51
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Leghtas Z, Kirchmair G, Vlastakis B, Schoelkopf RJ, Devoret MH, Mirrahimi M. Hardware-efficient autonomous quantum memory protection. PHYSICAL REVIEW LETTERS 2013; 111:120501. [PMID: 24093235 DOI: 10.1103/physrevlett.111.120501] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2013] [Indexed: 06/02/2023]
Abstract
We propose to encode a quantum bit of information in a superposition of coherent states of an oscillator, with four different phases. Our encoding in a single cavity mode, together with a protection protocol, significantly reduces the error rate due to photon loss. This protection is ensured by an efficient quantum error correction scheme employing the nonlinearity provided by a single physical qubit coupled to the cavity. We describe in detail how to implement these operations in a circuit quantum electrodynamics system. This proposal directly addresses the task of building a hardware-efficient quantum memory and can lead to important shortcuts in quantum computing architectures.
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Affiliation(s)
- Zaki Leghtas
- INRIA Paris-Rocquencourt, Domaine de Voluceau, Boîte Postale 105, 78153 Le Chesnay Cedex, France and Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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52
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Carretta S, Chiesa A, Troiani F, Gerace D, Amoretti G, Santini P. Quantum information processing with hybrid spin-photon qubit encoding. PHYSICAL REVIEW LETTERS 2013; 111:110501. [PMID: 24074061 DOI: 10.1103/physrevlett.111.110501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2013] [Indexed: 06/02/2023]
Abstract
We introduce a scheme to perform quantum information processing that is based on a hybrid spin-photon qubit encoding. The proposed qubits consist of spin ensembles coherently coupled to microwave photons in coplanar waveguide resonators. The quantum gates are performed solely by shifting the resonance frequencies of the resonators on a nanosecond time scale. An additional cavity containing a Cooper-pair box is exploited as an auxiliary degree of freedom to implement two-qubit gates. The generality of the scheme allows its potential implementation with a wide class of spin systems.
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Affiliation(s)
- S Carretta
- Dipartimento di Fisica e Scienze della Terra, Università di Parma, I-43124 Parma, Italy
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53
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Barends R, Kelly J, Megrant A, Sank D, Jeffrey E, Chen Y, Yin Y, Chiaro B, Mutus J, Neill C, O'Malley P, Roushan P, Wenner J, White TC, Cleland AN, Martinis JM. Coherent Josephson qubit suitable for scalable quantum integrated circuits. PHYSICAL REVIEW LETTERS 2013; 111:080502. [PMID: 24010421 DOI: 10.1103/physrevlett.111.080502] [Citation(s) in RCA: 121] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2013] [Indexed: 06/02/2023]
Abstract
We demonstrate a planar, tunable superconducting qubit with energy relaxation times up to 44 μs. This is achieved by using a geometry designed to both minimize radiative loss and reduce coupling to materials-related defects. At these levels of coherence, we find a fine structure in the qubit energy lifetime as a function of frequency, indicating the presence of a sparse population of incoherent, weakly coupled two-level defects. We elucidate this defect physics by experimentally varying the geometry and by a model analysis. Our "Xmon" qubit combines facile fabrication, straightforward connectivity, fast control, and long coherence, opening a viable route to constructing a chip-based quantum computer.
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Affiliation(s)
- R Barends
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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54
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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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55
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Pirkkalainen JM, Cho SU, Li J, Paraoanu GS, Hakonen PJ, Sillanpää MA. Hybrid circuit cavity quantum electrodynamics with a micromechanical resonator. Nature 2013; 494:211-5. [DOI: 10.1038/nature11821] [Citation(s) in RCA: 204] [Impact Index Per Article: 18.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2012] [Accepted: 11/27/2012] [Indexed: 11/09/2022]
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56
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Viehmann O, von Delft J, Marquardt F. Observing the nonequilibrium dynamics of the quantum transverse-field Ising chain in circuit QED. PHYSICAL REVIEW LETTERS 2013; 110:030601. [PMID: 23373908 DOI: 10.1103/physrevlett.110.030601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2012] [Indexed: 06/01/2023]
Abstract
We show how a quantum Ising spin chain in a time-dependent transverse magnetic field can be simulated and experimentally probed in the framework of circuit QED with current technology. The proposed setup provides a new platform for observing the nonequilibrium dynamics of interacting many-body systems. We calculate its spectrum to offer a guideline for its initial experimental characterization. We demonstrate that quench dynamics and the propagation of localized excitations can be observed with the proposed setup and discuss further possible applications and modifications of this circuit QED quantum simulator.
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Affiliation(s)
- Oliver Viehmann
- Physics Department, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität, München, Germany
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57
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Menzel EP, Di Candia R, Deppe F, Eder P, Zhong L, Ihmig M, Haeberlein M, Baust A, Hoffmann E, Ballester D, Inomata K, Yamamoto T, Nakamura Y, Solano E, Marx A, Gross R. Path entanglement of continuous-variable quantum microwaves. PHYSICAL REVIEW LETTERS 2012; 109:250502. [PMID: 23368439 DOI: 10.1103/physrevlett.109.250502] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2012] [Indexed: 06/01/2023]
Abstract
Path entanglement constitutes an essential resource in quantum information and communication protocols. Here, we demonstrate frequency-degenerate entanglement between continuous-variable quantum microwaves propagating along two spatially separated paths. We combine a squeezed and a vacuum state using a microwave beam splitter. Via correlation measurements, we detect and quantify the path entanglement contained in the beam splitter output state. Our experiments open the avenue to quantum teleportation, quantum communication, or quantum radar with continuous variables at microwave frequencies.
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Affiliation(s)
- E P Menzel
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany.
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58
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Leung PM, Sanders BC. Coherent control of microwave pulse storage in superconducting circuits. PHYSICAL REVIEW LETTERS 2012; 109:253603. [PMID: 23368461 DOI: 10.1103/physrevlett.109.253603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2012] [Indexed: 06/01/2023]
Abstract
Coherent pulse control for quantum memory is viable in the optical domain but nascent in microwave quantum circuits. We show how to realize coherent storage and on-demand pulse retrieval entirely within a superconducting circuit by exploiting and extending existing electromagnetically induced transparency technology in superconducting quantum circuits. Our scheme employs a linear array of superconducting artificial atoms coupled to a microwave transmission line.
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Affiliation(s)
- Patrick M Leung
- Institute for Quantum Information Science, University of Calgary, Alberta T2N 1N4, Canada.
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59
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Ristè D, Bultink CC, Lehnert KW, DiCarlo L. Feedback control of a solid-state qubit using high-fidelity projective measurement. PHYSICAL REVIEW LETTERS 2012; 109:240502. [PMID: 23368293 DOI: 10.1103/physrevlett.109.240502] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2012] [Indexed: 06/01/2023]
Abstract
We demonstrate feedback control of a superconducting transmon qubit using discrete, projective measurement and conditional coherent driving. Feedback realizes a fast and deterministic qubit reset to a target state with 2.4% error averaged over input superposition states, and allows concatenating experiments more than 10 times faster than by passive initialization. This closed-loop qubit control is necessary for measurement-based protocols such as quantum error correction and teleportation.
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Affiliation(s)
- D Ristè
- Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands
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60
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Strauch FW. All-resonant control of superconducting resonators. PHYSICAL REVIEW LETTERS 2012; 109:210501. [PMID: 23215585 DOI: 10.1103/physrevlett.109.210501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2012] [Revised: 08/17/2012] [Indexed: 06/01/2023]
Abstract
An all-resonant method is proposed to control the quantum state of superconducting resonators. This approach uses a tunable artificial atom linearly coupled to resonators, and allows for efficient routes to Fock state synthesis, qudit logic operations, and synthesis of NOON states. This resonant approach is theoretically analyzed, and found to perform significantly better than existing proposals using the same technology.
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61
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Li J, Paraoanu GS, Cicak K, Altomare F, Park JI, Simmonds RW, Sillanpää MA, Hakonen PJ. Dynamical Autler-Townes control of a phase qubit. Sci Rep 2012; 2:645. [PMID: 22966420 PMCID: PMC3437518 DOI: 10.1038/srep00645] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2012] [Accepted: 08/22/2012] [Indexed: 11/23/2022] Open
Abstract
Routers, switches, and repeaters are essential components of modern information-processing systems. Similar devices will be needed in future superconducting quantum computers. In this work we investigate experimentally the time evolution of Autler-Townes splitting in a superconducting phase qubit under the application of a control tone resonantly coupled to the second transition. A three-level model that includes independently determined parameters for relaxation and dephasing gives excellent agreement with the experiment. The results demonstrate that the qubit can be used as a ON/OFF switch with 100 ns operating time-scale for the reflection/transmission of photons coming from an applied probe microwave tone. The ON state is realized when the control tone is sufficiently strong to generate an Autler-Townes doublet, suppressing the absorption of the probe tone photons and resulting in a maximum of transmission.
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Affiliation(s)
- Jian Li
- O.V. Lounasmaa Laboratory, Aalto University, PO Box 15100, FI-00076 AALTO, Finland.
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62
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Walther A, Ziesel F, Ruster T, Dawkins ST, Ott K, Hettrich M, Singer K, Schmidt-Kaler F, Poschinger U. Controlling fast transport of cold trapped ions. PHYSICAL REVIEW LETTERS 2012; 109:080501. [PMID: 23002727 DOI: 10.1103/physrevlett.109.080501] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2012] [Indexed: 06/01/2023]
Abstract
We realize fast transport of ions in a segmented microstructured Paul trap. The ion is shuttled over a distance of more than 10(4) times its ground state wave function size during only five motional cycles of the trap (280 μm in 3.6 μs). Starting from a ground-state-cooled ion, we find an optimized transport such that the energy increase is as low as 0.10±0.01 motional quanta. In addition, we demonstrate that quantum information stored in a spin-motion entangled state is preserved throughout the transport. Shuttling operations are concatenated, as a proof-of-principle for the shuttling-based architecture to scalable ion trap quantum computing.
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Affiliation(s)
- A Walther
- QUANTUM, Institut für Physik, Universität Mainz, Mainz, Germany
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63
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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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64
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Johnson JE, Macklin C, Slichter DH, Vijay R, Weingarten EB, Clarke J, Siddiqi I. Heralded state preparation in a superconducting qubit. PHYSICAL REVIEW LETTERS 2012; 109:050506. [PMID: 23006157 DOI: 10.1103/physrevlett.109.050506] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2012] [Indexed: 06/01/2023]
Abstract
We demonstrate high-fidelity, quantum nondemolition, single-shot readout of a superconducting flux qubit in which the pointer state distributions can be resolved to below one part in 1000. In the weak excitation regime, continuous measurement permits the use of heralding to ensure initialization to a fiducial state, such as the ground state. This procedure boosts readout fidelity to 93.9% by suppressing errors due to spurious thermal population. Furthermore, heralding potentially enables a simple, fast qubit reset protocol without changing the system parameters to induce Purcell relaxation.
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Affiliation(s)
- J E Johnson
- Department of Physics, University of California, Berkeley, 94720, USA
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65
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Ristè D, van Leeuwen JG, Ku HS, Lehnert KW, DiCarlo L. Initialization by measurement of a superconducting quantum bit circuit. PHYSICAL REVIEW LETTERS 2012; 109:050507. [PMID: 23006158 DOI: 10.1103/physrevlett.109.050507] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2012] [Indexed: 06/01/2023]
Abstract
We demonstrate initialization by joint measurement of two transmon qubits in 3D circuit quantum electrodynamics. Homodyne detection of cavity transmission is enhanced by Josephson parametric amplification to discriminate the two-qubit ground state from single-qubit excitations nondestructively and with 98.1% fidelity. Measurement and postselection of a steady-state mixture with 4.7% residual excitation per qubit achieve 98.8% fidelity to the ground state, thus outperforming passive initialization.
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Affiliation(s)
- D Ristè
- Kavli Institute of Nanoscience, Delft University of Technology, The Netherlands
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66
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67
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Douçot B, Ioffe LB. Physical implementation of protected qubits. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:072001. [PMID: 22790777 DOI: 10.1088/0034-4885/75/7/072001] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We review the general notion of topological protection of quantum states in spin models and its relation with the ideas of quantum error correction. We show that topological protection can be viewed as a Hamiltonian realization of error correction: for a quantum code for which the minimal number of errors that remain undetected is N, the corresponding Hamiltonian model of the effects of the environment noise appears only in the Nth order of the perturbation theory.We discuss the simplest model Hamiltonians that realize topological protection and their implementation in superconducting arrays. We focus on two dual realizations: in one the protected state is stored in the parity of the Cooper pair number, in the other, in the parity of the flux number. In both cases the superconducting arrays allow a number of fault-tolerant operations that should make the universal quantum computation possible.
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Affiliation(s)
- B Douçot
- Laboratoire de Physique Théorique et Hautes Énergies, CNRS UMR 7589 et Université Paris 6, Boîte 126, 4 place Jussieu, 75252 Paris Cedex 05, France
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68
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Siewert J, Eltschka C. Quantifying tripartite entanglement of three-qubit generalized Werner states. PHYSICAL REVIEW LETTERS 2012; 108:230502. [PMID: 23003929 DOI: 10.1103/physrevlett.108.230502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2012] [Indexed: 06/01/2023]
Abstract
Multipartite entanglement is a key concept in quantum mechanics for which, despite the experimental progress in entangling three or more quantum devices, there is still no general quantitative theory that exists. In order to characterize the robustness of multipartite entanglement, one often employs generalized Werner states, that is, mixtures of a Greenberger-Horne-Zeilinger (GHZ) state and the completely unpolarized state. While two-qubit Werner states have been instrumental for various important advancements in quantum information, as of now there is no quantitative account for such states of more than two qubits. By using the GHZ symmetry introduced recently, we find exact results for tripartite entanglement in three-qubit generalized Werner states and, moreover, the entire family of full-rank mixed states that share the same symmetries.
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Affiliation(s)
- Jens Siewert
- Departamento de Química Física, Universidad del País Vasco UPV/EHU, 48080 Bilbao, Spain
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69
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Fowler AG, Whiteside AC, Hollenberg LCL. Towards practical classical processing for the surface code. PHYSICAL REVIEW LETTERS 2012; 108:180501. [PMID: 22681050 DOI: 10.1103/physrevlett.108.180501] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2011] [Indexed: 06/01/2023]
Abstract
The surface code is unarguably the leading quantum error correction code for 2D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and flexible, arbitrarily long-range logical gates. These highly desirable features come at the cost of significant classical processing complexity. We show how to perform the processing associated with an n×n lattice of qubits, each being manipulated in a realistic, fault-tolerant manner, in O(n2) average time per round of error correction. We also describe how to parallelize the algorithm to achieve O(1) average processing per round, using only constant computing resources per unit area and local communication. Both of these complexities are optimal.
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Affiliation(s)
- Austin G Fowler
- Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Victoria 3010, Australia
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70
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Gustavsson S, Bylander J, Yan F, Forn-Díaz P, Bolkhovsky V, Braje D, Fitch G, Harrabi K, Lennon D, Miloshi J, Murphy P, Slattery R, Spector S, Turek B, Weir T, Welander PB, Yoshihara F, Cory DG, Nakamura Y, Orlando TP, Oliver WD. Driven dynamics and rotary echo of a qubit tunably coupled to a harmonic oscillator. PHYSICAL REVIEW LETTERS 2012; 108:170503. [PMID: 22680846 DOI: 10.1103/physrevlett.108.170503] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2011] [Indexed: 06/01/2023]
Abstract
We have investigated the driven dynamics of a superconducting flux qubit that is tunably coupled to a microwave resonator. We find that the qubit experiences an oscillating field mediated by off-resonant driving of the resonator, leading to strong modifications of the qubit Rabi frequency. This opens an additional noise channel, and we find that low-frequency noise in the coupling parameter causes a reduction of the coherence time during driven evolution. The noise can be mitigated with the rotary-echo pulse sequence, which, for driven systems, is analogous to the Hahn-echo sequence.
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Affiliation(s)
- S Gustavsson
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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71
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Romero G, Ballester D, Wang YM, Scarani V, Solano E. Ultrafast quantum gates in circuit QED. PHYSICAL REVIEW LETTERS 2012; 108:120501. [PMID: 22540561 DOI: 10.1103/physrevlett.108.120501] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2011] [Indexed: 05/10/2023]
Abstract
We present a method to implement ultrafast two-qubit gates valid for the ultrastrong coupling and deep strong coupling regimes of light-matter interaction, considering state-of-the-art circuit quantum electrodynamics technology. Our proposal includes a suitable qubit architecture and is based on a four-step sequential displacement of the intracavity field, operating at a time proportional to the inverse of the resonator frequency. Through ab initio calculations, we show that these quantum gates can be performed at subnanosecond time scales while keeping a fidelity above 99%.
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Affiliation(s)
- G Romero
- Departamento de Química Física, Universidad del País Vasco UPV/EHU, Apartado 644, 48080 Bilbao, Spain
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72
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Dewes A, Ong FR, Schmitt V, Lauro R, Boulant N, Bertet P, Vion D, Esteve D. Characterization of a two-transmon processor with individual single-shot qubit readout. PHYSICAL REVIEW LETTERS 2012; 108:057002. [PMID: 22400953 DOI: 10.1103/physrevlett.108.057002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2011] [Indexed: 05/31/2023]
Abstract
We report the characterization of a two-qubit processor implemented with two capacitively coupled tunable superconducting qubits of the transmon type, each qubit having its own nondestructive single-shot readout. The fixed capacitive coupling yields the sqrt[iSWAP] two-qubit gate for a suitable interaction time. We reconstruct by state tomography the coherent dynamics of the two-bit register as a function of the interaction time, observe a violation of the Bell inequality by 22 standard deviations after correcting readout errors, and measure by quantum process tomography a gate fidelity of 90%.
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Affiliation(s)
- A Dewes
- Quantronics group, Service de Physique de l'État Condensé (CNRS URA 2464), IRAMIS, DSM, CEA-Saclay, 91191 Gif-sur-Yvette, France
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73
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Realization of three-qubit quantum error correction with superconducting circuits. Nature 2012; 482:382-5. [PMID: 22297844 DOI: 10.1038/nature10786] [Citation(s) in RCA: 104] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2011] [Accepted: 12/07/2011] [Indexed: 11/08/2022]
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74
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Fedorov A, Steffen L, Baur M, da Silva MP, Wallraff A. Implementation of a Toffoli gate with superconducting circuits. Nature 2011; 481:170-2. [PMID: 22170609 DOI: 10.1038/nature10713] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2011] [Accepted: 11/15/2011] [Indexed: 11/09/2022]
Abstract
The Toffoli gate is a three-quantum-bit (three-qubit) operation that inverts the state of a target qubit conditioned on the state of two control qubits. It makes universal reversible classical computation possible and, together with a Hadamard gate, forms a universal set of gates in quantum computation. It is also a key element in quantum error correction schemes. The Toffoli gate has been implemented in nuclear magnetic resonance, linear optics and ion trap systems. Experiments with superconducting qubits have also shown significant progress recently: two-qubit algorithms and two-qubit process tomography have been implemented, three-qubit entangled states have been prepared, first steps towards quantum teleportation have been taken and work on quantum computing architectures has been done. Implementation of the Toffoli gate with only single- and two-qubit gates requires six controlled-NOT gates and ten single-qubit operations, and has not been realized in any system owing to current limits on coherence. Here we implement a Toffoli gate with three superconducting transmon qubits coupled to a microwave resonator. By exploiting the third energy level of the transmon qubits, we have significantly reduced the number of elementary gates needed for the implementation of the Toffoli gate, relative to that required in theoretical proposals using only two-level systems. Using full process tomography and Monte Carlo process certification, we completely characterize the Toffoli gate acting on three independent qubits, measuring a fidelity of 68.5 ± 0.5 per cent. A similar approach to realizing characteristic features of a Toffoli-class gate has been demonstrated with two qubits and a resonator and achieved a limited characterization considering only the phase fidelity. Our results reinforce the potential of macroscopic superconducting qubits for the implementation of complex quantum operations with the possibility of quantum error correction.
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Affiliation(s)
- A Fedorov
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland.
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75
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Affiliation(s)
- David P. DiVincenzo
- Rheinisch-Westfaelische Technische Hochschule Aachen, Forschungszentrum Juelich, Juelich 52425 Germany
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