In-situ tunable nonlinearity and competing signal paths in coupled superconducting resonators

  1. Michael Fischer,
  2. Qi-Ming Chen,
  3. Christian Besson,
  4. Peter Eder,
  5. Jan Goetz,
  6. Stefan Pogorzalek,
  7. Michael Renger,
  8. Edwar Xie,
  9. Michael J. Hartmann,
  10. Kirill G. Fedorov,
  11. Achim Marx,
  12. Frank Deppe,
  13. and Rudolf Gross
We have fabricated and studied a system of two tunable and coupled nonlinear superconducting resonators. The nonlinearity is introduced by galvanically coupled dc-SQUIDs. We simulate
the system response by means of a circuit model, which includes an additional signal path introduced by the electromagnetic environment. Furthermore, we present two methods allowing us to experimentally determine the nonlinearity. First, we fit the measured frequency and flux dependence of the transmission data to simulations based on the equivalent circuit model. Second, we fit the power dependence of the transmission data to a model that is predicted by the nonlinear equation of motion describing the system. Our results show that we are able to tune the nonlinearity of the resonators by almost two orders of magnitude via an external coil and two on-chip antennas. The studied system represents the basic building block for larger systems, allowing for quantum simulations of bosonic many-body systems with a larger number of lattice sites.

Quantum Fourier Transform in Oscillating Modes

  1. Qi-Ming Chen,
  2. Frank Deppe,
  3. Re-Bing Wu,
  4. Luyan Sun,
  5. Yu-xi Liu,
  6. Yuki Nojiri,
  7. Stefan Pogorzalek,
  8. Michael Renger,
  9. Matti Partanen,
  10. Kirill G. Fedorov,
  11. Achim Marx,
  12. and Rudolf Gross
Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms. In typical applications such as phase estimation, a considerable number of ancilla qubits and gates are
used to form a Hilbert space large enough for high-precision results. Qubit recycling reduces the number of ancilla qubits to one, but it is only applicable to semi-classical QFT and requires repeated measurements and feedforward within the coherence time of the qubits. In this work, we explore a novel approach based on resonators that forms a high-dimensional Hilbert space for the realization of QFT. By employing the perfect state-transfer method, we map an unknown multi-qubit state to a single resonator, and obtain the QFT state in the second oscillator through cross-Kerr interaction and projective measurement. A quantitive analysis shows that our method allows for high-dimensional and fully-quantum QFT employing the state-of-the-art superconducting quantum circuits. This paves the way for implementing various QFT related quantum algorithms.

Challenges in Open-air Microwave Quantum Communication and Sensing

  1. Mikel Sanz,
  2. Kirill G. Fedorov,
  3. Frank Deppe,
  4. and Enrique Solano
Quantum communication is a holy grail to achieve secure communication among a set of partners, since it is provably unbreakable by physical laws. Quantum sensing employs quantum entanglement
as an extra resource to determine parameters by either using less resources or attaining a precision unachievable in classical protocols. A paradigmatic example is the quantum radar, which allows one to detect an object without being detected oneself, by making use of the additional asset provided by quantum entanglement to reduce the intensity of the signal. In the optical regime, impressive technological advances have been reached in the last years, such as the first quantum communication between ground and satellites, as well as the first proof-of-principle experiments in quantum sensing. The development of microwave quantum technologies turned out, nonetheless, to be more challenging. Here, we will discuss the challenges regarding the use of microwaves for quantum communication and sensing. Based on this analysis, we propose a roadmap to achieve real-life applications in these fields.

Scalable 3D quantum memory

  1. Edwar Xie,
  2. Frank Deppe,
  3. Daniel Repp,
  4. Peter Eder,
  5. Michael Fischer,
  6. Jan Goetz,
  7. Stefan Pogorzalek,
  8. Kirill G. Fedorov,
  9. Achim Marx,
  10. and Rudolf Gross
Superconducting 3D microwave cavities offer state-of-the-art coherence times and a well controlled environment for superconducting qubits. In order to realize at the same time fast
readout and long-lived quantum information storage, one can couple the qubit both to a low-quality readout and a high-quality storage cavity. However, such systems are bulky compared to their less coherent 2D counterparts. A more compact and scalable approach is achieved by making use of the multimode structure of a 3D cavity. In our work, we investigate such a device where a transmon qubit is capacitively coupled to two modes of a single 3D cavity. The external coupling is engineered so that the memory mode has an about 100 times larger quality factor than the readout mode. Using an all-microwave second-order protocol, we realize a lifetime enhancement of the stored state over the qubit lifetime by a factor of 6 with a Z-fidelity of 82%. We also find that this enhancement is not limited by fundamental constraints.

Parity-engineered light-matter interaction

  1. Jan Goetz,
  2. Frank Deppe,
  3. Kirill G. Fedorov,
  4. Peter Eder,
  5. Michael Fischer,
  6. Stefan Pogorzalek,
  7. Edwar Xie,
  8. Achim Marx,
  9. and Rudolf Gross
The concept of parity describes the inversion symmetry of a system and is of fundamental relevance in the standard model, quantum information processing, and field theory. In quantum
electrodynamics, parity is conserved and selection rules (SRs) appear when matter is probed with electromagnetic radiation. However, typically large field gradients are required to engineer the parity of the light-matter interaction operator for natural atoms. In this work, we instead irradiate a specifically designed superconducting artificial atom with spatially shaped microwave fields to select the interaction parity in situ. In this way, we observe dipole and quadrupole SRs for single state transitions and induce transparency via longitudinal coupling. Furthermore, we engineer an artificial potassium-like atom with adjustable wave function parity originating from an artificial orbital momentum provided by a resonator. Our work advances light-matter interaction to a new level with promising application perspectives in simulations of chemical compounds, quantum state engineering, and relativistic physics.

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.

Flux-driven Josephson parametric amplifiers: Hysteretic flux response and nondegenerate gain measurements

  1. Stefan Pogorzalek,
  2. Kirill G. Fedorov,
  3. Ling Zhong,
  4. Jan Goetz,
  5. Friedrich Wulschner,
  6. Michael Fischer,
  7. Peter Eder,
  8. Edwar Xie,
  9. Kunihiro Inomata,
  10. Tsuyoshi Yamamoto,
  11. Yasunobu Nakamura,
  12. Achim Marx,
  13. Frank Deppe,
  14. and Rudolf Gross
Josephson parametric amplifiers (JPA) have become key devices in quantum science and technology with superconducting circuits. In particular, they can be utilized as quantum-limited
amplifiers or as a source of squeezed microwave fields. Here, we report on the detailed measurements of five flux-driven JPAs, three of them exhibiting a hysteretic dependence of the resonant frequency versus the applied magnetic flux. We model the measured characteristics by numerical simulations based on the two-dimensional potential landscape of the dc superconducting quantum interference devices (dc-SQUID), which provide the JPA nonlinearity, for a finite screening parameter βL>0 and demonstrate excellent agreement between the numerical results and the experimental data. Furthermore, we study the nondegenerate response of different JPAs and accurately describe the experimental results with our theory.

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.

Loss mechanisms in superconducting thin film microwave resonators

  1. Jan Goetz,
  2. Frank Deppe,
  3. Max Haeberlein,
  4. Friedrich Wulschner,
  5. Christoph W. Zollitsch,
  6. Sebastian Meier,
  7. Michael Fischer,
  8. Peter Eder,
  9. Edwar Xie,
  10. Kirill G. Fedorov,
  11. Edwin P. Menzel,
  12. Achim Marx,
  13. and Rudolf Gross
We present a systematic analysis of the internal losses of superconducting coplanar waveguide microwave resonators based on niobium thin films on silicon substrates. At millikelvin
temperatures and low power, we find that the characteristic saturation power of two-level state (TLS) losses shows a pronounced temperature dependence. Furthermore, TLS losses can also be introduced by Nb/Al interfaces in the center conductor, when the interfaces are not positioned at current nodes of the resonator. In addition, we confirm that TLS losses can be reduced by proper surface treatment. For resonators including Al, quasiparticle losses become relevant above \SI{200}{\milli\kelvin}. Finally, we investigate how losses generated by eddy currents in the conductive material on the backside of the substrate can be minimized by using thick enough substrates or metals with high conductivity on the substrate backside.

Fluxon readout of a superconducting qubit

  1. Kirill G. Fedorov,
  2. Anastasia V. Shcherbakova,
  3. Michael J. Wolf,
  4. Detlef Beckmann,
  5. and Alexey V. Ustinov
Quantum computing using superconducting circuits underwent rapid development in the last decade. This field has propelled from quantum manipulation of single two-level systems to complex
designs employing multiple coupled qubits allowing one to execute simple quantum algorithms. On the way to a practical quantum computer, a need for scalable interfaces between classical circuits and the quantum counterparts has arisen. Low-temperature superconducting single-flux quantum (SFQ) logic employs magnetic fluxons in Josephson transmission lines (JTLs) as basic bits for classical computation. Here, we report on an experiment implementing a direct link between SFQ electronics and a superconducting qubit. We demonstrate a readout of the state of a flux qubit through a frequency shift of a single fluxon oscillating in a JTL. The energy spectrum of the flux qubit is measured using this technique. The demonstrated approach may open ways to future full-scale integration of solid-state quantum computers with digital SFQ electronics.