengths, whereas for the average coherence times we find an optimum at intermediate coupling strengths. We explain both the lifetime and the coherence results using the standard TLS model, including dipole radiation by phonons and anticorrelated dependence of the energy parameters on environmental fluctuations.
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Affiliation(s)
- Yoni Shalibo
- Racah Institute of Physics, The Hebrew University of Jerusalem, Israel
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24
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Ferber J, Wilhelm FK. Efficient creation of multipartite entanglement in flux qubits. NANOTECHNOLOGY 2010; 21:274015. [PMID: 20571202 DOI: 10.1088/0957-4484/21/27/274015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We investigate three superconducting flux qubits coupled in a loop. In this setup, tripartite entanglement can be created in a natural, controllable, and stable way. Both generic kinds of tripartite entanglement--the W type as well as the GHZ type entanglement--can be identified among the eigenstates. We also discuss the violation of Bell inequalities in this system and show the impact of a limited measurement fidelity on the detection of entanglement and quantum nonlocality.
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Affiliation(s)
- J Ferber
- Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
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25
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Kelly WR, Dutton Z, Schlafer J, Mookerji B, Ohki TA, Kline JS, Pappas DP. Direct observation of coherent population trapping in a superconducting artificial atom. PHYSICAL REVIEW LETTERS 2010; 104:163601. [PMID: 20482047 DOI: 10.1103/physrevlett.104.163601] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2009] [Revised: 01/26/2010] [Indexed: 05/29/2023]
Abstract
The phenomenon of coherent population trapping (CPT) of an atom (or solid state "artificial atom"), and the associated effect of electromagnetically induced transparency (EIT), are clear demonstrations of quantum interference due to coherence in multilevel quantum systems. We report observation of CPT in a superconducting phase qubit by simultaneously driving two coherent transitions in a Lambda-type configuration, utilizing the three lowest lying levels of a local minimum of a phase qubit. We observe 60(+/-7)% suppression of the excited state population under conditions of CPT resonance. We present data and matching theoretical simulations showing the development of CPT in time. Finally, we used the observed time dependence of the excited state population to characterize quantum dephasing times of the system.
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Affiliation(s)
- William R Kelly
- Raytheon BBN Technologies, Cambridge, Massachusetts 02138, USA.
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26
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Wang H, Hofheinz M, Ansmann M, Bialczak RC, Lucero E, Neeley M, O'Connell AD, Sank D, Weides M, Wenner J, Cleland AN, Martinis JM. Decoherence dynamics of complex photon states in a superconducting circuit. PHYSICAL REVIEW LETTERS 2009; 103:200404. [PMID: 20365967 DOI: 10.1103/physrevlett.103.200404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2009] [Indexed: 05/29/2023]
Abstract
Quantum states inevitably decay with time into a probabilistic mixture of classical states due to their interaction with the environment and measurement instrumentation. We present the first measurement of the decoherence dynamics of complex photon states in a condensed-matter system. By controllably preparing a number of distinct quantum-superposed photon states in a superconducting microwave resonator, we show that the subsequent decay dynamics can be quantitatively described by taking into account only two distinct decay channels: energy relaxation and pure dephasing. Our ability to prepare specific initial quantum states allows us to measure the evolution of specific elements in the quantum density matrix in a very detailed manner that can be compared with theory.
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Affiliation(s)
- H Wang
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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27
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Sillanpää MA, Li J, Cicak K, Altomare F, Park JI, Simmonds RW, Paraoanu GS, Hakonen PJ. Autler-Townes effect in a superconducting three-level system. PHYSICAL REVIEW LETTERS 2009; 103:193601. [PMID: 20365921 DOI: 10.1103/physrevlett.103.193601] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2009] [Indexed: 05/29/2023]
Abstract
When a three-level quantum system is irradiated by an intense coupling field resonant with one of the three possible transitions, the absorption peak of an additional probe field involving the remaining level is split. This process is known in quantum optics as the Autler-Townes effect. We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an "artificial atom" with a multilevel quantum structure. The spectroscopy peaks can be explained reasonably well by a simple three-level Hamiltonian model. Simulation of a more complete model (including dissipation, higher levels, and cross coupling) provides excellent agreement with all of the experimental data.
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Affiliation(s)
- Mika A Sillanpää
- Helsinki University of Technology, Low Temperature Laboratory, Puumiehenkuja 2B, Espoo, FIN-02015 HUT Finland.
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28
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Violation of Bell's inequality in Josephson phase qubits. Nature 2009; 461:504-6. [PMID: 19779447 DOI: 10.1038/nature08363] [Citation(s) in RCA: 85] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2009] [Accepted: 08/04/2009] [Indexed: 11/08/2022]
Abstract
The measurement process plays an awkward role in quantum mechanics, because measurement forces a system to 'choose' between possible outcomes in a fundamentally unpredictable manner. Therefore, hidden classical processes have been considered as possibly predetermining measurement outcomes while preserving their statistical distributions. However, a quantitative measure that can distinguish classically determined correlations from stronger quantum correlations exists in the form of the Bell inequalities, measurements of which provide strong experimental evidence that quantum mechanics provides a complete description. Here we demonstrate the violation of a Bell inequality in a solid-state system. We use a pair of Josephson phase qubits acting as spin-1/2 particles, and show that the qubits can be entangled and measured so as to violate the Clauser-Horne-Shimony-Holt (CHSH) version of the Bell inequality. We measure a Bell signal of 2.0732 +/- 0.0003, exceeding the maximum amplitude of 2 for a classical system by 244 standard deviations. In the experiment, we deterministically generate the entangled state, and measure both qubits in a single-shot manner, closing the detection loophole. Because the Bell inequality was designed to test for non-classical behaviour without assuming the applicability of quantum mechanics to the system in question, this experiment provides further strong evidence that a macroscopic electrical circuit is really a quantum system.
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29
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Motzoi F, Gambetta JM, Rebentrost P, Wilhelm FK. Simple pulses for elimination of leakage in weakly nonlinear qubits. PHYSICAL REVIEW LETTERS 2009; 103:110501. [PMID: 19792356 DOI: 10.1103/physrevlett.103.110501] [Citation(s) in RCA: 95] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2009] [Indexed: 05/28/2023]
Abstract
In realizations of quantum computing, a two-level system (qubit) is often singled out from the many levels of an anharmonic oscillator. In these cases, simple qubit control fails on short time scales because of coupling to leakage levels. We provide an easy to implement analytic formula that inhibits this leakage from any single-control analog or pixelated pulse. It is based on adding a second control that is proportional to the time derivative of the first. For realistic parameters of superconducting qubits, this strategy reduces the error by an order of magnitude relative to the state of the art, all based on smooth and feasible pulse shapes. These results show that even weak anharmonicity is sufficient and in general not a limiting factor for implementing quantum gates.
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Affiliation(s)
- F Motzoi
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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30
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Martinis JM, Ansmann M, Aumentado J. Energy decay in superconducting Josephson-junction qubits from nonequilibrium quasiparticle excitations. PHYSICAL REVIEW LETTERS 2009; 103:097002. [PMID: 19792820 DOI: 10.1103/physrevlett.103.097002] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2009] [Indexed: 05/28/2023]
Abstract
We calculate the energy decay rate of Josephson qubits and superconducting resonators from nonequilibrium quasiparticles. The decay rates from experiments are shown to be consistent with predictions based on a prior measurement of the quasiparticle density n(qp) = 10/microm(3), which suggests that nonequilibrium quasiparticles are an important decoherence source for Josephson qubits. Calculations of the energy-decay and diffusion of quasiparticles also indicate that prior engineered gap and trap structures, which reduce the density of quasiparticles, should be redesigned to improve their efficacy. This model also explains a striking feature in Josephson qubits and resonators-a small reduction in decay rate with increasing temperature.
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Affiliation(s)
- John M Martinis
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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31
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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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32
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Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 2009; 460:240-4. [PMID: 19561592 DOI: 10.1038/nature08121] [Citation(s) in RCA: 206] [Impact Index Per Article: 13.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2009] [Accepted: 05/05/2009] [Indexed: 11/08/2022]
Abstract
Quantum computers, which harness the superposition and entanglement of physical states, could outperform their classical counterparts in solving problems with technological impact-such as factoring large numbers and searching databases. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized register of qubits, which coherently evolves into a final state containing the result of the computation. Building a quantum processor is challenging because of the need to meet simultaneously requirements that are in conflict: state preparation, long coherence times, universal gate operations and qubit readout. Processors based on a few qubits have been demonstrated using nuclear magnetic resonance, cold ion trap and optical systems, but a solid-state realization has remained an outstanding challenge. Here we demonstrate a two-qubit superconducting processor and the implementation of the Grover search and Deutsch-Jozsa quantum algorithms. We use a two-qubit interaction, tunable in strength by two orders of magnitude on nanosecond timescales, which is mediated by a cavity bus in a circuit quantum electrodynamics architecture. This interaction allows the generation of highly entangled states with concurrence up to 94 per cent. Although this processor constitutes an important step in quantum computing with integrated circuits, continuing efforts to increase qubit coherence times, gate performance and register size will be required to fulfil the promise of a scalable technology.
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33
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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. PHYSICAL REVIEW LETTERS 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] [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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34
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Wang H, Hofheinz M, Ansmann M, Bialczak RC, Lucero E, Neeley M, O'Connell AD, Sank D, Wenner J, Cleland AN, Martinis JM. Measurement of the decay of Fock states in a superconducting quantum circuit. PHYSICAL REVIEW LETTERS 2008; 101:240401. [PMID: 19113602 DOI: 10.1103/physrevlett.101.240401] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2008] [Indexed: 05/27/2023]
Abstract
We demonstrate the controlled generation of Fock states with up to 15 photons in a microwave coplanar waveguide resonator coupled to a superconducting phase qubit. The subsequent decay of the Fock states, due to dissipation, is then monitored by varying the time delay between preparing the state and performing a number-state analysis. We find that the decay dynamics can be described by a master equation where the lifetime of the n-photon Fock state scales as 1/n, in agreement with theory. We have also generated a coherent state in the microwave resonator, and monitored its decay process. We demonstrate that the coherent state maintains a Poisson distribution as it decays, with an average photon number that decreases with the same characteristic decay time as the one-photon Fock state.
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Affiliation(s)
- H Wang
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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35
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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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36
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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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