Solomon equations for qubit and two-level systems

  1. Martin Spiecker,
  2. Andrei I. Pavlov,
  3. Alexander Shnirman,
  4. and Ioan M. Pop
We model and measure the combined relaxation of a qubit, a.k.a. central spin, coupled to a discrete two-level system (TLS) environment. We present a derivation of the Solomon equations
starting from a general Lindblad equation for the qubit and an arbitrary number of TLSs. If the TLSs are much longer lived than the qubit, the relaxation becomes non-exponential. In the limit of large numbers of TLSs the populations are likely to follow a power law, which we illustrate by measuring the relaxation of a superconducting fluxonium qubit. Moreover, we show that the Solomon equations predict non-Poissonian quantum jump statistics, which we confirm experimentally.

A quantum Szilard engine for two-level systems coupled to a qubit

  1. Martin Spiecker,
  2. Patrick Paluch,
  3. Niv Drucker,
  4. Shlomi Matityahu,
  5. Daria Gusenkova,
  6. Nicolas Gosling,
  7. Simon Günzler,
  8. Dennis Rieger,
  9. Ivan Takmakov,
  10. Francesco Valenti,
  11. Patrick Winkel,
  12. Richard Gebauer,
  13. Oliver Sander,
  14. Gianluigi Catelani,
  15. Alexander Shnirman,
  16. Alexey V. Ustinov,
  17. Wolfgang Wernsdorfer,
  18. Yonatan Cohen,
  19. and Ioan M. Pop
The innate complexity of solid state physics exposes superconducting quantum circuits to interactions with uncontrolled degrees of freedom degrading their coherence. By using a simple
stabilization sequence we show that a superconducting fluxonium qubit is coupled to a two-level system (TLS) environment of unknown origin, with a relatively long energy relaxation time exceeding 50ms. Implementing a quantum Szilard engine with an active feedback control loop allows us to decide whether the qubit heats or cools its TLS environment. The TLSs can be cooled down resulting in a four times lower qubit population, or they can be heated to manifest themselves as a negative temperature environment corresponding to a qubit population of ∼80%. We show that the TLSs and the qubit are each other’s dominant loss mechanism and that the qubit relaxation is independent of the TLS populations. Understanding and mitigating TLS environments is therefore not only crucial to improve qubit lifetimes but also to avoid non-Markovian qubit dynamics.

Operating in a deep underground facility improves the locking of gradiometric fluxonium qubits at the sweet spots

  1. Daria Gusenkova,
  2. Francesco Valenti,
  3. Martin Spiecker,
  4. Simon Günzler,
  5. Patrick Paluch,
  6. Dennis Rieger,
  7. Larisa-Milena Pioraş-Ţimbolmaş,
  8. Liviu P. Zârbo,
  9. Nicola Casali,
  10. Ivan Colantoni,
  11. Angelo Cruciani,
  12. Stefano Pirro,
  13. Laura Cardani,
  14. Alexandru Petrescu,
  15. Wolfgang Wernsdorfer,
  16. Patrick Winkel,
  17. and Ioan M. Pop
We demonstrate flux-bias locking and operation of a gradiometric fluxonium artificial atom using two symmetric granular aluminum (grAl) loops to implement the superinductor. The gradiometric
fluxonium shows two orders of magnitude suppression of sensitivity to homogeneous magnetic fields, which can be an asset for hybrid quantum systems requiring strong magnetic field biasing. By cooling down the device in an external magnetic field while crossing the metal-to-superconductor transition, the gradiometric fluxonium can be locked either at 0 or Φ0/2 effective flux bias, corresponding to an even or odd number of trapped fluxons, respectively. At mK temperatures, the fluxon parity prepared during initialization survives to magnetic field bias exceeding 100Φ0. However, even for states biased in the vicinity of 1Φ0, we observe unexpectedly short fluxon lifetimes of a few hours, which cannot be explained by thermal or quantum phase slips. When operating in a deep-underground cryostat of the Gran Sasso laboratory, the fluxon lifetimes increase to days, indicating that ionizing events activate phase slips in the grAl superinductor.

Quantum non-demolition dispersive readout of a superconducting artificial atom using large photon numbers

  1. Daria Gusenkova,
  2. Martin Spiecker,
  3. Richard Gebauer,
  4. Madita Willsch,
  5. Francesco Valenti,
  6. Nick Karcher,
  7. Lukas Grünhaupt,
  8. Ivan Takmakov,
  9. Patrick Winkel,
  10. Dennis Rieger,
  11. Alexey V. Ustinov,
  12. Nicolas Roch,
  13. Wolfgang Wernsdorfer,
  14. Kristel Michielsen,
  15. Oliver Sander,
  16. and Ioan M. Pop
Reading out the state of superconducting artificial atoms typically relies on dispersive coupling to a readout resonator. For a given system noise temperature, increasing the circulating
photon number n¯ in the resonator enables a shorter measurement time and is therefore expected to reduce readout errors caused by spontaneous atom transitions. However, increasing n¯ is generally observed to also increase these transition rates. Here we present a fluxonium artificial atom in which we measure an overall flat dependence of the transition rates between its first two states as a function of n¯, up to n¯≈200. Despite the fact that we observe the expected decrease of the dispersive shift with increasing readout power, the signal-to-noise ratio continuously improves with increasing n¯. Even without the use of a parametric amplifier, at n¯=74, we measure fidelities of 99% and 93% for feedback-assisted ground and excited state preparation, respectively.

State preparation of a fluxonium qubit with feedback from a custom FPGA-based platform

  1. Richard Gebauer,
  2. Nick Karcher,
  3. Daria Gusenkova,
  4. Martin Spiecker,
  5. Lukas Grünhaupt,
  6. Ivan Takmakov,
  7. Patrick Winkel,
  8. Luca Planat,
  9. Nicolas Roch,
  10. Wolfgang Wernsdorfer,
  11. Alexey V. Ustinov,
  12. Marc Weber,
  13. Martin Weides,
  14. Ioan M. Pop,
  15. and Oliver Sander
We developed a versatile integrated control and readout instrument for experiments with superconducting quantum bits (qubits), based on a field-programmable gate array (FPGA) platform.
Using this platform, we perform measurement-based, closed-loop feedback operations with 428ns platform latency. The feedback capability is instrumental in realizing active reset initialization of the qubit into the ground state in a time much shorter than its energy relaxation time T1. We show experimental results demonstrating reset of a fluxonium qubit with 99.4% fidelity, using a readout-and-drive pulse sequence approximately 1.5μs long. Compared to passive ground state initialization through thermalization, with the time constant given by T1= 80μs, the use of the FPGA-based platform allows us to improve both the fidelity and the time of the qubit initialization by an order of magnitude.

Implementation of a transmon qubit using superconducting granular aluminum

  1. Patrick Winkel,
  2. Kiril Borisov,
  3. Lukas Grünhaupt,
  4. Dennis Rieger,
  5. Martin Spiecker,
  6. Francesco Valenti,
  7. Alexey V. Ustinov,
  8. Wolfgang Wernsdorfer,
  9. and Ioan M. Pop
The high kinetic inductance offered by granular aluminum (grAl) has recently been employed for linear inductors in superconducting high-impedance qubits and kinetic inductance detectors.
Due to its large critical current density compared to typical Josephson junctions, its resilience to external magnetic fields, and its low dissipation, grAl may also provide a robust source of non-linearity for strongly driven quantum circuits, topological superconductivity, and hybrid systems. Having said that, can the grAl non-linearity be sufficient to build a qubit? Here we show that a small grAl volume (10×200×500nm3) shunted by a thin film aluminum capacitor results in a microwave oscillator with anharmonicity α two orders of magnitude larger than its spectral linewidth Γ01, effectively forming a transmon qubit. With increasing drive power, we observe several multi-photon transitions starting from the ground state, from which we extract α=2π×4.48MHz. Resonance fluorescence measurements of the |0>→|1> transition yield an intrinsic qubit linewidth γ=2π×10kHz, corresponding to a lifetime of 16μs. This linewidth remains below 2π×150kHz for in-plane magnetic fields up to ∼70mT.

Transmon Qubit in a Magnetic Field: Evolution of Coherence and Transition Frequency

  1. Andre Schneider,
  2. Tim Wolz,
  3. Marco Pfirrmann,
  4. Martin Spiecker,
  5. Hannes Rotzinger,
  6. Alexey V. Ustinov,
  7. and Martin Weides
We report on spectroscopic and time-domain measurements on a fixed-frequency concentric transmon qubit in an applied in-plane magnetic field to explore its limits of magnetic field
compatibility. We demonstrate quantum coherence of the qubit up to field values of B=40mT, even without an optimized chip design or material combination of the qubit. The dephasing rate Γφ is shown to be not affected by the magnetic field in a broad range of the qubit transition frequency. For the evolution of the qubit transition frequency, we find the unintended second junction created in the shadow angle evaporation process to be non-negligible and deduce an analytic formula for the field-dependent qubit energies. We discuss the relevant field-dependent loss channels, which can not be distinguished by our measurements, inviting further theoretical and experimental investigation. Using well-known and well-studied standard components of the superconducting quantum architecture, we are able to reach a field regime relevant for quantum sensing and hybrid applications of magnetic spins and spin systems.

Granular aluminum: A superconducting material for high impedance quantum circuits

  1. Lukas Grünhaupt,
  2. Martin Spiecker,
  3. Daria Gusenkova,
  4. Nataliya Maleeva,
  5. Sebastian T. Skacel,
  6. Ivan Takmakov,
  7. Francesco Valenti,
  8. Patrick Winkel,
  9. Hannes Rotzinger,
  10. Alexey V. Ustinov,
  11. and Ioan M. Pop
Superconducting quantum information processing machines are predominantly based on microwave circuits with relatively low characteristic impedance, of about 100 Ohm, and small anharmonicity,
which can limit their coherence and logic gate fidelity. A promising alternative are circuits based on so-called superinductors, with characteristic impedances exceeding the resistance quantum RQ=6.4 kΩ. However, previous implementations of superinductors, consisting of mesoscopic Josephson junction arrays, can introduce unintended nonlinearity or parasitic resonant modes in the qubit vicinity, degrading its coherence. Here we present a fluxonium qubit design using a granular aluminum (grAl) superinductor strip. Granular aluminum is a particularly attractive material, as it self-assembles into an effective junction array with a remarkably high kinetic inductance, and its fabrication can be in-situ integrated with standard aluminum circuit processing. The measured qubit coherence time TR2 up to 30 μs illustrates the potential of grAl for applications ranging from protected qubit designs to quantum limited amplifiers and detectors.