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.

Broadband Tunable Phase Shifter For Microwaves

  1. Jinli Zhang,
  2. Tianyi Li,
  3. Roope Kokkoniemi,
  4. Chengyu Yan,
  5. Wei Liu,
  6. Matti Partanen,
  7. Kuan Yen Tan,
  8. Ming He,
  9. Lu Ji,
  10. Leif Grönberg,
  11. and Mikko Möttönen
We implement a broadly tunable phase shifter for microwaves based on superconducting quantum interference devices (SQUIDs) and study it both experimentally and theoretically. At different
frequencies, a unit transmission coefficient, |S21|=1, can be theoretically achieved along a curve where the phase shift is controllable by magnetic flux. The fabricated device consists of three equidistant SQUIDs interrupting a transmission line. We model each SQUID embedded at different positions along the transmission line with two parameters, capacitance and inductance, the values of which we extract from the experiments. In our experiments, the tunability of the phase shift varies from from 0.07×π to 0.14×π radians along the full-transmission curve with the input frequency ranging from 6.00 to 6.28~GHz. The reported measurements are in good agreement with simulations, which is promising for future design work of phase shifters for different applications.

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.

Fast control of dissipation in a superconducting resonator

  1. Vasilii Sevriuk,
  2. Kuan Yen Tan,
  3. Eric Hyyppä,
  4. Matti Silveri,
  5. Matti Partanen,
  6. Máté Jenei,
  7. Shumpei Masuda,
  8. Jan Goetz,
  9. Visa Vesterinen,
  10. Leif Grönberg,
  11. and Mikko Möttönen
We report on fast tunability of an electromagnetic environment coupled to a superconducting coplanar waveguide resonator. Namely, we utilize a recently-developed quantum-circuit refrigerator
(QCR) to experimentally demonstrate a dynamic tunability in the total damping rate of the resonator up to almost two orders of magnitude. Based on the theory it corresponds to a change in the internal damping rate by nearly four orders of magnitude. The control of the QCR is fully electrical, with the shortest implemented operation times in the range of 10 ns. This experiment constitutes a fast active reset of a superconducting quantum circuit. In the future, a similar scheme can potentially be used to initialize superconducting quantum bits.

Efficient protocol for qubit initialization with a tunable environment

  1. Jani Tuorila,
  2. Matti Partanen,
  3. Tapio Ala-Nissila,
  4. and Mikko Möttönen
We propose an efficient qubit initialization protocol based on a dissipative environment that can be dynamically adjusted. Here the qubit is coupled to a thermal bath through a tunable
harmonic oscillator. On-demand initialization is achieved by sweeping the oscillator rapidly into resonance with the qubit. This resonant coupling with the engineered environment induces fast relaxation to the ground state of the system, and a consecutive rapid sweep back to off resonance guarantees weak excess dissipation during quantum computations. We solve the corresponding quantum dynamics using a Markovian master equation for the reduced density operator of the qubit-bath system. This allows us to optimize the parameters and the initialization protocol for the qubit. Our analytical calculations show that the ground-state occupation of our system is well protected during the fast sweeps of the environmental coupling and, consequently, we obtain an estimate for the duration of our protocol by solving the transition rates between the low-energy eigenstates with the Jacobian diagonalization method. Our results suggest that the current experimental state of the art for the initialization speed of superconducting qubits at a given fidelity can be considerably improved.