From 535b53b337c1bc1328c565b6eec010e88aa0682c Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Wed, 6 Sep 2023 16:13:42 -0400 Subject: [PATCH] refs --- codes/classical/analog/lattice/root/eeight.yml | 3 ++- codes/quantum/oscillators/stabilizer/lattice/gkp.yml | 1 + 2 files changed, 3 insertions(+), 1 deletion(-) diff --git a/codes/classical/analog/lattice/root/eeight.yml b/codes/classical/analog/lattice/root/eeight.yml index 000b2b4b8..b0527f592 100644 --- a/codes/classical/analog/lattice/root/eeight.yml +++ b/codes/classical/analog/lattice/root/eeight.yml @@ -12,7 +12,8 @@ short_name: '\(E_8\)' introduced: '\cite{manual:{Gosset, Thorold. "On the regular and semi-regular figures in space of n dimensions." Messenger of Mathematics 29 (1900): 43-48.}}' description: | - BW lattice in dimension \(8\), which is the lattice corresponding to the \([8,4,4]\) Hamming code via the mod-two lattice construction. + Unimodular even BW lattice in dimension \(8\), consisting of the Cayley integral octonions rescaled by \(\sqrt{2}\). + The lattice corresponds to the \([8,4,4]\) Hamming code via the mod-two lattice construction. protection: | The \(E_8\) lattice has a nominal coding gain of \(2\). diff --git a/codes/quantum/oscillators/stabilizer/lattice/gkp.yml b/codes/quantum/oscillators/stabilizer/lattice/gkp.yml index 0223b47a0..f2cf73ca4 100644 --- a/codes/quantum/oscillators/stabilizer/lattice/gkp.yml +++ b/codes/quantum/oscillators/stabilizer/lattice/gkp.yml @@ -53,6 +53,7 @@ notes: realizations: - 'Motional degree of freedom of a trapped ion: square-lattice GKP encoding realized with the help of post-selection \cite{arxiv:1807.01033,arXiv:1907.06478}, followed by realization of reduced form of GKP error correction, where displacement error syndromes are measured to one bit of precision using an ion electronic state \cite{arxiv:2010.09681}.' - 'Microwave cavity coupled to superconducting circuits: reduced form of square-lattice GKP error correction, where displacement error syndromes are measured to one bit of precision using an ancillary transmon \cite{arxiv:1907.12487}. Subsequent paper \cite{arxiv:2211.09116} uses reinforcement learning for error-correction cycle design and is the first to go beyond break-even error-correction, with the lifetime of a logical qubit exceeding the cavity lifetime by about a factor of two (see also \cite{arxiv:2211.09319}).' + - 'GKP states and homodyne measurements have been realized in propagating telecom light by the Furusawa group \cite{arxiv:2309.02306}.' - 'Single-qubit \(Z\)-gate has been demonstrated in the single-photon subspace of an infinite-mode space \cite{arxiv:1904.01351}, in which time and frequency become bosonic conjugate variables of a single effective bosonic mode.' - 'In signal processing, GKP state position-state wavefunctions are related to Dirac combs \cite{doi:10.1007/978-1-4612-2016-9}.'