Nature  Letter
Autonomously stabilized entanglement between two superconducting quantum bits
 S. Shankar^{1}^{, }
 M. Hatridge^{1}^{, }
 Z. Leghtas^{1}^{, }
 K. M. Sliwa^{1}^{, }
 A. Narla^{1}^{, }
 U. Vool^{1}^{, }
 S. M. Girvin^{1}^{, }
 L. Frunzio^{1}^{, }
 M. Mirrahimi^{1, 2}^{, }
 M. H. Devoret^{1}^{, }
 Journal name:
 Nature
 Volume:
 504,
 Pages:
 419–422
 Date published:
 DOI:
 doi:10.1038/nature12802
 Received
 Accepted
 Published online
Quantum error correction codes are designed to protect an arbitrary state of a multiqubit register from decoherenceinduced errors^{1}, but their implementation is an outstanding challenge in the development of largescale quantum computers. The first step is to stabilize a nonequilibrium state of a simple quantum system, such as a quantum bit (qubit) or a cavity mode, in the presence of decoherence. This has recently been accomplished using measurementbased feedback schemes^{2, 3, 4, 5}. The next step is to prepare and stabilize a state of a composite system^{6, 7, 8}. Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result is achieved using an autonomous feedback scheme that combines continuous drives along with a specifically engineered coupling between the twoqubit register and a dissipative reservoir. Similar autonomous feedback techniques have been used for qubit reset^{9}, singlequbit state stabilization^{10}, and the creation^{11} and stabilization^{6} of states of multipartite quantum systems. Unlike conventional, measurementbased schemes, the autonomous approach uses engineered dissipation to counteract decoherence^{12, 13, 14, 15}, obviating the need for a complicated external feedback loop to correct errors. Instead, the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building block for quantum information processing. Such autonomous schemes, which are broadly applicable to a variety of physical systems, as demonstrated by the accompanying paper on trapped ion qubits^{16}, will be an essential tool for the implementation of quantum error correction.
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At a glance
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References
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Author information
Affiliations

Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
 S. Shankar,
 M. Hatridge,
 Z. Leghtas,
 K. M. Sliwa,
 A. Narla,
 U. Vool,
 S. M. Girvin,
 L. Frunzio,
 M. Mirrahimi &
 M. H. Devoret

INRIA ParisRocquencourt, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France
 M. Mirrahimi
Contributions
S.S. performed the experiment and analysed the data with assistance from M.H. and Z.L. Z.L. proposed the autonomous feedback protocol and performed numerical simulations under the guidance of M.M. K.M.S., A.N. and L.F. contributed to the experimental apparatus, and U.V. contributed to the theoretical modelling under the guidance of S.M.G. M.H.D. supervised the project. S.S., M.H. and M.H.D. wrote the manuscript. All authors provided suggestions for the experiment, discussed the results and contributed to the manuscript.
Competing financial interests
The authors declare no competing financial interests.
Author details
S. Shankar
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M. Hatridge
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Z. Leghtas
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K. M. Sliwa
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A. Narla
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U. Vool
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S. M. Girvin
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L. Frunzio
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M. Mirrahimi
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M. H. Devoret
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Extended data figures and tables
Extended Data Figures
 Extended Data Figure 1: Experiment schematic. (212 KB)
The qubit–cavity setup as well as the JPC amplifier is mounted on the base stage of a dilution refrigerator (bottom of diagram) which is operated at less than 20 mK. The roomtemperature setup consists of electronics used for qubit control (top left) and for qubit measurement (top right). The experiment is controlled by an arbitrary waveform generator (AWG), which produces analogue waveforms and also supplies digital markers (not shown) to the pulsed microwave sources. The drives for stabilization and qubit control are generated from four microwave sources in the present experiment, although the two cavity drives, and , could be produced in principle from the same source. These drives were combined with a measurement drive and sent through filtered and attenuated lines to the cavity input at the base of the fridge. The cavity output is directed to the signal port of a JPC, whose idler is terminated in a 50Ω load. The JPC is powered by a drive applied to its pump port. The fridge input for JPC tuning is used solely for initial tune up and is terminated during the stabilization experiment. The cavity output signal is amplified in reflection by the JPC and then output from the fridge after further amplification. The output signal is demodulated at room temperature and then digitized by an analoguetodigital converter along with a reference copy of the measurement drive.
 Extended Data Figure 2: Singleshot readout of the observable gggg. (168 KB)
a, Histogram of measurement outcomes recorded by the projective readout used for tomography. Outcome I_{m} = 0 implies that no microwave field was received in the I quadrature for that measurement. The GG histogram (blue dots) was recorded with the qubits initially prepared in gg with a fidelity of 99.5%. The histogram (red dots) was recorded after identical preparation followed by a πpulse on Alice. Solid lines are Gaussian fits. The horizontal axis of measurement outcomes I_{m} is scaled by the average of the standard deviations of the two Gaussians, showing 5.5 standard deviations between the centres of the two distributions. Dashed line indicates the threshold that distinguishes GG from : an outcome of is associated with GG, whereas is associated with . b. Summary of the fidelity of a single projective readout of the state of the two qubits assuming the separatrix .
 Extended Data Figure 3: Calibration of systematic errors in tomography. (163 KB)
Fidelity of twoqubit Clifford states measured by tomography identical to that used in the Bell state stabilization protocol. Clifford states are prepared by starting in gg with a fidelity of 99.5% and then performing individual singlequbit rotations. The fidelity varies from a maximum of 94% for the state −Z, −Z, to a minimum of 87% for the state +Y, +Z, averaging 90% over the 36 states (dashed line).
 Extended Data Figure 4: Predicted fidelity to ϕ_{−} as a function of drive parameters and Ω^{n} under the conditions of the present experiment. (249 KB)
Ω^{0} is taken to be κ/2 in this simulation. A broad distribution of parameter values resulting in a fidelity of about 70% indicates the robustness of the autonomous feedback protocol to variations in the drives.
Additional data

Extended Data Figure 1: Experiment schematic.Hover over figure to zoom

Extended Data Figure 2: Singleshot readout of the observable gggg.Hover over figure to zoom

Extended Data Figure 3: Calibration of systematic errors in tomography.Hover over figure to zoom

Extended Data Figure 4: Predicted fidelity to ϕ_{−} as a function of drive parameters and Ω^{n} under the conditions of the present experiment.Hover over figure to zoom