Dynamical automorphism (DA) code[1]
Description
Dynamically-generated stabilizer-based code whose (not necessarily periodic) sequence of few-body measurements implements state initialization, logical gates and error detection.
After each measurement in the sequence, the codespace is a joint \(+1\) eigenspace of an instantaneous stabilizer group (ISG), i.e., a particular stabilizer group corresponding to the measurement. The ISG specifies the state of the system as a Pauli stabilizer state at a particular round of measurement, and it evolves into a (potentially) different ISG via code switching using the group \(\mathsf{F}\) of check operators measured in the next step in the sequence.
As opposed to subsystem codes, only specific measurement sequences maintain the codespace, and not all sequences implement error detection. Aperiodic measurement sequences provide a way to implement logical gates [1].
For DA codes based on topological phases, the phase associated with each ISG of the code can be obtained from a single parent topological phase associated with the DA code [2] via as anyon condensation. In this way, measurements cycle logical quantum information between the various condensed phases.
Gates
Parent
- Dynamically-generated QECC — DA code state initialization, logical gates, and error correction are done by a sequence of different (usually weight-two) stabilizer measurements.
Child
- Hastings-Haah Floquet code — Floquet codes are DA codes with periodic measurement sequences.
Cousins
- Color code — The parent topological phase of the 2D (3D) DA color code is realized by two (three) copies of the 2D (3D) color code.
- Kitaev surface code — One of the instantaneous stabilizer codes of the 2D DA color code are stacks of toric/surface codes
- Abelian topological code — Useful measurement sequences of DA Floquet codes can be extracted from topological quantum field theory [1].
References
- [1]
- M. Davydova et al., “Quantum computation from dynamic automorphism codes”, (2023) arXiv:2307.10353
- [2]
- M. S. Kesselring et al., “Anyon condensation and the color code”, (2022) arXiv:2212.00042
Page edit log
- Victor V. Albert (2023-07-21) — most recent
- Shankar N. Balasubramanian (2023-07-21)
- Nathanan Tantivasadakarn (2023-07-21)
Cite as:
“Dynamical automorphism (DA) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/da