ref

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}.'
 
 
 

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}.'
 
 
 

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.'