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Deterministic quantum teleportation with feed-forward in a solid state system


Engineered macroscopic quantum systems based on superconducting electronic circuits are attractive for experimentally exploring diverse questions in quantum information science1,2,3. At the current state of the art, quantum bits (qubits) are fabricated, initialized, controlled, read out and coupled to each other in simple circuits. This enables the realization of basic logic gates4, the creation of complex entangled states5,6 and the demonstration of algorithms7 or error correction8. Using different variants of low-noise parametric amplifiers9, dispersive quantum non-demolition single-shot readout of single-qubit states with high fidelity has enabled continuous10 and discrete11 feedback control of single qubits. Here we realize full deterministic quantum teleportation with feed-forward in a chip-based superconducting circuit architecture12,13,14. We use a set of two parametric amplifiers for both joint two-qubit and individual qubit single-shot readout, combined with flexible real-time digital electronics. Our device uses a crossed quantum bus technology that allows us to create complex networks with arbitrary connecting topology in a planar architecture. The deterministic teleportation process succeeds with order unit probability for any input state, as we prepare maximally entangled two-qubit states as a resource and distinguish all Bell states in a single two-qubit measurement with high efficiency and high fidelity. We teleport quantum states between two macroscopic systems separated by 6 mm at a rate of 104 s−1, exceeding other reported implementations. The low transmission loss of superconducting waveguides is likely to enable the range of this and other schemes to be extended to significantly larger distances, enabling tests of non-locality and the realization of elements for quantum communication at microwave frequencies. The demonstrated feed-forward may also find application in error correction schemes.

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Figure 1: Circuit diagram of quantum teleportation.
Figure 2: Diagrams of sample and measurement setup.
Figure 3: State-transfer process matrix for quantum teleportation.


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We thank A. Blais, F. Marquardt, S. Filipp and R. Renner for discussion and feedback; and J. Heinsoo, L. Heinzle, A. Landig, Y. Liu, F. Lüthi and T. Menke for technical contributions to the experimental work. This work was supported financially by Eidgenössische Technische Hochschule Zurich (ETH Zurich), the EU Integrated Projects SOLID and SCALEQIT, and the Swiss National Science Foundation’s National Centre of Competence in Research ‘Quantum Science & Technology’.

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Authors and Affiliations



The experiments were performed by L.S., A.F., Y.S., M.O., P.K. and M.B. The teleportation sample and parametric amplifiers were fabricated by A.F., L.S. and M.B. The air-bridge technology was developed by G.P.-H. and L.S. The FPGA firmware was implemented by Y.S. and C.L. The parametric amplifiers were designed by C.E., who also oversaw their operation. The manuscript was written by L.S., A.F. and A.W. All authors commented on the manuscript. The project was led by A.F. and A.W.

Corresponding authors

Correspondence to L. Steffen or A. Wallraff.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Pulse sequence of the teleportation protocol with feed-forward.

The pulses implement the creation of an entangled pair between Q2 and Q3 (blue), the preparation of the state to be teleported on Q1 (green), the basis transformation from the Bell to the computational basis and the subsequent readout of Q1 and Q2 (red), the dynamical decoupling (DD) pulses, conditional rotations and the state tomography on Q3 (green). Gaussian-shaped sinusoids represent the microwave pulses applied to the respective charge bias lines of the qubits; sinusoids on the resonators represent the readout tones; and the squares labelled cphase represent the flux pulses that shift the frequency of a qubit to implement a controlled-phase gate between the marked qubits, where the interaction is mediated through the resonator indicated with a bar of the same colour as the flux pulse. The inset shows the time used for implementing the conditional feed-forward rotations. The total feed-forward time is the sum of the ramp-up time of the measurement tone, the integration time of the measurement signal and the delay times induced by the FPGA signal processing, the AWG trigger and the cables.

Extended Data Figure 2 Characterization of the joint readout of Q1 and Q2.

a, Histogram of the integrated signal quadrature-amplitude amplified phase-sensitively when preparing the states |00〉 (blue), |01〉 (red), |10〉 (yellow) and |11〉 (green). b, Scatter plot of integrated (I, Q) quadratures of the measurement signal amplified in the phase-preserving mode when preparing the states |00〉 (blue), |01〉 (red), |10〉 (yellow) and |11〉 (green).

Extended Data Figure 3 Characterization of the output states.

Real (blue) and imaginary (red) parts of the reconstructed density matrices of the state |ψout〉 for the indicated input states |ψin〉 obtained from state tomography when (a) post-selecting data on a 00 outcome of the Bell measurement (b) using averaged readout on Q3 while performing fully deterministic teleportation with feed-forward. The ideally expected outcomes are indicated with wireframes. The state fidelities are indicated in the black boxes.

Extended Data Table 1 Success probabilities for the joint readout
Extended Data Table 2 Process fidelities of the feed-forward pulses

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Steffen, L., Salathe, Y., Oppliger, M. et al. Deterministic quantum teleportation with feed-forward in a solid state system. Nature 500, 319–322 (2013).

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