diff --git a/codes/quantum/oscillators/stabilizer/lattice/gkp_concatenated.yml b/codes/quantum/oscillators/stabilizer/lattice/gkp_concatenated.yml index cba351f26..519be82ff 100644 --- a/codes/quantum/oscillators/stabilizer/lattice/gkp_concatenated.yml +++ b/codes/quantum/oscillators/stabilizer/lattice/gkp_concatenated.yml @@ -44,6 +44,10 @@ relations: detail: 'GKP codes have been concatenated with QPCs \cite{arxiv:2102.01374}.' - code_id: 488_color detail: 'GKP codes have been concatenated with 4.8.8 color codes \cite{arxiv:2112.14447}.' + - code_id: triangular_color + detail: 'GKP codes have been concatenated with the 6.6.6 color code \cite{arxiv:2411.04277}.' + - code_id: stab_5_1_3 + detail: 'GKP codes have been concatenated with the five-qubit code \cite{arxiv:2411.04277}.' diff --git a/codes/quantum/oscillators/stabilizer/lattice/gkp_surface_concatenated.yml b/codes/quantum/oscillators/stabilizer/lattice/gkp_surface_concatenated.yml index 4b32b794f..382e0c535 100644 --- a/codes/quantum/oscillators/stabilizer/lattice/gkp_surface_concatenated.yml +++ b/codes/quantum/oscillators/stabilizer/lattice/gkp_surface_concatenated.yml @@ -15,6 +15,7 @@ description: | features: + rate: 'The error threshold under ML decoding of GKP-rotated-surface codes comes close to \(\sigma\approx 0.6065\), at which the best-known lower bound \cite{arxiv:quant-ph/9912067} on the capacity vanishes \cite{arxiv:2411.04277}.' decoders: - 'Decoder for GKP-toric code \cite{arxiv:1810.00047}.' - 'MWPM closest point decoder \cite{arxiv:2303.04702}.' @@ -24,7 +25,7 @@ features: - '\(0.602\) threshold displacement standard deviation for GKP-surface codes with analog side information using MWPM closest point decoder \cite{arxiv:2303.04702}.' threshold: - 'The threshold under displacement noise using ML decoding of GKP-toric codes corresponds to the value of a critical point of a 3D compact QED model in the presence of a quenched random gauge field \cite{arxiv:1810.00047}. The GKP-toric decoder yields a threshold displacement standard deviation of \(\sigma = 0.243\) \cite{arxiv:1810.00047}, but this noise model did not properly take into account error propagation \cite{arxiv:1908.03579}.' - - '\(11.2\)dB of squeezing under displacement noise using MWPM decoding for GKP-rotated-surface codes \cite{arxiv:1908.03579,arxiv:2103.06994}.' + - '\(11.2\)dB of squeezing under displacement noise using MWPM decoding for GKP-rotated-surface codes \cite{arxiv:1908.03579,arxiv:2103.06994}. The error threshold under ML decoding of GKP-rotated-surface codes comes close to \(\sigma\approx 0.6065\), at which the best-known lower bound \cite{arxiv:quant-ph/9912067} on the capacity vanishes \cite{arxiv:2411.04277}.' diff --git a/codes/quantum/oscillators/stabilizer/lattice/multimodegkp.yml b/codes/quantum/oscillators/stabilizer/lattice/multimodegkp.yml index a561b7b4d..12bf183ba 100644 --- a/codes/quantum/oscillators/stabilizer/lattice/multimodegkp.yml +++ b/codes/quantum/oscillators/stabilizer/lattice/multimodegkp.yml @@ -22,8 +22,7 @@ description: | protection: 'The level of protection against displacement errors is quantified by the Euclidean code distance \(\Delta=\min_{x\in {\mathcal{L}}^{\perp}\setminus {\mathcal{L}}} \|x\|_2\) \cite{arxiv:2109.14645}.' features: - rate: 'Transmission schemes with multimode GKP codes achieve, up to a constant-factor offset, the capacity of \hyperref[topic:ad]{AD}, displacement-noise, and thermal-noise Gaussian loss channels \cite{arxiv:quant-ph/0105058,arxiv:1708.07257,arxiv:1801.04731,arxiv:1801.07271}. - Particular random lattice families of multimode GKP codes achieve the hashing bound of the displacement noise channel \cite{arxiv:quant-ph/0105058}.' + rate: 'Transmission schemes with multimode GKP codes achieve, up to a constant-factor offset, the capacity of \hyperref[topic:ad]{AD}, a lower bound on displacement-noise, and a lower bound on thermal-noise Gaussian channel capacities \cite{arxiv:quant-ph/0105058,arxiv:1708.07257,arxiv:1801.04731,arxiv:1801.07271}. Particular random lattice families of multimode GKP codes achieve the hashing bound of the displacement noise channel \cite{arxiv:quant-ph/0105058}.' encoders: - 'GKP codes with fixed \(n\) and prime-dimensional logical Hilbert space are symplectically related to a disjoint product of single-mode GKP codes on \(n\) modes, such that encoding via Gaussian unitaries is possible.'