Description
Encodes \(K\)-dimensional Hilbert space into \(n\) bosonic modes.
Decoding
Given an encoding of a finite-dimensional code, a decoder that yields the optimal entanglement fidelity can be obtained by solving a semi-definite program [1,2] (see also Ref. [3]). This approximate QEC technique can be adapted to bosonic codes as long as they are restricted to a finite-dimensional subspace of the oscillator Hilbert space [4].
Parent
- Bosonic code — Qudit-into-oscillator codes are bosonic codes with a finite-dimensional logical subspace.
Children
Cousins
- Approximate quantum error-correcting code (AQECC) — Approximate QEC techniques of finding the entanglement fidelity can be adapted to bosonic codes with a finite-dimensional codespace [4].
- Hybrid qudit-oscillator code — A hybrid qudit-oscillator code with \(n_1=0\) is a qudit-into-oscillator code.
References
- [1]
- K. Audenaert and B. De Moor, “Optimizing completely positive maps using semidefinite programming”, Physical Review A 65, (2002) arXiv:quant-ph/0109155 DOI
- [2]
- M. Reimpell and R. F. Werner, “Iterative Optimization of Quantum Error Correcting Codes”, Physical Review Letters 94, (2005) arXiv:quant-ph/0307138 DOI
- [3]
- A. S. Fletcher, “Channel-Adapted Quantum Error Correction”, (2007) arXiv:0706.3400
- [4]
- V. V. Albert et al., “Performance and structure of single-mode bosonic codes”, Physical Review A 97, (2018) arXiv:1708.05010 DOI
Page edit log
- Victor V. Albert (2022-05-17) — most recent
- Victor V. Albert (2021-10-29)
Cite as:
“Qudit-into-oscillator code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/qudits_into_oscillators