diff --git a/codes/classical/bits/quantum_inspired/newman_moore.yml b/codes/classical/bits/quantum_inspired/newman_moore.yml index e77731872..a6c347f25 100644 --- a/codes/classical/bits/quantum_inspired/newman_moore.yml +++ b/codes/classical/bits/quantum_inspired/newman_moore.yml @@ -14,7 +14,7 @@ description: | Member of a family of \([L^2,O(L),O(L^{\frac{\log 3}{\log 2}})]\) binary linear codes on \(L\times L\) square lattices that form the ground-state subspace of a class of exactly solvable spin-glass models with three-body interactions. The codewords resemble the Sierpinski triangle on a square lattice, which can be generated by a cellular automaton \cite{doi:10.1109/12.286310}. -protection: 'Code parameters nearly saturate the classical version of the BPT bound, based on numerical simulations and analytical arguments \cite[Appx. A]{arxiv:0909.5200}.' +protection: 'Code parameters nearly saturate the classical version of the \hyperref[topic:BPT-bound]{BPT bound}, based on numerical simulations and analytical arguments \cite[Appx. A]{arxiv:0909.5200}.' features: decoders: diff --git a/codes/classical/q-ary_digits/quantum_inspired/classical_fractal_liquid.yml b/codes/classical/q-ary_digits/quantum_inspired/classical_fractal_liquid.yml index d9fce84b1..c5ccb215e 100644 --- a/codes/classical/q-ary_digits/quantum_inspired/classical_fractal_liquid.yml +++ b/codes/classical/q-ary_digits/quantum_inspired/classical_fractal_liquid.yml @@ -13,7 +13,7 @@ introduced: '\cite{arXiv:1111.3275,arxiv:1302.6248}' description: | Member of a family of \([L^D,O(L^{D-1}),O(L^{D-\epsilon})]_p\) linear codes on \(D\)-dimensional square lattices of side length \(L\) and for some prime \(p\) and \(\epsilon > 0\) that is based on \(p\)-ary generalizations of the Sierpinski triangle. -protection: 'Parameters of some code families saturate the classical version of the BPT bound \cite{arxiv:1111.3275}.' +protection: 'Parameters of some code families saturate the classical version of the \hyperref[topic:BPT-bound]{BPT bound} \cite{arxiv:1111.3275}.' relations: diff --git a/codes/quantum/properties/stabilizer/qldpc/good_qldpc.yml b/codes/quantum/properties/stabilizer/qldpc/good_qldpc.yml index da66b885f..7e75103b5 100644 --- a/codes/quantum/properties/stabilizer/qldpc/good_qldpc.yml +++ b/codes/quantum/properties/stabilizer/qldpc/good_qldpc.yml @@ -34,7 +34,7 @@ relations: - code_id: qldpc cousins: - code_id: translationally_invariant_stabilizer - detail: 'Chain complexes describing some good QLDPC codes can be ''lifted'' into higher-dimensional manifolds admitting some notion of geometric locality \cite{arXiv:2012.02249,arxiv:2309.16104}. Applying this procedure to good QLDPC codes yiels \([[n,n^{1-2/D},n^{1-1/D}]]\) lattice stabilizer codes in \(D\) spatial dimensions that saturate the BPT bound, up to corrections poly-logarithmic in \(n\) \cite{arxiv:2303.06755}.' + detail: 'Chain complexes describing some good QLDPC codes can be ''lifted'' into higher-dimensional manifolds admitting some notion of geometric locality \cite{arXiv:2012.02249,arxiv:2309.16104}. Applying this procedure to good QLDPC codes yiels \([[n,n^{1-2/D},n^{1-1/D}]]\) lattice stabilizer codes in \(D\) spatial dimensions that saturate the \hyperref[topic:BPT-bound]{BPT bound}, up to corrections poly-logarithmic in \(n\) \cite{arxiv:2303.06755}.' # Begin Entry Meta Information diff --git a/codes/quantum/properties/stabilizer/topological_stabilizer/translationally_invariant_stabilizer.yml b/codes/quantum/properties/stabilizer/topological_stabilizer/translationally_invariant_stabilizer.yml index ce910e0ab..2a66636ed 100644 --- a/codes/quantum/properties/stabilizer/topological_stabilizer/translationally_invariant_stabilizer.yml +++ b/codes/quantum/properties/stabilizer/topological_stabilizer/translationally_invariant_stabilizer.yml @@ -39,9 +39,12 @@ description: | # equivalently expressed by the Laurent polynomial \(x_1x_2^2x_3^3e_1 + x_1^{-1}x_2^2x_3^4e_{q+2}\). protection: | + \begin{defterm}{BPT bound} + \label{topic:BPT-bound} Lattice qubit codes are limited by the \textit{Bravyi-Poulin-Terhal (BPT) bound} \cite{arxiv:0909.5200} (see also \cite{arxiv:0810.1983,arxiv:1008.1029,arxiv:1610.06169}), which states that \(d \leq O(n^{1-1/D})\) and \(k d^{2/D-1} = O(n)\) for \(D\)-dimensional lattice geometries. The \textit{Bravyi-Terhal (BT) bound} states that \(d = O(L^{D-1})\) \cite{arxiv:0810.1983}. Codes on a \(D\)-dimensional homogeneous Riemannian manifold with diameter \(L\) satisfy \(k = O(L^{D-2})\) \cite{arxiv:2009.13551}. + \end{defterm} features: diff --git a/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/layer.yml b/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/layer.yml index e57568cae..e4e30ce3f 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/layer.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/layer.yml @@ -15,7 +15,7 @@ description: | Geometric locality is maintained because, instead of being concatenated, each pair of parallel surface-code squares are fused (or quasi-concatenated) with perpendicular surface-code squares via lattice surgery. features: - rate: 'Code parameters on a cube, \([[n,\Theta(n^{1/3}),\Theta(n^{1/3})]]\), achieve the 3D BPT bound when asymptotically good QLDPC codes are used in the construction.' + rate: 'Code parameters on a cube, \([[n,\Theta(n^{1/3}),\Theta(n^{1/3})]]\), achieve the 3D \hyperref[topic:BPT-bound]{BPT bound} when asymptotically good QLDPC codes are used in the construction.' relations: @@ -27,7 +27,7 @@ relations: detail: 'The Layer code realizes 2D layers of \(\mathbb{Z}_2\) gauge theory connected by defects.' cousins: - code_id: good_qldpc - detail: 'Layer code parameters, \([[n,\Theta(n^{1/3}),\Theta(n^{1/3})]]\), achieve the BPT bound in 3D when asymptotically good QLDPC codes are used in the construction.' + detail: 'Layer code parameters, \([[n,\Theta(n^{1/3}),\Theta(n^{1/3})]]\), achieve the \hyperref[topic:BPT-bound]{BPT bound} in 3D when asymptotically good QLDPC codes are used in the construction.' - code_id: quantum_concatenated detail: 'Each pair of surface-code squares in a layer code are fused (or quasi-concatenated) with perpendicular surface-code squares via lattice surgery.' - code_id: self_correct diff --git a/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml index d50c195c1..981c33bb5 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml @@ -58,7 +58,7 @@ protection: | features: rate: | - Both the planar and toric codes saturate the BPT bound, which states that \(k d^2 = O(L^2)\) for codes on a 2D lattice of length \(O(L)\). + Both the planar and toric codes saturate the \hyperref[topic:BPT-bound]{BPT bound}, which states that \(k d^2 = O(L^2)\) for codes on a 2D lattice of length \(O(L)\). encoders: - 'A depth-\(L^2\) circuit that grows the code out of a small patch on an \(L\times L\) square lattice using CNOT gates (i.e., "local moves") \cite{arxiv:quant-ph/0110143,arxiv:0712.0348}.'