Enhancing dissipative cat qubit protection by squeezing

  1. Rémi Rousseau,
  2. Diego Ruiz,
  3. Emanuele Albertinale,
  4. Pol d'Avezac,
  5. Danielius Banys,
  6. Ugo Blandin,
  7. Nicolas Bourdaud,
  8. Giulio Campanaro,
  9. Gil Cardoso,
  10. Nathanael Cottet,
  11. Charlotte Cullip,
  12. Samuel Deléglise,
  13. Louise Devanz,
  14. Adam Devulder,
  15. Antoine Essig,
  16. Pierre Février,
  17. Adrien Gicquel,
  18. Élie Gouzien,
  19. Antoine Gras,
  20. Jérémie Guillaud,
  21. Efe Gümüş,
  22. Mattis Hallén,
  23. Anissa Jacob,
  24. Paul Magnard,
  25. Antoine Marquet,
  26. Salim Miklass,
  27. Théau Peronnin,
  28. Stéphane Polis,
  29. Felix Rautschke,
  30. Ulysse Réglade,
  31. Julien Roul,
  32. Jeremy Stevens,
  33. Jeanne Solard,
  34. Alexandre Thomas,
  35. Jean-Loup Ville,
  36. Pierre Wan-Fat,
  37. Raphaël Lescanne,
  38. Zaki Leghtas,
  39. Joachim Cohen,
  40. Sébastien Jezouin,
  41. and Anil Murani
Dissipative cat-qubits are a promising architecture for quantum processors due to their built-in quantum error correction. By leveraging two-photon stabilization, they achieve an exponentially
suppressed bit-flip error rate as the distance in phase-space between their basis states increases, incurring only a linear increase in phase-flip rate. This property substantially reduces the number of qubits required for fault-tolerant quantum computation. Here, we implement a squeezing deformation of the cat qubit basis states, further extending the bit-flip time while minimally affecting the phase-flip rate. We demonstrate a steep reduction in the bit-flip error rate with increasing mean photon number, characterized by a scaling exponent γ=4.3, rising by a factor of 74 per added photon. Specifically, we measure bit-flip times of 22 seconds for a phase-flip time of 1.3 μs in a squeezed cat qubit with an average photon number n¯=4.1, a 160-fold improvement in bit-flip time compared to a standard cat. Moreover, we demonstrate a two-fold reduction in Z-gate infidelity, with an estimated phase-flip probability of ϵX=0.085 and a bit-flip probability of ϵZ=2.65⋅10−9 which confirms the gate bias-preserving property. This simple yet effective technique enhances cat qubit performances without requiring design modification, moving multi-cat architectures closer to fault-tolerant quantum computation.

Autoparametric resonance extending the bit-flip time of a cat qubit up to 0.3 s

  1. Antoine Marquet,
  2. Antoine Essig,
  3. Joachim Cohen,
  4. Nathanaël Cottet,
  5. Anil Murani,
  6. Emanuele Abertinale,
  7. Simon Dupouy,
  8. Audrey Bienfait,
  9. Théau Peronnin,
  10. Sébastien Jezouin,
  11. Raphaël Lescanne,
  12. and Benjamin Huard
Cat qubits, for which logical |0⟩ and |1⟩ are coherent states |±α⟩ of a harmonic mode, offer a promising route towards quantum error correction. Using dissipation to our advantage
so that photon pairs of the harmonic mode are exchanged with single photons of its environment, it is possible to stabilize the logical states and exponentially increase the bit-flip time of the cat qubit with the photon number |α|2. Large two-photon dissipation rate κ2 ensures fast qubit manipulation and short error correction cycles, which are instrumental to correct the remaining phase-flip errors in a repetition code of cat qubits. Here we introduce and operate an autoparametric superconducting circuit that couples a mode containing the cat qubit to a lossy mode whose frequency is set at twice that of the cat mode. This passive coupling does not require a parametric pump and reaches a rate κ2/2π≈2 MHz. With such a strong two-photon dissipation, bit-flip errors of the autoparametric cat qubit are prevented for a characteristic time up to 0.3 s with only a mild impact on phase-flip errors. Besides, we illustrate how the phase of a quantum superposition between |α⟩ and |−α⟩ can be arbitrarily changed by driving the harmonic mode while keeping the engineered dissipation active.

Number-resolved photocounter for propagating microwave mode

  1. Rémy Dassonneville,
  2. Réouven Assouly,
  3. Théau Peronnin,
  4. Pierre Rouchon,
  5. and Benjamin Huard
Detectors of propagating microwave photons have recently been realized using superconducting circuits. However a number-resolved photocounter is still missing. In this letter, we demonstrate
a single-shot counter for propagating microwave photons that can resolve up to 3 photons. It is based on a pumped Josephson Ring Modulator that can catch an arbitrary propagating mode by frequency conversion and store its quantum state in a stationary memory mode. A transmon qubit then counts the number of photons in the memory mode using a series of binary questions. Using measurement based feedback, the number of questions is minimal and scales logarithmically with the maximal number of photons. The detector features a detection efficiency of 0.96±0.04, and a dark count probability of 0.030±0.002 for an average dead time of 4.5 μs. To maximize its performance, the device is first used as an \emph{in situ} waveform detector from which an optimal pump is computed and applied. Depending on the number of incoming photons, the detector succeeds with a probability that ranges from 56% to 99%.

Multiplexed photon number measurement

  1. Antoine Essig,
  2. Quentin Ficheux,
  3. Théau Peronnin,
  4. Nathanaël Cottet,
  5. Raphaël Lescanne,
  6. Alain Sarlette,
  7. Pierre Rouchon,
  8. Zaki Leghtas,
  9. and Benjamin Huard
The evolution of quantum systems under measurement is a central aspect of quantum mechanics. When a two level system — a qubit — is used as a probe of a larger system, it
naturally leads to answering a single yes-no question about the system state followed by its corresponding quantum collapse. Here, we report an experiment where a single superconducting qubit is counter-intuitively able to answer not a single but nine yes-no questions about the number of photons in a microwave resonator at the same time. The key ingredients are twofold. First, we exploit the fact that observing the color of a qubit carries additional information to the conventional readout of its state. The qubit-system interaction is hence designed so that the qubit color encodes the number of photons in the resonator. Secondly, we multiplex the qubit color observation by recording how the qubit reflects a frequency comb. Interestingly the amount of extracted information reaches a maximum at a finite drive amplitude of the comb. We evidence it by direct Wigner tomography of the quantum state of the resonator. Our experiment unleashes the full potential of quantum meters by bringing the measurement process in the frequency domain.

Exponential suppression of bit-flips in a qubit encoded in an oscillator

  1. Raphaël Lescanne,
  2. Marius Villiers,
  3. Théau Peronnin,
  4. Alain Sarlette,
  5. Matthieu Delbecq,
  6. Benjamin Huard,
  7. Takis Kontos,
  8. Mazyar Mirrahimi,
  9. and Zaki Leghtas
A quantum system interacts with its environment, if ever so slightly, no matter how much care is put into isolating it. As a consequence, quantum bits (qubits) undergo errors, putting
dauntingly difficult constraints on the hardware suitable for quantum computation. New strategies are emerging to circumvent this problem by encoding a qubit non-locally across the phase space of a physical system. Since most sources of decoherence are due to local fluctuations, the foundational promise is to exponentially suppress errors by increasing a measure of this non-locality. Prominent examples are topological qubits which delocalize quantum information over real space and where spatial extent measures non-locality. In this work, we encode a qubit in the field quadrature space of a superconducting resonator endowed with a special mechanism that dissipates photons in pairs. This process pins down two computational states to separate locations in phase space. As we increase this separation, we measure an exponential decrease of the bit-flip rate while only linearly increasing the phase-flip rate. Since bit-flips are continuously and autonomously corrected at the single qubit level, only phase-flips are left to be corrected via a one-dimensional quantum error correction code. This exponential scaling demonstrates that resonators with non-linear dissipation are promising building blocks for universal fault-tolerant quantum computation with drastically reduced hardware overhead.

Sequential measurement of a superconducting qubit

  1. Théau Peronnin,
  2. Danijela Marković,
  3. Quentin Ficheux,
  4. and Benjamin Huard
We present a superconducting device that realizes the sequential measurement of a transmon qubit. The unitary evolution between system and probe is indeed separated in time and space
from the measurement of the probe itself. The device disables common limitations of dispersive readout such as Purcell effect or transients in the cavity mode by tuning the coupling to the measurement channel on demand. The probe is initially stored in a memory mode and coupled to the qubit until a microwave pump releases it into an output line in a characteristic time as low as 10 ns, which is 400 times shorter than the memory lifetime. The Wigner function of the memory allows us to characterize the non-Gaussian nature of the probe and its dynamics. A direct measurement of the released probe field quadratures demonstrates a readout fidelity of 97.5 % in a total measurement time of 220 ns.