From ae6d9ae1a119532a390fe62eeb04210b993daa09 Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Fri, 3 May 2024 14:52:35 -0400 Subject: [PATCH] unentangled_permutation_invariant --- ...stant_excitation_permutation_invariant.yml | 2 +- .../block/symmetric/permutation_invariant.yml | 5 ++- .../properties/stabilizer/qldpc/qldpc.yml | 2 + codes/quantum/qubits/nonstabilizer/eth.yml | 2 +- .../binary_dihedral_permutation_invariant.yml | 14 +++---- .../combinatorial_permutation_invariant.yml | 4 +- .../gnu/four_qubit_permutation_invariant.yml | 4 +- .../gnu/gnu_permutation_invariant.yml | 13 +++--- .../gnu/qudit_gnu_permutation_invariant.yml | 6 +-- .../permutation_invariant/gnu/ruskai.yml | 6 +-- .../icosahedral_permutation_invariant.yml | 4 +- .../qubit_permutation_invariant.yml | 8 ++-- .../unentangled_permutation_invariant.yml | 41 +++++++++++++++++++ codes/quantum/qubits/qubits_into_qubits.yml | 2 + .../qubits/stabilizer/qubit_stabilizer.yml | 2 + .../surface/2d_surface/surface/surface.yml | 1 + codes/quantum/spins/single_spin/j_gross.yml | 2 +- .../quantum/spins/single_spin/single_spin.yml | 6 +-- codes/quantum/spins/single_spin/spin_cat.yml | 2 +- 19 files changed, 89 insertions(+), 37 deletions(-) create mode 100644 codes/quantum/qubits/permutation_invariant/unentangled_permutation_invariant.yml diff --git a/codes/quantum/oscillators/fock_state/constant_excitation/constant_excitation_permutation_invariant.yml b/codes/quantum/oscillators/fock_state/constant_excitation/constant_excitation_permutation_invariant.yml index 643221a68..14f1bca4f 100644 --- a/codes/quantum/oscillators/fock_state/constant_excitation/constant_excitation_permutation_invariant.yml +++ b/codes/quantum/oscillators/fock_state/constant_excitation/constant_excitation_permutation_invariant.yml @@ -6,7 +6,7 @@ code_id: constant_excitation_permutation_invariant physical: oscillators -name: 'Ouyang-Chao constant-excitation permutation-invariant code' +name: 'Ouyang-Chao constant-excitation PI code' short_name: 'Ouyang-Chao' introduced: '\cite{arxiv:1809.09801}' diff --git a/codes/quantum/properties/block/symmetric/permutation_invariant.yml b/codes/quantum/properties/block/symmetric/permutation_invariant.yml index 513cacf5c..62807628a 100644 --- a/codes/quantum/properties/block/symmetric/permutation_invariant.yml +++ b/codes/quantum/properties/block/symmetric/permutation_invariant.yml @@ -5,7 +5,8 @@ code_id: permutation_invariant -name: 'Permutation-invariant code' +name: 'Permutation-invariant (PI) code' +short_name: 'PI' introduced: '\cite{arxiv:quant-ph/0304153}' description: | @@ -18,7 +19,7 @@ protection: | Permutation invariant codes of distance \(d\) can protect against \(d-1\) deletion errors \cite{arxiv:2001.08405,arxiv:2004.00814,arxiv:2102.02494,arxiv:2102.03015}, i.e., erasures of subsystems at unknown locations. Other protection depends on the code family. - The GNU permutation-invariant family (parameterized by \(t\)) protects against arbitrary weight \(t\) qubit errors and approximately corrects spontaneous decay errors \cite{arxiv:1302.3247,doi:10.1103/PhysRevA.93.042340}. + The GNU PI family (parameterized by \(t\)) protects against arbitrary weight \(t\) qubit errors and approximately corrects spontaneous decay errors \cite{arxiv:1302.3247,doi:10.1103/PhysRevA.93.042340}. Other related codes protect against amplitude damping \cite{doi:10.1109/TIT.2019.2956142} while admitting a constant number of excitations. features: diff --git a/codes/quantum/properties/stabilizer/qldpc/qldpc.yml b/codes/quantum/properties/stabilizer/qldpc/qldpc.yml index b2bcaf1c6..cd4263cea 100644 --- a/codes/quantum/properties/stabilizer/qldpc/qldpc.yml +++ b/codes/quantum/properties/stabilizer/qldpc/qldpc.yml @@ -61,6 +61,7 @@ protection: | \delta = \frac{d}{n} \leq \frac{1}{2} - \Omega\left(\frac{1}{r}\right)~. \end{align} + features: rate: | Asymptotic scaling of \(k\) and \(d\) with \(n\) depends heavily on the code construction. @@ -101,6 +102,7 @@ notes: - 'Infleqtion QLDPC package for estimating distance and creating various qubit and Galois-qudit QLDPC CSS codes \cite{manual:{Michael A. Perlin. qLDPC. https://github.com/Infleqtion/qLDPC, 2023.}}' - 'Links to code tables of notable QLDPC codes \cite{arxiv:2103.06309}.' - 'Reviews of QLDPC codes provided in Refs. \cite{doi:10.1109/ACCESS.2015.2503267,arxiv:2103.06309}.' + - 'There exist distance-dependent \cite[Thm. 1]{arxiv:2405.01332} and rate-dependent \cite[Thm. 3ii]{arxiv:2405.01332} lower bounds on the degree of entanglement of a qubit QLDPC code.' relations: parents: diff --git a/codes/quantum/qubits/nonstabilizer/eth.yml b/codes/quantum/qubits/nonstabilizer/eth.yml index 5267de54a..b1eaad5d7 100644 --- a/codes/quantum/qubits/nonstabilizer/eth.yml +++ b/codes/quantum/qubits/nonstabilizer/eth.yml @@ -47,7 +47,7 @@ relations: - code_id: topological detail: 'ETH codewords, like topological codewords, are locally indistinguishable.' - code_id: qubit_permutation_invariant - detail: 'Several instances of ETH codes contain permutation-invariant qubit codewords.' + detail: 'Several instances of ETH codes contain PI qubit codewords.' # Begin Entry Meta Information diff --git a/codes/quantum/qubits/permutation_invariant/binary_dihedral_permutation_invariant.yml b/codes/quantum/qubits/permutation_invariant/binary_dihedral_permutation_invariant.yml index 676cb161c..da44b64f4 100644 --- a/codes/quantum/qubits/permutation_invariant/binary_dihedral_permutation_invariant.yml +++ b/codes/quantum/qubits/permutation_invariant/binary_dihedral_permutation_invariant.yml @@ -7,7 +7,7 @@ code_id: binary_dihedral_permutation_invariant physical: qubits logical: qubits -name: 'Binary dihedral permutation-invariant code' +name: 'Binary dihedral PI code' introduced: '\cite{arxiv:2310.17652}' description: | @@ -29,20 +29,20 @@ relations: parents: - code_id: qubit_permutation_invariant - code_id: j_gross - detail: 'Binary dihedral permutation-invariant codes can be interpreted as Clifford single-spin codes.' + detail: 'Binary dihedral PI codes can be interpreted as Clifford single-spin codes.' cousins: - code_id: small_distance_quantum - detail: 'The first and second families of binary dihedral permutation-invariant codes have distance three, and the third family has the member \(((27,2,5))\).' + detail: 'The first and second families of binary dihedral PI codes have distance three, and the third family has the member \(((27,2,5))\).' - code_id: combinatorial_permutation_invariant - detail: 'The \(Q_{3,1,2m-4,+}\) and \(Q_{3,1,2^m-4,+}\) combinatorial permutation-invariant codes reduce to the \(((2m+3,2,3))\) and \(((2^{m-1}+3,2,3))\) binary dihedral permutation-invariant codes, respectively \cite[Prop. 5.6]{arxiv:2310.05358}.' + detail: 'The \(Q_{3,1,2m-4,+}\) and \(Q_{3,1,2^m-4,+}\) combinatorial PI codes reduce to the \(((2m+3,2,3))\) and \(((2^{m-1}+3,2,3))\) binary dihedral PI codes, respectively \cite[Prop. 5.6]{arxiv:2310.05358}.' - code_id: xp_stabilizer detail: 'Binary dihedral permutation invariant codewords form error spaces of XP stabilizer codes.' - code_id: diagonal_clifford - detail: 'The \(((2^{r-1}+3,2,3))\) family of binary dihedral permutation-invariant codes realizes the same transversal gates as the \([[2^r-1,1,3]]\) quantum Reed-Muller codes, but require fewer qubits in almost all cases.' + detail: 'The \(((2^{r-1}+3,2,3))\) family of binary dihedral PI codes realizes the same transversal gates as the \([[2^r-1,1,3]]\) quantum Reed-Muller codes, but require fewer qubits in almost all cases.' - code_id: stab_49_1_5 - detail: 'The \(((27,2,5))\) binary dihedral permutation-invariant code realizes the \(T\) gate transversally, but requires fewer qubits than the \([[49,1,5]]\) triorthogonal code.' + detail: 'The \(((27,2,5))\) binary dihedral PI code realizes the \(T\) gate transversally, but requires fewer qubits than the \([[49,1,5]]\) triorthogonal code.' - code_id: stab_15_1_3 - detail: 'The \(((11,2,3))\) binary dihedral permutation-invariant code realizes the \(T\) gate transversally, but requires fewer qubits than the \([[15,1,3]]\) quantum Reed-Muller code.' + detail: 'The \(((11,2,3))\) binary dihedral PI code realizes the \(T\) gate transversally, but requires fewer qubits than the \([[15,1,3]]\) quantum Reed-Muller code.' # Begin Entry Meta Information diff --git a/codes/quantum/qubits/permutation_invariant/combinatorial_permutation_invariant.yml b/codes/quantum/qubits/permutation_invariant/combinatorial_permutation_invariant.yml index 37eb1790b..112eeaeae 100644 --- a/codes/quantum/qubits/permutation_invariant/combinatorial_permutation_invariant.yml +++ b/codes/quantum/qubits/permutation_invariant/combinatorial_permutation_invariant.yml @@ -7,11 +7,11 @@ code_id: combinatorial_permutation_invariant physical: qubits logical: qubits -name: 'Combinatorial permutation-invariant code' +name: 'Combinatorial PI code' introduced: '\cite{arxiv:2310.05358}' description: | - A member of a family of permutation-invariant quantum codes whose correction properties are derived from solving a family of combinatorial identities. + A member of a family of PI quantum codes whose correction properties are derived from solving a family of combinatorial identities. The code encodes one logical qubit in superpositions of \hyperref[topic:dicke]{Dicke states} whose coefficients are square roots of ratios of binomial coefficients. protection: | diff --git a/codes/quantum/qubits/permutation_invariant/gnu/four_qubit_permutation_invariant.yml b/codes/quantum/qubits/permutation_invariant/gnu/four_qubit_permutation_invariant.yml index cd9002445..b82b822aa 100644 --- a/codes/quantum/qubits/permutation_invariant/gnu/four_qubit_permutation_invariant.yml +++ b/codes/quantum/qubits/permutation_invariant/gnu/four_qubit_permutation_invariant.yml @@ -9,7 +9,7 @@ name: 'Four-qubit single-deletion code' introduced: '\cite{arxiv:2001.08405,arxiv:2004.00814}' description: | - Four-qubit permutation-invariant code that is the smallest qubit code to correct one deletion error. + Four-qubit PI code that is the smallest qubit code to correct one deletion error. In terms of \hyperref[topic:dicke]{Dicke states}, a basis of logical codewords is \begin{align} @@ -34,7 +34,7 @@ relations: - code_id: stab_4_2_2 detail: 'A basis of codewords for the four-qubit single-deletion code consists of the \(|\overline{00}\rangle\) and \(|\overline{01}\rangle+|\overline{10}\rangle+|\overline{11}\rangle\)states of the four-qubit code.' - code_id: combinatorial_permutation_invariant - detail: 'The combinatorial permutation-invariant code \(Q_{1,1,1,-}\) is another example of a four-qubit code correcting a single deletion error \cite[Sec. 5.1]{arxiv:2310.05358}.' + detail: 'The combinatorial PI code \(Q_{1,1,1,-}\) is another example of a four-qubit code correcting a single deletion error \cite[Sec. 5.1]{arxiv:2310.05358}.' # Begin Entry Meta Information diff --git a/codes/quantum/qubits/permutation_invariant/gnu/gnu_permutation_invariant.yml b/codes/quantum/qubits/permutation_invariant/gnu/gnu_permutation_invariant.yml index 6289e53f8..8864c0513 100644 --- a/codes/quantum/qubits/permutation_invariant/gnu/gnu_permutation_invariant.yml +++ b/codes/quantum/qubits/permutation_invariant/gnu/gnu_permutation_invariant.yml @@ -7,12 +7,12 @@ code_id: gnu_permutation_invariant physical: spins logical: qubits -name: 'GNU permutation-invariant code' +name: 'GNU PI code' short_name: 'GNU' introduced: '\cite{arxiv:1302.3247,arxiv:1512.02469}' description: | - Permutation-invariant code whose codewords can be expressed as superpositions of \hyperref[topic:dicke]{Dicke states} with coefficients are square-roots of the binomial distribution. + PI code whose codewords can be expressed as superpositions of \hyperref[topic:dicke]{Dicke states} with coefficients are square-roots of the binomial distribution. In terms of \hyperref[topic:dicke]{Dicke states}, logical codewords for codes encoding a single qubit \cite{arxiv:1302.3247} are \begin{align} @@ -29,6 +29,9 @@ features: decoders: - 'For a family of shifted gnu codes, decoding can be done using projection, probability amplitude rebalancing, and gate teleportation in time \(O(n^2)\) \cite{arxiv:2102.02494}.' +notes: + - 'The degree of entanglement in (non-concatenated) GNU codes scales at most logarithmically in their distance \cite[Appx. D]{arxiv:2405.01332}.' + relations: parents: @@ -36,9 +39,9 @@ relations: detail: 'Qudit GNU codes encoding logical qubits reduce to GNU codes.' cousins: - code_id: combinatorial_permutation_invariant - detail: 'Combinatorial permutation-invariant codes \(Q_{g,(m-1)/2,g-1,+}\) are GNU codes for odd \(m\) \cite[Prop. 5.4]{arxiv:2310.05358}.' + detail: 'Combinatorial PI codes \(Q_{g,(m-1)/2,g-1,+}\) are GNU codes for odd \(m\) \cite[Prop. 5.4]{arxiv:2310.05358}.' - code_id: bacon_shor - detail: 'GNU codes of length \((2t+1)^2\) result from projecting Bacon-Shor codes into the permutation-invariant qubit subspace \cite{arxiv:1302.3247}.' + detail: 'GNU codes of length \((2t+1)^2\) result from projecting Bacon-Shor codes into the PI qubit subspace \cite{arxiv:1302.3247}.' - code_id: hamiltonian detail: 'GNU codes lie within the ground state of ferromagnetic Heisenberg models without an external magnetic field \cite{arxiv:1904.01458}.' - code_id: approximate_qecc @@ -46,7 +49,7 @@ relations: - code_id: binomial detail: 'Binomial codes and GNU codes related via the Holstein-Primakoff mapping \cite{doi:10.1103/PhysRev.58.1098} (see also \cite{doi:10.2307/3212170}). A qudit generalization of GNU codes can be obtained from qudit binomial codes \cite[Appx. C]{arxiv:1708.05010}.' - code_id: metopt - detail: 'GNU codes can be used to sense signals within the permutation-invariant subspace \cite{arxiv:2212.06285}.' + detail: 'GNU codes can be used to sense signals within the PI subspace \cite{arxiv:2212.06285}.' # - code_id: gkp diff --git a/codes/quantum/qubits/permutation_invariant/gnu/qudit_gnu_permutation_invariant.yml b/codes/quantum/qubits/permutation_invariant/gnu/qudit_gnu_permutation_invariant.yml index 010527881..d32d02bd6 100644 --- a/codes/quantum/qubits/permutation_invariant/gnu/qudit_gnu_permutation_invariant.yml +++ b/codes/quantum/qubits/permutation_invariant/gnu/qudit_gnu_permutation_invariant.yml @@ -7,13 +7,13 @@ code_id: qudit_gnu_permutation_invariant physical: spins logical: qudits -name: 'Qudit GNU permutation-invariant code' +name: 'Qudit GNU PI code' short_name: 'Qudit GNU' introduced: '\cite{arxiv:1604.07925}' description: | - Extension of the GNU permutation-invariant codes to those encoding logical qudits into physical qubits. - Codewords can be expressed as superpositions of \hyperref[topic:dicke]{Dicke states} with coefficients are square-roots of polynomial coefficients, with the case of binomial coefficients reducing to the GNU permutation-invariant codes. + Extension of the GNU PI codes to those encoding logical qudits into physical qubits. + Codewords can be expressed as superpositions of \hyperref[topic:dicke]{Dicke states} with coefficients are square-roots of polynomial coefficients, with the case of binomial coefficients reducing to the GNU PI codes. relations: diff --git a/codes/quantum/qubits/permutation_invariant/gnu/ruskai.yml b/codes/quantum/qubits/permutation_invariant/gnu/ruskai.yml index dc0906304..3ab19becc 100644 --- a/codes/quantum/qubits/permutation_invariant/gnu/ruskai.yml +++ b/codes/quantum/qubits/permutation_invariant/gnu/ruskai.yml @@ -11,7 +11,7 @@ name: '\(((9,2,3))\) Ruskai code' introduced: '\cite{arxiv:quant-ph/9906114}' description: | - Nine-qubit permutation-invariant code that protects against single-qubit errors as well as two-qubit errors arising from exchange processes. + Nine-qubit PI code that protects against single-qubit errors as well as two-qubit errors arising from exchange processes. In terms of \hyperref[topic:dicke]{Dicke states}, the codewords are \begin{align} @@ -28,11 +28,11 @@ protection: | relations: parents: - code_id: gnu_permutation_invariant - detail: 'The \(((9,2,3))\) Ruskai code is a GNU permutation-invariant code \cite{arxiv:1302.3247}.' + detail: 'The \(((9,2,3))\) Ruskai code is a GNU PI code \cite{arxiv:1302.3247}.' - code_id: small_distance_quantum cousins: - code_id: shor_nine - detail: 'The \(((9,2,3))\) Ruskai code results from projecting the Shor code into the permutation-invariant qubit subspace \cite{arxiv:quant-ph/9906114}.' + detail: 'The \(((9,2,3))\) Ruskai code results from projecting the Shor code into the PI qubit subspace \cite{arxiv:quant-ph/9906114}.' # Begin Entry Meta Information diff --git a/codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml b/codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml index 1d8d25de3..59782d5f1 100644 --- a/codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml +++ b/codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml @@ -11,7 +11,7 @@ name: '\(((7,2,3))\) Pollatsek-Ruskai code' introduced: '\cite{arxiv:quant-ph/0304153,arxiv:2005.10910,arxiv:2305.07023}' description: | - Seven-qubit permutation-invariant code that realizes gates from the binary icosahedral group transversally. + Seven-qubit PI code that realizes gates from the binary icosahedral group transversally. Can also be interpreted as a spin-\(7/2\) single-spin code. The codespace projection is a projection onto an irrep of the binary icosahedral group \(2I\). @@ -30,7 +30,7 @@ features: relations: parents: - code_id: combinatorial_permutation_invariant - detail: 'The Pollatsek-Ruskai code is equivalent to the \(Q_{2,1,2,-}\) combinatorial permutation-invariant code \cite[Sec. 5.2]{arxiv:2310.05358}.' + detail: 'The Pollatsek-Ruskai code is equivalent to the \(Q_{2,1,2,-}\) combinatorial PI code \cite[Sec. 5.2]{arxiv:2310.05358}.' - code_id: t_group detail: 'The \(((7,2,3))\) Pollatsek-Ruskai code admits a transversal representation of the twisted \(1\)-group \(2I\) \cite{arxiv:2402.01638}.' - code_id: j_gross diff --git a/codes/quantum/qubits/permutation_invariant/qubit_permutation_invariant.yml b/codes/quantum/qubits/permutation_invariant/qubit_permutation_invariant.yml index 9cdae3977..c5398861f 100644 --- a/codes/quantum/qubits/permutation_invariant/qubit_permutation_invariant.yml +++ b/codes/quantum/qubits/permutation_invariant/qubit_permutation_invariant.yml @@ -7,20 +7,20 @@ code_id: qubit_permutation_invariant physical: qubits # Qudit GNU codes don't encode logical qubits -name: 'Permutation-invariant qubit code' +name: 'PI qubit code' description: | Block quantum code defined on two-dimensional subsystems such that any permutation of the subsystems leaves any codeword invariant. \begin{defterm}{Dicke states} \label{topic:dicke} - For \(n\)-qubit block codes, an often used basis for the \(n+1\)-dimensional permutation-invariant subspace consists of the Dicke states \(|D^n_w\rangle\) -- normalized permutation-invariant states of \(w\) excitations, i.e., a normalized sum over all binary-string basis elements with \(w\) ones and \(n - w\) zeroes. + For \(n\)-qubit block codes, an often used basis for the \(n+1\)-dimensional PI subspace consists of the Dicke states \(|D^n_w\rangle\) -- normalized PI states of \(w\) excitations, i.e., a normalized sum over all binary-string basis elements with \(w\) ones and \(n - w\) zeroes. For example, the single-excitation Dicke state on three qubits is \begin{align} |D_{1}^{3}\rangle=\frac{1}{\sqrt{3}}\left(|001\rangle+|010\rangle+|100\rangle\right)~. \end{align} - The \(n+1\)-dimensional permutation-invariant space can be thought of as a standalone spin-\(n/2\) quantum system, yielding a way to convert between permutation-invatiant qubit codes and \(SU(2)\) spin codes. - A single-spin code for the \(SU(2)\) group correcting spherical tensors can be mapped into a permutation-invariant qubit code with an analogous distance \cite{arxiv:2304.08611}\cite[Thm. 1]{arxiv:2310.17652}. + The \(n+1\)-dimensional PI space can be thought of as a standalone spin-\(n/2\) quantum system, yielding a way to convert between permutation-invatiant qubit codes and \(SU(2)\) spin codes. + A single-spin code for the \(SU(2)\) group correcting spherical tensors can be mapped into a PI qubit code with an analogous distance \cite{arxiv:2304.08611}\cite[Thm. 1]{arxiv:2310.17652}. \end{defterm} protection: | diff --git a/codes/quantum/qubits/permutation_invariant/unentangled_permutation_invariant.yml b/codes/quantum/qubits/permutation_invariant/unentangled_permutation_invariant.yml new file mode 100644 index 000000000..3da98808b --- /dev/null +++ b/codes/quantum/qubits/permutation_invariant/unentangled_permutation_invariant.yml @@ -0,0 +1,41 @@ +####################################################### +## This is a code entry in the error correction zoo. ## +## https://github.com/errorcorrectionzoo ## +####################################################### + +code_id: unentangled_permutation_invariant +physical: qubits +logical: qubits + +name: '\(((n,1,2))\) Bravyi-Lee-Li-Yoshida PI code' +introduced: '\cite{arxiv:2405.01332}' + +description: | + PI distance-two code on \(n\geq4\) qubits whose degree of entanglement vanishes asymptotically with \(n\) \cite[Appx. D]{arxiv:2405.01332}. + + In terms of \hyperref[topic:dicke]{Dicke states}, the codewords are + \begin{align} + \begin{split} + |0_{L}\rangle&=\sqrt{1-\frac{2}{n}}|D_{0}^{n}\rangle+\sqrt{\frac{2}{n}}|D_{n}^{n}\rangle\\ + |1_{L}\rangle&=|D_{2}^{n}\rangle~. + \end{split} + \end{align} + + +relations: + parents: + - code_id: qubit_permutation_invariant + - code_id: movassagh_ouyang + detail: 'The \(((n,1,2))\) PI code is a Movassagh-Ouyang Hamiltonian code constructed from a binary code consisting of all codewords of weight 0, 2, or \(n\) \cite[Appx. D]{arxiv:2405.01332}.' + - code_id: small_distance_quantum + cousins: + - code_id: quantum_concatenated + detail: 'The Bravyi-Lee-Li-Yoshida PI code can be concatenated to yield codes that have higher distance and that admit codewords with vanishing entanglement \cite[Appx. D]{arxiv:2405.01332}.' + + +# Begin Entry Meta Information +_meta: + # Change log - most recent first + changelog: + - user_id: VictorVAlbert + date: '2024-02-07' diff --git a/codes/quantum/qubits/qubits_into_qubits.yml b/codes/quantum/qubits/qubits_into_qubits.yml index 85736fa2a..ddf72d8ff 100644 --- a/codes/quantum/qubits/qubits_into_qubits.yml +++ b/codes/quantum/qubits/qubits_into_qubits.yml @@ -122,6 +122,8 @@ features: notes: - 'There is a relation between one-way entanglement distillation protocols and QECCs \cite{arxiv:quant-ph/9604024}.' - 'See \href{https://github.com/qiskit-community/qiskit-qec}{Qiskit QEC framework} for realizing protocols on IBM machines.' + - 'There exists a distance- and rate-dependent lower bound on the degree of entanglement of a qubit code \cite[Thm. 3i]{arxiv:2405.01332}.' + relations: parents: diff --git a/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml b/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml index 83aeffa98..8d364308c 100644 --- a/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml +++ b/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml @@ -133,6 +133,8 @@ notes: - 'Tables of bounds and examples of stabilizer codes for various \(n\) and \(k\), based on algorithms developed in Ref. \cite{doi:10.1007/978-3-540-37634-7_13}, are maintained by M. Grassl at this \href{http://codetables.markus-grassl.de/}{website}.' - 'Stabilizer error-recovery circuits can be simulated efficiently using dedicated software (e.g., STIM \cite{arxiv:2103.02202}).' - 'There is a correspondence between stabilizer codes and bilocal Clifford entanglement distillation circuits \cite{arxiv:2303.11465}.' + - 'The overlap between any stabilizer codeword and any \(n\)-qubit product state is at most \(2/2^d\) \cite[Thm. 2]{arxiv:2405.01332}.' + relations: parents: diff --git a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface/surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface/surface.yml index 8e5b99508..9488fd00c 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface/surface.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface/surface.yml @@ -126,6 +126,7 @@ features: - 'Markov-chain Monte Carlo \cite{arxiv:1302.2669}.' - 'Cellular automaton decoders \cite{doi:10.7907/AHMQ-EG82,arxiv:1406.2338,arxiv:1511.05579}; see also \cite{arxiv:1512.04528}.' - 'Neural network \cite{arxiv:1610.04238,arxiv:1802.06441,arxiv:2208.05758}, reinforcement learning \cite{arxiv:1810.07207,arxiv:2212.11890}, and transformer-based \cite{arxiv:2311.16082} decoders.' + - 'Lightweight low-latency look-up table (LILLIPUT) decoder for small surface codes \cite{arxiv:2108.06569}.' - 'Decoders can be augmented with a pre-decoder \cite{arxiv:2001.11427,arxiv:2208.04660}, which can allow for some processing to be done inside the cryogenic environment of the quantum system \cite{arxiv:2208.08547}.' - 'Sliding-window \cite{arxiv:2209.09219,arxiv:2209.08552} and parallel-window \cite{arxiv:2209.09219} parallelizable decoders, designed to overcome the backlog problem, can be combined with many inner decoders, such as MWPM or union-find.' - 'Modifications of BP: diff --git a/codes/quantum/spins/single_spin/j_gross.yml b/codes/quantum/spins/single_spin/j_gross.yml index 7404c2379..e97cac62e 100644 --- a/codes/quantum/spins/single_spin/j_gross.yml +++ b/codes/quantum/spins/single_spin/j_gross.yml @@ -43,7 +43,7 @@ relations: - code_id: group_representation detail: 'Clifford spin codes are group-representation codes with \(G\) being a subgroup of \(SU(2)\) \cite{arxiv:2306.11621}.' - code_id: qubit_permutation_invariant - detail: 'Clifford codes for spins housing representations of \(SU(2)\) yield permutation-invariant qubit codes with non-trivial distance when the single spin-\(n/2\) is treated as the permutationally invariant subspace of \(n\) qubits via the \hyperref[topic:dicke]{Dicke-state mapping}. + detail: 'Clifford codes for spins housing representations of \(SU(2)\) yield PI qubit codes with non-trivial distance when the single spin-\(n/2\) is treated as the permutationally invariant subspace of \(n\) qubits via the \hyperref[topic:dicke]{Dicke-state mapping}. The subgroup of gates of a Clifford spin code is implemented transversally via this mapping \cite{arxiv:2304.08611}.' diff --git a/codes/quantum/spins/single_spin/single_spin.yml b/codes/quantum/spins/single_spin/single_spin.yml index 45ab8cfa3..45173a7a8 100644 --- a/codes/quantum/spins/single_spin/single_spin.yml +++ b/codes/quantum/spins/single_spin/single_spin.yml @@ -15,10 +15,10 @@ description: | protection: | Noise models can be categorized as those that cause the state to leave the maximally symmetric subspace and those that do not. - Noise models that do not preserve the permutation-invariant subspace correspond to models for the tensor-product case. + Noise models that do not preserve the PI subspace correspond to models for the tensor-product case. Single spin-half errors do not preserve permutation symmetry and correspond to qubit Pauli noise. - Noise models that preserve the permutation-invariant subspace are typically relevant to the case of a monolithic spin. + Noise models that preserve the PI subspace are typically relevant to the case of a monolithic spin. They include collective rotations or decays. A continuous-time single-spin noise channel akin to the depolarizing channel is the Landau-Streater channel \cite{doi:10.1016/0024-3795(93)90274-R}. A particular error basis of interest consists of the spherical tensors \cite{arxiv:2304.08611}. @@ -35,7 +35,7 @@ relations: - code_id: qecc_finite cousins: - code_id: qubit_permutation_invariant - detail: 'Single-spin codes are subspaces of a single large spin, which can be either standalone or correspond to the permutation-invariant subspace of a set of spins via the \hyperref[topic:dicke]{Dicke state mapping}.' + detail: 'Single-spin codes are subspaces of a single large spin, which can be either standalone or correspond to the PI subspace of a set of spins via the \hyperref[topic:dicke]{Dicke state mapping}.' # Begin Entry Meta Information diff --git a/codes/quantum/spins/single_spin/spin_cat.yml b/codes/quantum/spins/single_spin/spin_cat.yml index 9ff12a497..9f91d3a45 100644 --- a/codes/quantum/spins/single_spin/spin_cat.yml +++ b/codes/quantum/spins/single_spin/spin_cat.yml @@ -11,7 +11,7 @@ name: 'Spin cat code' introduced: '\cite{arxiv:2101.03662,arxiv:2401.04271}' description: | - An analogue of the two-component cat code designed for a large spin, which is often realized in the permutation-invariant subspace of atomic ensembles. + An analogue of the two-component cat code designed for a large spin, which is often realized in the PI subspace of atomic ensembles. The encoding was designed by using the Holstein-Primakoff mapping \cite{doi:10.1103/PhysRev.58.1098} (see also \cite{doi:10.2307/3212170}) to pull back the phase-space structure of a bosonic system to the compact phase space of a quantum spin.