From 90e2235b99c5feb088a5418343544c8fc9250097 Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Mon, 4 Mar 2024 11:05:29 -0700 Subject: [PATCH] ~ --- codes/classical/q-ary_digits/easy/q-ary_hamming.yml | 2 +- .../qubits/stabilizer/magic/quantum_k-orthogonal.yml | 3 ++- .../qubits/stabilizer/qldpc/concatenated/lresc.yml | 2 +- .../qubits/{ => stabilizer}/rm/diagonal_clifford.yml | 0 .../qubits/{ => stabilizer}/rm/quantum_hamming_css.yml | 0 .../qubits/{ => stabilizer}/rm/quantum_reed_muller.yml | 2 -- .../{ => stabilizer}/rm/single_qubit_clifford.yml | 0 .../topological/color/capped_color.yml | 2 +- .../subsystem/topological/color/doubled_color.yml | 2 +- .../subsystem/topological/color/subsystem_color.yml | 10 ++++++---- codes/quantum/qudits/frobenius.yml | 2 +- .../quantum/qudits/{ => stabilizer/ag}/polynomial.yml | 4 ++-- .../qudits/{ => stabilizer/ag}/qudit_hamming_css.yml | 3 ++- .../{small => stabilizer/ag}/qudit_reed_muller.yml | 3 ++- codes/quantum/qudits/{ => stabilizer}/qudit_css.yml | 0 codes/quantum/qudits/{ => stabilizer}/qudit_gkp.yml | 0 .../qudits/{ => stabilizer}/qudit_stabilizer.yml | 0 .../{ => stabilizer}/topological/double_semion.yml | 0 .../topological/fracton/fractal_liquid.yml | 0 .../topological/fracton/qudit_cubic.yml | 0 .../topological/quantum_double_abelian.yml | 0 .../{ => stabilizer}/topological/qudit_color.yml | 0 .../{ => stabilizer}/topological/qudit_surface.yml | 0 .../{ => stabilizer}/topological/tqd_abelian.yml | 0 24 files changed, 19 insertions(+), 16 deletions(-) rename codes/quantum/qubits/{ => stabilizer}/rm/diagonal_clifford.yml (100%) rename codes/quantum/qubits/{ => stabilizer}/rm/quantum_hamming_css.yml (100%) rename codes/quantum/qubits/{ => stabilizer}/rm/quantum_reed_muller.yml (94%) rename codes/quantum/qubits/{ => stabilizer}/rm/single_qubit_clifford.yml (100%) rename codes/quantum/qubits/{stabilizer => subsystem}/topological/color/capped_color.yml (97%) rename codes/quantum/qudits/{ => stabilizer/ag}/polynomial.yml (97%) rename codes/quantum/qudits/{ => stabilizer/ag}/qudit_hamming_css.yml (80%) rename codes/quantum/qudits/{small => stabilizer/ag}/qudit_reed_muller.yml (91%) rename codes/quantum/qudits/{ => stabilizer}/qudit_css.yml (100%) rename codes/quantum/qudits/{ => stabilizer}/qudit_gkp.yml (100%) rename codes/quantum/qudits/{ => stabilizer}/qudit_stabilizer.yml (100%) rename codes/quantum/qudits/{ => stabilizer}/topological/double_semion.yml (100%) rename codes/quantum/qudits/{ => stabilizer}/topological/fracton/fractal_liquid.yml (100%) rename codes/quantum/qudits/{ => stabilizer}/topological/fracton/qudit_cubic.yml (100%) rename codes/quantum/qudits/{ => stabilizer}/topological/quantum_double_abelian.yml (100%) rename codes/quantum/qudits/{ => stabilizer}/topological/qudit_color.yml (100%) rename codes/quantum/qudits/{ => stabilizer}/topological/qudit_surface.yml (100%) rename codes/quantum/qudits/{ => stabilizer}/topological/tqd_abelian.yml (100%) diff --git a/codes/classical/q-ary_digits/easy/q-ary_hamming.yml b/codes/classical/q-ary_digits/easy/q-ary_hamming.yml index fa00e36c3..77d3445cb 100644 --- a/codes/classical/q-ary_digits/easy/q-ary_hamming.yml +++ b/codes/classical/q-ary_digits/easy/q-ary_hamming.yml @@ -30,7 +30,7 @@ relations: - code_id: bch detail: 'Some narrow sense BCH codes of length \(n=(q^r-1)/(q-1)\) such that \(\text{gcd}(r,q-1)=1\) are \(q\)-ary Hamming codes (\cite{doi:10.1017/CBO9780511807077}, Thm. 5.1.4).' - code_id: generalized_reed_muller - detail: 'Hamming codes are dual to first-order GRM codes (\cite{doi:10.1007/978-94-011-3810-9}, pg. 45).' + detail: '\(q\)-ary Hamming codes are dual to first-order GRM codes \cite[pg. 45]{doi:10.1007/978-94-011-3810-9}.' # Begin Entry Meta Information diff --git a/codes/quantum/qubits/stabilizer/magic/quantum_k-orthogonal.yml b/codes/quantum/qubits/stabilizer/magic/quantum_k-orthogonal.yml index 360a2d7a4..7c06c93de 100644 --- a/codes/quantum/qubits/stabilizer/magic/quantum_k-orthogonal.yml +++ b/codes/quantum/qubits/stabilizer/magic/quantum_k-orthogonal.yml @@ -12,6 +12,7 @@ introduced: '\cite{arxiv:1503.08800,arXiv:2210.14066}' description: | Stabilizer code whose \(X\)-type generators form a \(k\)-orthogonal matrix (defined below) in the symplectic representation. + This entry is formulated for qubits, but an extension exists for modular qudits \cite{arxiv:1503.08800}. A matrix is \(k\)-orthogonal \cite[Def. 4]{arxiv:2210.14066} if \begin{align} @@ -28,7 +29,7 @@ relations: - code_id: qubit_stabilizer cousins: - code_id: qudit_color - detail: '\(k\)-orthogonality can be extended to modular-qudit codes and is known as \(k^{\star}\)-orthogonality \cite[Def. 2]{arxiv:1503.08800}. + detail: 'The notion of \(k\)-orthogonality can be extended to modular-qudit codes and is known as \(k^{\star}\)-orthogonality \cite[Def. 2]{arxiv:1503.08800}. Modular-qudit color codes defined on lattices in \(D\) spatial dimension whose \(X\)-type stabilizers are placed on cells of dimension \(\nu \leq D\) are \(k^{\star}\)-orthogonal for all \(k \leq \nu\) \cite[Lemma 5]{arxiv:1503.08800}.' diff --git a/codes/quantum/qubits/stabilizer/qldpc/concatenated/lresc.yml b/codes/quantum/qubits/stabilizer/qldpc/concatenated/lresc.yml index b9c579243..8105deb00 100644 --- a/codes/quantum/qubits/stabilizer/qldpc/concatenated/lresc.yml +++ b/codes/quantum/qubits/stabilizer/qldpc/concatenated/lresc.yml @@ -12,7 +12,7 @@ short_name: 'LRESC' introduced: '\cite{arxiv:2309.11719}' description: |- - Code constructed using the hypergraph product of two copies of a concatanated LDPC-repetition code. + Code constructed using the hypergraph product of two copies of a concatenated LDPC-repetition code. This family interpolates between surface codes and hypergraph codes since the hypergraph product of two repetition codes yields the planar surface code. diff --git a/codes/quantum/qubits/rm/diagonal_clifford.yml b/codes/quantum/qubits/stabilizer/rm/diagonal_clifford.yml similarity index 100% rename from codes/quantum/qubits/rm/diagonal_clifford.yml rename to codes/quantum/qubits/stabilizer/rm/diagonal_clifford.yml diff --git a/codes/quantum/qubits/rm/quantum_hamming_css.yml b/codes/quantum/qubits/stabilizer/rm/quantum_hamming_css.yml similarity index 100% rename from codes/quantum/qubits/rm/quantum_hamming_css.yml rename to codes/quantum/qubits/stabilizer/rm/quantum_hamming_css.yml diff --git a/codes/quantum/qubits/rm/quantum_reed_muller.yml b/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml similarity index 94% rename from codes/quantum/qubits/rm/quantum_reed_muller.yml rename to codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml index 8034a7367..9525740b3 100644 --- a/codes/quantum/qubits/rm/quantum_reed_muller.yml +++ b/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml @@ -32,8 +32,6 @@ relations: - code_id: qubit_css - code_id: qudit_reed_muller detail: 'Prime-qudit RM codes reduce to quantum RM codes when \(q=p=2\).' - - code_id: galois_reed_muller - detail: 'Galois-qudit RM codes reduce to quantum RM codes when \(q=2\).' cousins: - code_id: reed_muller - code_id: quantum_convolutional diff --git a/codes/quantum/qubits/rm/single_qubit_clifford.yml b/codes/quantum/qubits/stabilizer/rm/single_qubit_clifford.yml similarity index 100% rename from codes/quantum/qubits/rm/single_qubit_clifford.yml rename to codes/quantum/qubits/stabilizer/rm/single_qubit_clifford.yml diff --git a/codes/quantum/qubits/stabilizer/topological/color/capped_color.yml b/codes/quantum/qubits/subsystem/topological/color/capped_color.yml similarity index 97% rename from codes/quantum/qubits/stabilizer/topological/color/capped_color.yml rename to codes/quantum/qubits/subsystem/topological/color/capped_color.yml index cdbc9b038..4c6990aa7 100644 --- a/codes/quantum/qubits/stabilizer/topological/color/capped_color.yml +++ b/codes/quantum/qubits/subsystem/topological/color/capped_color.yml @@ -25,7 +25,7 @@ features: relations: parents: - - code_id: color + - code_id: subsystem_color # Begin Entry Meta Information diff --git a/codes/quantum/qubits/subsystem/topological/color/doubled_color.yml b/codes/quantum/qubits/subsystem/topological/color/doubled_color.yml index 4ee6e2ade..1701f6817 100644 --- a/codes/quantum/qubits/subsystem/topological/color/doubled_color.yml +++ b/codes/quantum/qubits/subsystem/topological/color/doubled_color.yml @@ -21,7 +21,7 @@ features: relations: parents: - - code_id: subsystem_css + - code_id: subsystem_color - code_id: translationally_invariant_subsystem cousins: - code_id: quantum_divisible diff --git a/codes/quantum/qubits/subsystem/topological/color/subsystem_color.yml b/codes/quantum/qubits/subsystem/topological/color/subsystem_color.yml index d0ab47995..9c3733c04 100644 --- a/codes/quantum/qubits/subsystem/topological/color/subsystem_color.yml +++ b/codes/quantum/qubits/subsystem/topological/color/subsystem_color.yml @@ -7,6 +7,7 @@ code_id: subsystem_color physical: qubits logical: qubits +# general class encapsulating capped and doubled, so not necessarily translation invariant. Consider peeling off original lattice codes to separate entries name: 'Subsystem color code' introduced: '\cite{arxiv:0908.4246,arxiv:1311.0879}' @@ -14,11 +15,12 @@ alternative_names: - 'Gauge color code' description: | - Subsystem version of the color code that is obtained by expanding the vertices of a two-colex embedded in a surface of genus \(g\). + A subsystem version of the color code. + One way to obtain it is by expanding the vertices of a two-colex embedded in a surface of genus \(g\). Vertex expansion consists of splitting every vertex into a triangle and splitting every edge into a pair of edges. protection: | - The family of subsystem codes has parameters \([[3m,2g,2m+2g-2,d]]\), where \(m\) is the number of vertices of the original embedded two-colex, where \(g\) is the genus of the surface embedding the two-colex, and where the distance is bounded from below by the length of the smallest nontrivial homological cycle of the two-colex \(\Gamma\) \cite[Construction B]{arxiv:1207.0479}\cite[Lemma 2]{arxiv:1805.12542}. + One family of subsystem codes has parameters \([[3m,2g,2m+2g-2,d]]\), where \(m\) is the number of vertices of the original embedded two-colex, where \(g\) is the genus of the surface embedding the two-colex, and where the distance is bounded from below by the length of the smallest nontrivial homological cycle of the two-colex \(\Gamma\) \cite[Construction B]{arxiv:1207.0479}\cite[Lemma 2]{arxiv:1805.12542}. features: general_gates: @@ -38,13 +40,13 @@ relations: - code_id: subsystem_css - code_id: qudit_subsystem_color detail: 'Modular-qudit subsystem color codes reduce to subsystem color codes for \(q=2\).' - - code_id: translationally_invariant_subsystem cousins: - code_id: color - code_id: single_shot detail: 'The 3D subsystem color code is a single-shot code \cite{arxiv:1404.5504,arxiv:1503.08217}.' - code_id: symmetry_protected_self_correct - detail: 'A particular gauge-fixed version of this code on a 3D lattice yields a self-correcting memory protected by one-form symmetries (see Sec. IV D of Ref. \cite{arXiv:1805.01474}). The symmetric energy barrier grows linearly with the length of a side of the lattice. When the system is coupled locally to a thermal bath respecting the symmetry and below a critical temperature, the memory time grows exponentially with the side length. + detail: 'A particular gauge-fixed version of a subsystem code on a 3D lattice yields a self-correcting memory protected by one-form symmetries \cite[Sec. IV D]{arXiv:1805.01474}. + The symmetric energy barrier grows linearly with the length of a side of the lattice. When the system is coupled locally to a thermal bath respecting the symmetry and below a critical temperature, the memory time grows exponentially with the side length. The subsystem color code is not a self-correcting quantum memory if symmetry protection is removed \cite{arxiv:2305.06389}.' diff --git a/codes/quantum/qudits/frobenius.yml b/codes/quantum/qudits/frobenius.yml index 11bff7041..564e304be 100644 --- a/codes/quantum/qudits/frobenius.yml +++ b/codes/quantum/qudits/frobenius.yml @@ -23,7 +23,7 @@ notes: relations: parents: - - code_id: qudit_stabilizer + - code_id: qudits_into_qudits - code_id: quantum_cyclic diff --git a/codes/quantum/qudits/polynomial.yml b/codes/quantum/qudits/stabilizer/ag/polynomial.yml similarity index 97% rename from codes/quantum/qudits/polynomial.yml rename to codes/quantum/qudits/stabilizer/ag/polynomial.yml index 7893f5d6d..f3ad1d52d 100644 --- a/codes/quantum/qudits/polynomial.yml +++ b/codes/quantum/qudits/stabilizer/ag/polynomial.yml @@ -7,7 +7,7 @@ code_id: polynomial physical: qudits logical: qudits -name: 'Prime-qudit quantum RS code' +name: 'Prime-qudit RS code' introduced: '\cite{arxiv:quant-ph/9910059}' # doi:10.1103/PhysRevA.77.012308? @@ -37,7 +37,7 @@ relations: parents: - code_id: qudit_css - code_id: galois_polynomial - detail: 'Galois-qudit RS codes for prime-dimensional qudits are quantum RS codes.' + detail: 'Galois-qudit RS codes for prime-dimensional qudits are prime-qudit RS codes.' cousins: - code_id: quantum_triorthogonal detail: 'Triorthogonality can be generalized to qudit codes. diff --git a/codes/quantum/qudits/qudit_hamming_css.yml b/codes/quantum/qudits/stabilizer/ag/qudit_hamming_css.yml similarity index 80% rename from codes/quantum/qudits/qudit_hamming_css.yml rename to codes/quantum/qudits/stabilizer/ag/qudit_hamming_css.yml index a7d499e57..54fa6eac7 100644 --- a/codes/quantum/qudits/qudit_hamming_css.yml +++ b/codes/quantum/qudits/stabilizer/ag/qudit_hamming_css.yml @@ -17,7 +17,8 @@ description: 'A family of CSS codes extending \hyperref[code:quantum_hamming_css relations: parents: - - code_id: qudit_css + - code_id: qudit_reed_muller + detail: '\([[2^r-1, 2^r-2r-1, 3]]_p\) quantum Hamming codes are constructed using \(q\)-ary Hamming codes, which themselves are dual to first-order GRM codes \cite[pg. 45]{doi:10.1007/978-94-011-3810-9}.' - code_id: small_distance_quantum diff --git a/codes/quantum/qudits/small/qudit_reed_muller.yml b/codes/quantum/qudits/stabilizer/ag/qudit_reed_muller.yml similarity index 91% rename from codes/quantum/qudits/small/qudit_reed_muller.yml rename to codes/quantum/qudits/stabilizer/ag/qudit_reed_muller.yml index a7572e348..35ec3dd77 100644 --- a/codes/quantum/qudits/small/qudit_reed_muller.yml +++ b/codes/quantum/qudits/stabilizer/ag/qudit_reed_muller.yml @@ -10,8 +10,9 @@ logical: qudits name: 'Prime-qudit RM code' introduced: '\cite{arXiv:quant-ph/0502001,arxiv:1205.3104}' +# Dual added to include qudit_hamming_css as a child description: | - Modular-qudit stabilizer code constructed from generalized Reed-Muller (GRM) codes via the modular-qudit CSS construction. + Modular-qudit stabilizer code constructed from generalized Reed-Muller (GRM) codes or their duals via the modular-qudit CSS construction. An odd-prime-qudit CSS code family constructed from first-order punctured RM codes transversally implements a diagonal gate at any level of the \hyperref[topic:qudit-clifford-hierarchy]{qudit Clifford hierarchy} \cite{arxiv:1205.3104}. features: diff --git a/codes/quantum/qudits/qudit_css.yml b/codes/quantum/qudits/stabilizer/qudit_css.yml similarity index 100% rename from codes/quantum/qudits/qudit_css.yml rename to codes/quantum/qudits/stabilizer/qudit_css.yml diff --git a/codes/quantum/qudits/qudit_gkp.yml b/codes/quantum/qudits/stabilizer/qudit_gkp.yml similarity index 100% rename from codes/quantum/qudits/qudit_gkp.yml rename to codes/quantum/qudits/stabilizer/qudit_gkp.yml diff --git a/codes/quantum/qudits/qudit_stabilizer.yml b/codes/quantum/qudits/stabilizer/qudit_stabilizer.yml similarity index 100% rename from codes/quantum/qudits/qudit_stabilizer.yml rename to codes/quantum/qudits/stabilizer/qudit_stabilizer.yml diff --git a/codes/quantum/qudits/topological/double_semion.yml b/codes/quantum/qudits/stabilizer/topological/double_semion.yml similarity index 100% rename from codes/quantum/qudits/topological/double_semion.yml rename to codes/quantum/qudits/stabilizer/topological/double_semion.yml diff --git a/codes/quantum/qudits/topological/fracton/fractal_liquid.yml b/codes/quantum/qudits/stabilizer/topological/fracton/fractal_liquid.yml similarity index 100% rename from codes/quantum/qudits/topological/fracton/fractal_liquid.yml rename to codes/quantum/qudits/stabilizer/topological/fracton/fractal_liquid.yml diff --git a/codes/quantum/qudits/topological/fracton/qudit_cubic.yml b/codes/quantum/qudits/stabilizer/topological/fracton/qudit_cubic.yml similarity index 100% rename from codes/quantum/qudits/topological/fracton/qudit_cubic.yml rename to codes/quantum/qudits/stabilizer/topological/fracton/qudit_cubic.yml diff --git a/codes/quantum/qudits/topological/quantum_double_abelian.yml b/codes/quantum/qudits/stabilizer/topological/quantum_double_abelian.yml similarity index 100% rename from codes/quantum/qudits/topological/quantum_double_abelian.yml rename to codes/quantum/qudits/stabilizer/topological/quantum_double_abelian.yml diff --git a/codes/quantum/qudits/topological/qudit_color.yml b/codes/quantum/qudits/stabilizer/topological/qudit_color.yml similarity index 100% rename from codes/quantum/qudits/topological/qudit_color.yml rename to codes/quantum/qudits/stabilizer/topological/qudit_color.yml diff --git a/codes/quantum/qudits/topological/qudit_surface.yml b/codes/quantum/qudits/stabilizer/topological/qudit_surface.yml similarity index 100% rename from codes/quantum/qudits/topological/qudit_surface.yml rename to codes/quantum/qudits/stabilizer/topological/qudit_surface.yml diff --git a/codes/quantum/qudits/topological/tqd_abelian.yml b/codes/quantum/qudits/stabilizer/topological/tqd_abelian.yml similarity index 100% rename from codes/quantum/qudits/topological/tqd_abelian.yml rename to codes/quantum/qudits/stabilizer/topological/tqd_abelian.yml