ref tqsg

errorcorrectionzoo · Dec 20, 2024 · 6d472a6 · 6d472a6
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diff --git a/codes/quantum/qubits/stabilizer/qldpc/homological/balanced_product/quantum_expander.yml b/codes/quantum/qubits/stabilizer/qldpc/homological/balanced_product/quantum_expander.yml
@@ -41,6 +41,8 @@ relations:
       detail: 'Quantum expander codes are single-shot \cite{arxiv:1808.03821}.'
   cousins:
     - code_id: expander
+    - code_id: topological
+      detail: 'Quantum expander codes realize topological quantum spin glass order \cite{arxiv:2412.13248}.'
     #      detail: 'Quantum expander codes are constructed from classical expander codes.'
 
 

diff --git a/codes/quantum/qubits/stabilizer/qldpc/homological/dlv.yml b/codes/quantum/qubits/stabilizer/qldpc/homological/dlv.yml
@@ -26,6 +26,8 @@ relations:
     - code_id: qltc
       detail: 'DLV codes have linear dimension and inverse poly-logarithmic relative distance and soundness, assuming a conjecture about random linear maps \cite{arxiv:2402.07476}.
       Applying distance amplification and soundness amplification yields asymptotically constant soundness, \hyperref[topic:asymptotics]{order} \(\Theta(n)\) distance, \hyperref[topic:asymptotics]{order} \(\Theta(n)\) dimension, but poly-logarithmic locality \cite[Table 4]{arxiv:2309.05541}.'
+    - code_id: topological
+      detail: 'DLV codes are expected to realize topological quantum spin glass order \cite{arxiv:2412.13248}.'
 
 
 # Begin Entry Meta Information

diff --git a/...tum/qudits_galois/stabilizer/qldpc/balanced_product/lp/matrix/expander_lifted_product.yml b/...tum/qudits_galois/stabilizer/qldpc/balanced_product/lp/matrix/expander_lifted_product.yml
@@ -45,6 +45,8 @@ relations:
       detail: 'Expander lifted-product codes are products of regular \(q\)-ary Tanner codes defined on expander graphs \cite{doi:10.1090/S0273-0979-06-01126-8}.'
     - code_id: random
       detail: 'Expander lifted-product codes are quantum CSS codes that utilize short classical codes in their construction which need to satisfy some properties (Ref. \cite{arxiv:2111.03654}, Lemma 10). It is shown that such codes exist, but they are not explicitly constructed. Such codes can be obtained by repeated random sampling or by performing a search of all codes of desired length. Nevertheless, since the length of the desired short codes does not scale with \(n\), this construction is effectively explicit.'
+    - code_id: topological
+      detail: 'Expander lifted-product codes are expected to realize topological quantum spin glass order \cite{arxiv:2412.13248}.'
 
 
 # Begin Entry Meta Information