The scattering coefficients of superconducting microwave resonators: II. System-bath approach

  1. Qi-Ming Chen,
  2. Matti Partanen,
  3. Florian Fesquet,
  4. Kedar E. Honasoge,
  5. Fabian Kronowetter,
  6. Yuki Nojiri,
  7. Michael Renger,
  8. Kirill G. Fedorov,
  9. Achim Marx,
  10. Frank Deppe,
  11. and Rudolf Gross
We describe a unified quantum approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. We also generalize the method
to a chain of resonators in either hanger- or necklace-type, and reveal interesting transport properties similar to a photonic crystal. It is shown that both the quantum and classical analyses provide consistent results, and they together form a solid basis for analyzing the decoherence effect in a general microwave resonator. These results pave the way for designing and applying superconducting microwave resonators in complex circuits, and should stimulate the interest of distinguishing different decoherence mechanisms of a resonator mode beyond free energy relaxation.

The scattering coefficients of superconducting microwave resonators: I. Transfer-matrix approach

  1. Qi-Ming Chen,
  2. Meike Pfeiffer,
  3. Matti Partanen,
  4. Florian Fesquet,
  5. Kedar E. Honasoge,
  6. Fabian Kronowetter,
  7. Yuki Nojiri,
  8. Michael Renger,
  9. Kirill G. Fedorov,
  10. Achim Marx,
  11. Frank Deppe,
  12. and Rudolf Gross
We describe a unified classical approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. To fill the gap between experiment
and theory, we also consider the influences of small circuit asymmetry and the finite length of the feedlines, and describe a procedure to correct them in typical measurement results. We show that, similar to the transmission coefficient of a hanger-type resonator, the reflection coefficient of a necklace- or bridge-type resonator does also contain a reference point which can be used to characterize the electrical properties of a microwave resonator in a single measurement. Our results provide a comprehensive understanding of superconducting microwave resonators from the design concepts to the characterization details.

Tuning and Amplifying the Interactions in Superconducting Quantum Circuits with Subradiant Qubits

  1. Qi-Ming Chen,
  2. Florian Fesquet,
  3. Kedar E. Honasoge,
  4. Fabian Kronowetter,
  5. Yuki Nojiri,
  6. Michael Renger,
  7. Kirill G. Fedorov,
  8. Achim Marx,
  9. Frank Deppe,
  10. and Rudolf Gross
We propose a tunable coupler consisting of N off-resonant and fixed-frequency qubits that can tune and even amplify the effective interaction between two general circuit components.
The tuning range of the interaction is proportional to N, with a minimum value of zero and a maximum that can exceed the physical coupling rates in the system. The effective coupling rate is determined by the collective magnetic quantum number of the qubit ensemble, which takes only discrete values and is free from collective decay and decoherence. Using single-photon pi-pulses, the coupling rate can be switched between arbitrary initial and final values within the dynamic range in a single step without going through intermediate values. A cascade of the couplers for amplifying small interactions or weak signals is also discussed. These results should not only stimulate interest in exploring the collective effects in quantum information processing, but also enable development of applications in tuning and amplifying the interactions in a general cavity-QED system.

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.