Hastings-Haah Floquet code[1]
Description
Dynamical code whose sequence of check-operator measurements is periodic. The first instance of a dynamical code.Protection
Protects against single-qubit Pauli noise and check operator measurement errors.Fault Tolerance
Floquet codes on tri-colorable lattices can be made fault-tolerant in the presence of dead qubits [2,3].Cousins
- Subsystem qubit stabilizer code— This code can be viewed as a subsystem stabilizer code, albeit one with less logical qubits.
- Monitored random-circuit code— Both Floquet and monitored random circuit codes can have an instantaneous stabilizer group which evolves through unitary evolution and measurements. However, Floquet codewords are generated via a specific sequence of measurements, while random-circuit codes maintain a stabilizer group after any measurement. Floquet codes have the additional capability of detecting errors induced during the measurement process; see Appx. A of Ref. [1].
- Majorana stabilizer code— Floquet codes are viable candidates for storage in Majorana-qubit devices [4].
- Qubit stabilizer code— Using ZX calculus, an \([[n,k,d]]\) qubit stabilizer code admitting stabilizer generators of weight no more than \(m\) can be Floquetified (see also Ref. [5]) into an \([[n+\lceil m/2 \rceil+\ell,k,d^{\prime}]]\) Floquet code with single- and two-qubit operations, where \(\ell \leq \log_{2} m\) and \(d^{\prime} \geq d\) [6].
- Asymmetric quantum code— Floquet codes can be adapted for asymmetric noise [7].
- Five-qubit perfect code— Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed for the five-qubit code [8].
- Bacon-Shor code— The Bacon-Shor code admits a Floquet version with a particular stabilizer measurement schedule [9].
Primary Hierarchy
Parents
Floquet codes are dynamical codes with periodic measurement sequences.
The modular-qudit honeycomb Floquet code reduces to the Hastings-Haah Floquet code for \(q=2\).
Hastings-Haah Floquet code
Children
The honeycomb Floquet code is the first 2D Floquet code.
The ladder Floquet code is the first 1D Floquet code.
References
- [1]
- M. B. Hastings and J. Haah, “Dynamically Generated Logical Qubits”, Quantum 5, 564 (2021) arXiv:2107.02194 DOI
- [2]
- D. Aasen, J. Haah, P. Bonderson, Z. Wang, and M. Hastings, “Fault-Tolerant Hastings-Haah Codes in the Presence of Dead Qubits”, (2023) arXiv:2307.03715
- [3]
- C. McLauchlan, G. P. Gehér, and A. E. Moylett, “Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements”, Quantum 8, 1562 (2024) arXiv:2405.15854 DOI
- [4]
- A. Paetznick, C. Knapp, N. Delfosse, B. Bauer, J. Haah, M. B. Hastings, and M. P. da Silva, “Performance of Planar Floquet Codes with Majorana-Based Qubits”, PRX Quantum 4, (2023) arXiv:2202.11829 DOI
- [5]
- A. Townsend-Teague, J. Magdalena de la Fuente, and M. Kesselring, “Floquetifying the Colour Code”, Electronic Proceedings in Theoretical Computer Science 384, 265 (2023) arXiv:2307.11136 DOI
- [6]
- B. Rodatz, B. Poór, and A. Kissinger, “Floquetifying stabiliser codes with distance-preserving rewrites”, (2024) arXiv:2410.17240
- [7]
- F. Setiawan and C. McLauchlan, “Tailoring Dynamical Codes for Biased Noise: The X\(^3\)Z\(^3\) Floquet Code”, (2024) arXiv:2411.04974
- [8]
- L. Grans-Samuelsson, D. Aasen, and P. Bonderson, “A fault-tolerant pairwise measurement-based code on eight qubits”, (2024) arXiv:2409.13681
- [9]
- M. S. Alam and E. Rieffel, “Dynamical Logical Qubits in the Bacon-Shor Code”, (2024) arXiv:2403.03291
Page edit log
- Victor V. Albert (2022-07-12) — most recent
- Victor V. Albert (2022-01-01)
Cite as:
“Hastings-Haah Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/floquet