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.

Spectroscopic observation of crossover from classical Duffing oscillator to Kerr parametric oscillator

  1. T. Yamaji,
  2. S. Kagami,
  3. A. Yamaguchi,
  4. T. Satoh,
  5. K. Koshino,
  6. H. Goto,
  7. Z. R. Lin,
  8. Y. Nakamura,
  9. and T. Yamamoto
We study microwave response of a Josephson parametric oscillator consisting of a superconducting transmission-line resonator with an embedded dc-SQUID. The dc-SQUID allows to control
the magnitude of a Kerr nonlinearity over the ranges where it is smaller or larger than the photon loss rate. Spectroscopy measurements reveal the change of the microwave response from a classical Duffing oscillator to a Kerr parametric oscillator in a single device. In the single-photon Kerr regime, we observe parametric oscillations with a well-defined phase of either 0 or π, whose probability can be controlled by an externally injected signal.

Time molecules with periodically driven interacting qubits

  1. K. V. Shulga,
  2. I. Vakulchyk,
  3. Y. Nakamura,
  4. S. Flach,
  5. and M. V. Fistul
We provide numerical evidence for a temporal quantum-mechanical interference phenomenon: time molecules (TM). A variety of such stroboscopic states are observed in the dynamics of two
interacting qubits subject to a periodic sequence of π-pulses with the period T. The TMs appear periodically in time and have a large duration, δtTM≫T. All TMs demonstrate an almost zero value of the total polarization and a strong enhancement of the entanglement entropy S up to the maximum value S=ln2 of a corresponding Bell state. The TMs are generated by the commensurability of the Floquet eigenvalues and the presence of maximally entangled Floquet eigenstates. The TMs remain stable with detuned system parameters and with an increased number of qubits. The TMs can be observed in microwave experiments with an array of superconducting qubits.

Probing XY phase transitions in a Josephson junction array with tunable frustration

  1. R. Cosmic,
  2. K. Kawabata,
  3. Y. Ashida,
  4. H. Ikegami,
  5. S. Furukawa,
  6. P. Patil,
  7. J. M. Taylor,
  8. and Y. Nakamura
The seminal theoretical works of Berezinskii, Kosterlitz, and Thouless presented a new paradigm for phase transitions in condensed matter that are driven by topological excitations.
These transitions have been extensively studied in the context of two-dimensional XY models — coupled compasses — and have generated interest in the context of quantum simulation. Here, we use a circuit quantum-electrodynamics architecture to study the critical behavior of engineered XY models through their dynamical response. In particular, we examine not only the unfrustrated case but also the fully-frustrated case which leads to enhanced degeneracy associated with the spin rotational [U(1)] and discrete chiral (Z2) symmetries. The nature of the transition in the frustrated case has posed a challenge for theoretical studies while direct experimental probes remain elusive. Here we identify the transition temperatures for both the unfrustrated and fully-frustrated XY models by probing a Josephson junction array close to equilibrium using weak microwave excitations and measuring the temperature dependence of the effective damping obtained from the complex reflection coefficient. We argue that our probing technique is primarily sensitive to the dynamics of the U(1) part.

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.

Quantum non-demolition detection of an itinerant microwave photon

  1. S. Kono,
  2. K. Koshino,
  3. Y. Tabuchi,
  4. A. Noguchi,
  5. and Y. Nakamura
Photon detectors are an elementary tool to measure electromagnetic waves at the quantum limit and are heavily demanded in the emerging quantum technologies such as communication, sensing,
and computing. Of particular interest is a quantum non-demolition (QND) type detector, which projects the quantum state of a photonic mode onto the photon-number basis without affecting the temporal or spatial properties. This is in stark contrast to conventional photon detectors which absorb a photon to trigger a `click‘ and thus inevitably destroy the photon. The long-sought QND detection of a flying photon was recently demonstrated in the optical domain using a single atom in a cavity. However, the counterpart for microwaves has been elusive despite the recent progress in microwave quantum optics using superconducting circuits. Here, we implement a deterministic entangling gate between a superconducting qubit and a propagating microwave pulse mode reflected by a cavity containing the qubit. Using the entanglement and the high-fidelity qubit readout, we demonstrate a QND detection of a single photon with the quantum efficiency of 0.84, the photon survival probability of 0.87, and the dark-count probability of 0.0147. Our scheme can be a building block for quantum networks connecting distant qubit modules as well as a microwave photon counting device for multiple-photon signals.

Information-to-work conversion by Maxwell’s demon in a superconducting circuit-QED system

  1. Y. Masuyama,
  2. K. Funo,
  3. Y. Murashita,
  4. A. Noguchi,
  5. S. Kono,
  6. Y. Tabuchi,
  7. R. Yamazaki,
  8. M. Ueda,
  9. and Y. Nakamura
The gedanken experiment of Maxwell’s demon has led to the studies concerning the foundations of thermodynamics and statistical mechanics. The demon measures fluctuations of a
system’s observable and converts the information gain into work via feedback control. Recent developments have elucidated the relationship between the acquired information and the entropy production and generalized the second law of thermodynamics and the fluctuation theorems. Here we extend the scope to a system subject to quantum fluctuations by exploiting techniques in superconducting circuit quantum electrodynamics. We implement Maxwell’s demon equipped with coherent control and quantum nondemolition projective measurements on a superconducting qubit, where we verify the generalized integral fluctuation theorems and demonstrate the information-to-work conversion. This reveals the potential of superconducting circuits as a versatile platform for investigating quantum information thermodynamics under feedback control, which is closely linked to quantum error correction for computation and metrology.

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.

Nonclassical photon number distribution in a superconducting cavity under a squeezed drive

  1. S. Kono,
  2. Y. Masuyama,
  3. T. Ishikawa,
  4. Y. Tabuchi,
  5. R. Yamazaki,
  6. K. Usami,
  7. K. Koshino,
  8. and Y. Nakamura
A superconducting qubit in the strong dispersive regime of a circuit quantum electrodynamics system is a powerful probe for microwave photons in a cavity mode. In this regime, a qubit
spectrum is split into multiple peaks, with each peak corresponding to an individual photon number in the cavity (discrete ac Stark shift). Here, we measure the qubit spectrum in the cavity that is driven continuously with a squeezed vacuum field generated by a Josephson parametric amplifier. By fitting the qubit spectrum with a model which takes into account the finite qubit excitation power, the photon number distribution, which is dissimilar from the apparent peak area ratio in the spectrum, is determined. The photon number distribution shows the even-odd photon number oscillation and quantitatively fulfills Klyshko’s criterion for the nonclassicality.