Experimental quantum teleportation of propagating microwaves

  1. K. G. Fedorov,
  2. M. Renger,
  3. S. Pogorzalek,
  4. R. Di Candia,
  5. Q. Chen,
  6. Y. Nojiri,
  7. K. Inomata,
  8. Y. Nakamura,
  9. M. Partanen,
  10. A. Marx,
  11. R. Gross,
  12. and F. Deppe
The modern field of quantum communication thrives on promise to deliver efficient and unconditionally secure ways to exchange information by exploiting quantum laws of physics. Here,
quantum teleportation stands out as an exemplary protocol allowing for the disembodied and safe transfer of unknown quantum states using quantum entanglement and classical communication as resources. The experimental feasibility of quantum teleportation with propagating waves, relevant to communication scenarios, has been demonstrated in various physical settings. However, an analogous implementation of quantum teleportation in the microwave domain was missing so far. At the same time, recent breakthroughs in quantum computation with superconducting circuits have triggered a demand for quantum communication between spatially separated superconducting processors operated at microwave frequencies. Here, we demonstrate a realization of deterministic quantum teleportation of coherent microwave states by exploiting two-mode squeezing and analog feedforward over macroscopic distances d=42cm. We achieve teleportation fidelities F=0.689±0.004 exceeding the no-cloning Fnc=2/3 threshold for coherent states with an average photon number of up to nd=1.1. Our results provide a key ingredient for the teleportation-based quantum gate for modular quantum computing with superconducting circuits and establish a solid foundation for future microwave quantum local area networks.

Beyond the standard quantum limit of parametric amplification

  1. M. Renger,
  2. S. Pogorzalek,
  3. Q. Chen,
  4. Y. Nojiri,
  5. K. Inomata,
  6. Y. Nakamura,
  7. M. Partanen,
  8. A. Marx,
  9. R. Gross,
  10. F. Deppe,
  11. and K. G. Fedorov
The low-noise amplification of weak microwave signals is crucial for countless protocols in quantum information processing. Quantum mechanics sets an ultimate lower limit of half a
photon to the added input noise for phase-preserving amplification of narrowband signals, also known as the standard quantum limit (SQL). This limit, which is equivalent to a maximum quantum efficiency of 0.5, can be overcome by employing nondegenerate parametric amplification of broadband signals. We show that, in principle, a maximum quantum efficiency of 1 can be reached. Experimentally, we find a quantum efficiency of 0.69±0.02, well beyond the SQL, by employing a flux-driven Josephson parametric amplifier and broadband thermal signals. We expect that our results allow for fundamental improvements in the detection of ultraweak microwave signals.

Secure quantum remote state preparation of squeezed microwave states

  1. S. Pogorzalek,
  2. K. G. Fedorov,
  3. M. Xu,
  4. A. Parra-Rodriguez,
  5. M. Sanz,
  6. M. Fischer,
  7. E. Xie,
  8. K. Inomata,
  9. Y. Nakamura,
  10. E. Solano,
  11. A. Marx,
  12. F. Deppe,
  13. and R. Gross
Quantum communication protocols based on nonclassical correlations can be more efficient than known classical methods and offer intrinsic security over direct state transfer. In particular,
remote state preparation aims at the creation of a desired and known quantum state at a remote location using classical communication and quantum entanglement. We present an experimental realization of deterministic continuous-variable remote state preparation in the microwave regime over a distance of 35 cm. By employing propagating two-mode squeezed microwave states and feedforward, we achieve the remote preparation of squeezed states with up to 1.6 dB of squeezing below the vacuum level. We quantify security in our implementation using the concept of the one-time pad. Our results represent a significant step towards microwave quantum networks between superconducting circuits.

Finite-time quantum correlations of propagating squeezed microwaves

  1. Kirill G. Fedorov,
  2. S. Pogorzalek,
  3. U. Las Heras,
  4. M. Sanz,
  5. P. Yard,
  6. P. Eder,
  7. M. Fischer,
  8. J. Goetz,
  9. E. Xie,
  10. K. Inomata,
  11. Y. Nakamura,
  12. R. Di Candia,
  13. E. Solano,
  14. A. Marx,
  15. F. Deppe,
  16. and R. Gross
Two-mode squeezing is a fascinating example of quantum entanglement manifested in cross-correlations of incompatible observables between two subsystems. At the same time, these subsystems
themselves may contain no quantum signatures in their self-correlations. These properties make two-mode squeezed (TMS) states an ideal resource for applications in quantum communication, quantum computation, and quantum illumination. Propagating microwave TMS states can be produced by a beam splitter distributing single mode squeezing emitted from Josephson parametric amplifiers (JPA) into two output paths. In this work, we experimentally quantify the dephasing process of quantum correlations in propagating TMS microwave states and accurately describe it with a theory model. In this way, we gain an insight into quantum entanglement limits and predict high fidelities for benchmark quantum communication protocols such as remote state preparation and quantum teleportation.

Tunable quantum gate between a superconducting atom and a propagating microwave photon

  1. K. Koshino,
  2. K. Inomata,
  3. Z. R. Lin,
  4. Y. Tokunaga,
  5. T. Yamamoto,
  6. and Y. Nakamura
We propose a two-qubit quantum logic gate between a superconducting atom and a propagating microwave photon. The atomic qubit is encoded on its lowest two levels and the photonic qubit
is encoded on its carrier frequencies. The gate operation completes deterministically upon reflection of a photon, and various two-qubit gates (SWAP, SWAP‾‾‾‾‾‾‾√, and Identity) are realized through {\it in situ} control of the drive field. The proposed gate is applicable to construction of a network of superconducting atoms, which enables gate operations between non-neighboring atoms.

Displacement of propagating squeezed microwave states

  1. Kirill G. Fedorov,
  2. L. Zhong,
  3. S. Pogorzalek,
  4. P. Eder,
  5. M. Fischer,
  6. J. Goetz,
  7. E. Xie,
  8. F. Wulschner,
  9. K. Inomata,
  10. T. Yamamoto,
  11. Y. Nakamura,
  12. R. Di Candia,
  13. U. Las Heras,
  14. M. Sanz,
  15. E. Solano,
  16. E. P. Menzel,
  17. F. Deppe,
  18. A. Marx,
  19. and R. Gross
Displacement of propagating quantum states of light is a fundamental operation for quantum communication. It enables fundamental studies on macroscopic quantum coherence and plays an
important role in quantum teleportation protocols with continuous variables. In our experiments we have successfully implemented this operation for propagating squeezed microwave states. We demonstrate that, even for strong displacement amplitudes, there is no degradation of the squeezing level in the reconstructed quantum states. Furthermore, we confirm that path entanglement generated by using displaced squeezed states stays constant over a wide range of the displacement power.

Josephson parametric phase-locked oscillator and its application to dispersive readout of superconducting qubits

  1. Z. R. Lin,
  2. K. Inomata,
  3. K. Koshino,
  4. W. D. Oliver,
  5. Y. Nakamura,
  6. J. S. Tsai,
  7. and T. Yamamoto
The parametric phase-locked oscillator (PPLO), also known as a parametron, is a resonant circuit in which one of the reactances is periodically modulated. It can detect, amplify, and
store binary digital signals in the form of two distinct phases of self-oscillation. Indeed, digital computers using PPLOs based on a magnetic ferrite ring or a varactor diode as its fundamental logic element were successfully operated in 1950s and 1960s. More recently, basic bit operations have been demonstrated in an electromechanical resonator, and an Ising machine based on optical PPLOs has been proposed. Here, using a PPLO realized with Josephson-junction circuitry, we demonstrate the demodulation of a microwave signal digitally modulated by binary phase-shift keying. Moreover, we apply this demodulation capability to the dispersive readout of a superconducting qubit. This readout scheme enables a fast and latching-type readout, yet requires only a small number of readout photons in the resonator to which the qubit is coupled, thus featuring the combined advantages of several disparate schemes. We have achieved high-fidelity, single-shot, and non-destructive qubit readout with Rabi-oscillation contrast exceeding 90%, limited primarily by the qubit’s energy relaxation.

Microwave Down-Conversion with an Impedance-Matched Λ System in Driven Circuit QED

  1. K. Inomata,
  2. K. Koshino,
  3. Z. R. Lin,
  4. W. D. Oliver,
  5. J. S. Tsai,
  6. Y. Nakamura,
  7. and T. Yamamoto
By driving a dispersively coupled qubit-resonator system, we realize an „impedance-matched“ Λ system that has two identical radiative decay rates from the top level and
interacts with a semi-infinite waveguide. It has been predicted that a photon input from the waveguide deterministically induces a Raman transition in the system and switches its electronic state. We confirm this through microwave response to a continuous probe field, observing near-perfect (99.7%) extinction of the reflection and highly efficient (74%) frequency down-conversion. These proof-of-principle results lead to deterministic quantum gates between material qubits and microwave photons and open the possibility for scalable quantum networks interconnected with waveguide photons.

Single-shot readout of a superconducting flux qubit with a flux-driven Josephson parametric amplifier

  1. Z. R. Lin,
  2. K. Inomata,
  3. W. D. Oliver,
  4. K. Koshino,
  5. Y. Nakamura,
  6. J. S. Tsai,
  7. and T. Yamamoto
We report single-shot readout of a superconducting flux qubit by using a flux-driven Josephson parametric amplifier (JPA). After optimizing the readout power, gain of the JPA and timing
of the data acquisition, we observe the Rabi oscillations with a contrast of 74% which is mainly limited by the bandwidth of the JPA and the energy relaxation of the qubit. The observation of quantum jumps between the qubit eigenstates under continuous monitoring indicates the nondestructiveness of the readout scheme.

Squeezing with a flux-driven Josephson parametric amplifier

  1. L. Zhong,
  2. E. P. Menzel,
  3. R. Di Candia,
  4. P. Eder,
  5. M. Ihmig,
  6. A. Baust,
  7. M. Haeberlein,
  8. E. Hoffmann,
  9. K. Inomata,
  10. T. Yamamoto,
  11. Y. Nakamura,
  12. E. Solano,
  13. F. Deppe,
  14. A. Marx,
  15. and R. Gross
Josephson parametric amplifiers (JPA) are promising devices for applications in circuit quantum electrodynamics (QED) and for studies on propagating quantum microwaves because of their
good noise performance. In this work, we present a systematic characterization of a flux-driven JPA at millikelvin temperatures. In particular, we study in detail its squeezing properties by two different detection techniques. With the homodyne setup, we observe squeezing of vacuum fluctuations by superposing signal and idler bands. For a quantitative analysis we apply dual-path cross-correlation techniques to reconstruct the Wigner functions of various squeezed vacuum and thermal states. At 10 dB signal gain, we find 4.9+-0.2 dB squeezing below vacuum. In addition, we discuss the physics behind squeezed coherent microwave fields. Finally, we analyze the JPA noise temperature in the degenerate mode and find a value smaller than the standard quantum limit for phase-insensitive amplifiers.