Lucas St-Jean

Quantum error correction of a grid-state qubit with state preparation and measurement errors below 10−3

  1. Sara Turcotte,
  2. Lucas St-Jean,
  3. Amélie L. Pessonneaux,
  4. Ross Shillito,
  5. Bohdan Kulchytskyy,
  6. Eliott Ouellet,
  7. Jean Olivier Simoneau,
  8. Florian Hopfmueller,
  9. Matthew Hamer,
  10. Pascal Lemieux,
  11. Dany Lachance-Quirion,
  12. Baptiste Royer,
  13. and Nicholas E. Frattini
Grid state qubits offer a hardware-efficient approach to large-scale fault-tolerant quantum computing. They access the information redundancy required for quantum error correction by
exploiting the large Hilbert space naturally available in harmonic oscillators. Superconducting architectures are particularly suitable to implement grid state qubits due to their fast and high-fidelity operations. Grid states in superconducting circuits enable quantum error correction (QEC) with performance beyond break-even. However, the state preparation and measurements (SPAM) errors of grid states has been a significant limitation to computational performances. In this work, we leverage high-performance QEC to enable repeat-until-success state preparation of both cardinal and magic states of the single-mode grid-state qubit. We combine this with an improved measurement protocol that corrects for both finite-energy envelope and auxiliary qubit readout errors, and increases robustness to photon loss. Our experiments, using both techniques, achieve a combined state-preparation and measurement error below 10−3. This represents two orders-of-magnitude improvement over the state of the art, bringing this platform on par with standard SPAM error levels measured in transmon qubits.
arxiv pdf

Bias-preserving gates with stabilized cat qubits

  1. Shruti Puri,
  2. Lucas St-Jean,
  3. Jonathan A. Gross,
  4. Alexander Grimm,
  5. N. E. Frattini,
  6. Pavithran S. Iyer,
  7. Anirudh Krishna,
  8. Steven Touzard,
  9. Liang Jiang,
  10. Alexandre Blais,
  11. Steven T. Flammia,
  12. and S. M. Girvin
The code capacity threshold for error correction using qubits which exhibit asymmetric or biased noise channels is known to be much higher than with qubits without such structured noise.However, it is unclear how much this improvement persists when realistic circuit level noise is taken into account. This is because implementations of gates which do not commute with the dominant error un-bias the noise channel. In particular, a native bias-preserving controlled-NOT (CX) gate, which is an essential ingredient of stabilizer codes, is not possible in strictly two-level systems. Here we overcome the challenge of implementing a bias-preserving CX gate by using stabilized cat qubits in driven nonlinear oscillators. The physical noise channel of this qubit is biased towards phase-flips, which increase linearly with the size of the cat, while bit-flips are exponentially suppressed with cat size. Remarkably, the error channel of this native CX gate between two such cat qubits is also dominated by phase-flips, while bit-flips remain exponentially suppressed. This CX gate relies on the topological phase that arises from the rotation of the cat qubit in phase space. The availability of bias-preserving CX gates opens a path towards fault-tolerant codes tailored to biased-noise cat qubits with high threshold and low overhead. As an example, we analyze a scheme for concatenated error correction using cat qubits. We find that the availability of CX gates with moderately sized cat qubits, having mean photon number <10, improves a rigorous lower bound on the fault-tolerance threshold by a factor of two and decreases the overhead in logical Clifford operations by a factor of 5. We expect these estimates to improve significantly with further optimization and with direct use of other codes such as topological codes tailored to biased noise.[/expand]
arxiv pdf