Bosonic cat qubits with repetition codes
Algorithms and benchmarks / Error correction (enabling)
Cat qubits store information in superpositions of coherent states of a microwave resonator; bit flips are suppressed exponentially with photon number, so only phase flips need a simple repetition code.
- Era
- Fault-tolerant
- Problem class
- Error correction (enabling)
- Speedup
- Lower qubit overhead: the 256-bit elliptic curve logarithm needs about 126,000 cat qubits in the cited estimate.
How it works
A two-photon driven-dissipative process stabilises the cat states; a one-dimensional repetition code corrects phase errors; protected NOT, CNOT and Toffoli gates are built on top (Guillaud and Mirrahimi 2019).
Typical use cases
- Hardware-efficient fault-tolerant processors.
Resource estimates
Figures exactly as stated by their authors, with their assumptions. They are estimates under those assumptions, not forecasts, and they tend to fall as methods improve.
| Quantity | Value as stated |
|---|---|
| Cat qubits | 126,133 |
| Runtime | 9 hours |
Assumptions: Ratio between single- and two-photon losses of 10^-5, cycle time 500 ns, about 19 photons per cat state on average.
Source: É. Gouzien et al. 2023, Phys. Rev. Lett. 131, 040602 (2023); arXiv:2302.06639
Demonstrations
No logical-level demonstration was verified for this release.
Hardware platforms that fit
- Superconducting qubits: Cat qubits are built in superconducting microwave circuits, such as the processors of Alice & Bob listed in the software directory.
What you need to run it
- Classical simulation
- Emulators of cat-qubit processors are available through the Alice & Bob provider.
- Noisy hardware (NISQ)
- Not applicable for this family.
- Fault-tolerant machine
- Cat qubits with a strong noise bias and a repetition code; about 126,000 cat qubits for the elliptic-curve task under the cited assumptions.
- Annealer or analogue simulator
- Not applicable for this family.
Calculate the memory of a simulation
Where to run it in Europe
Superconducting qubits
- VLQ (Czechia; Inaugurated, per the EuroHPC JU): Superconducting; digital quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones VLQ
- Euro-Q-Exa (Germany; Inaugurated, per the EuroHPC JU): Superconducting; digital quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones Euro-Q-Exa
- EuroQCS-Spain (Spain; Inaugurated, per the EuroHPC JU): Superconducting annealing; analogue quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones EuroQCS-Spain
- Quantum Inspire (Netherlands; In operation, per the source): Online platform with superconducting transmon QPUs, a neutral-atom emulator and simulators; a Spin-2+ electron spin QPU is listed as archived. Access: Quantum Inspire registration.
- LRZ Quantum Integration Centre (QIC) (Germany; In operation, per the source): Superconducting systems from IQM (54 qubits, up to 150 in future), a 20-qubit AQT ion-trap system, and a neutral-atom system being developed by planqc (MAQCS project). Access: LRZ quantum computing consulting.
- Finnish Quantum-Computing Infrastructure (FiQCI) (Finland; In operation, per the source): Hybrid HPC and quantum computing platform: VTT Q50 (53 qubits) and Aalto Q20 (20 qubits), superconducting systems made by IQM, used through the LUMI supercomputer environment. Access: FiQCI calls for academic projects.
- Quantum Spain quantum computer at BSC-CNS (Spain; In operation, per the source): Superconducting; digital quantum computer with a 35-qubit processor, integrated into the MareNostrum 5 supercomputer. Access: Spanish Supercomputing Network (RES) quantum access. Deployment milestones Quantum Spain quantum computer at BSC-CNS
The full infrastructure catalogue · The infrastructure deployment tracker
Software
European tools in the software directory
Other open-source frameworks
- Qiskit (IBM (United States); non-European)
A listing is not an endorsement; check each tool for the features you need.
Limitations and open questions
- The estimate assumes a ratio of single- to two-photon losses of 10^-5; the result depends on reaching it.
In the Quantum Algorithm Zoo
No matching Zoo entry was found on 23 October 2026; the Zoo lists algorithms with a proven or conjectured speedup, not this family.
Index: the Quantum Algorithm Zoo by Stephen P. Jordan, last updated 2026-09-10, checked 2026-10-23. The portal links to it and copies no description from it. Browse the full Quantum Algorithm Zoo (external site)
Named in European procurements
None of the procurement documents read for this release names it.
Sources
- J. Guillaud, M. Mirrahimi (2019). Repetition Cat Qubits for Fault-Tolerant Quantum Computation. Phys. Rev. X 9, 041053 (2019); arXiv:1904.09474. Read: abstract page, retrieved 2026-10-23.
- É. Gouzien, D. Ruiz, F.-M. Le Régent, J. Guillaud, N. Sangouard (2023). Performance Analysis of a Repetition Cat Code Architecture: Computing 256-bit Elliptic Curve Logarithm in 9 Hours with 126133 Cat Qubits. Phys. Rev. Lett. 131, 040602 (2023); arXiv:2302.06639. Read: abstract page, retrieved 2026-10-23.