diff --git a/codes/quantum/oscillators/stabilizer/lattice/gkp.yml b/codes/quantum/oscillators/stabilizer/lattice/gkp.yml index 39f6ec373..bc3a5af5f 100644 --- a/codes/quantum/oscillators/stabilizer/lattice/gkp.yml +++ b/codes/quantum/oscillators/stabilizer/lattice/gkp.yml @@ -29,8 +29,7 @@ protection: 'For stabilizer \(\hat{S}_q(2\alpha),\hat{S}_p(2\beta)\), code can c features: encoders: - - 'Preparation of approximate square-lattice GKP states is studied both theoretically and experimentally by putting the GKP lattice inside a Gaussian envelope \cite{arxiv:1506.05033,arxiv:1709.08580,doi:10.1038/s41586-020-2603-3,arxiv:1910.03673}.' - - 'Dissipative stabilization of finite-energy square-lattice GKP states using stabilizers conjugated by a \textit{cooling} (\cite{arxiv:1310.7596}, Appx. B) or \textit{damping} operator, i.e., a damped exponential of the total occupation number \cite{arxiv:2009.07941,arxiv:2010.09681}.' + - 'Dissipative stabilization of finite-energy square-lattice GKP states using stabilizers conjugated by a \textit{cooling} (\cite{arxiv:1310.7596}, Appx. B) or \textit{damping} operator, i.e., a damped exponential of the total occupation number \cite{arxiv:2009.07941,arxiv:2010.09681}. Preparation of approximate square-lattice GKP states has been studied both theoretically and experimentally \cite{arxiv:1506.05033,arxiv:1709.08580,doi:10.1038/s41586-020-2603-3,arxiv:1910.03673}. Various damped versions of GKP states are equivalent \cite{arxiv:1910.08301,arxiv:2012.12488}.' - 'Two Josephson junctions coupled by a gyrator \cite{arxiv:2002.07718}.' - 'Periodic driving (a.k.a. Floquet engineering) \cite{arxiv:2303.03541}.' - 'Approximate GKP states can be prepared using Gaussian operations and photon detectors \cite{arxiv:1902.02323}.' diff --git a/codes/quantum/properties/approximate_qecc.yml b/codes/quantum/properties/approximate_qecc.yml index c39145e79..0747ccbe9 100644 --- a/codes/quantum/properties/approximate_qecc.yml +++ b/codes/quantum/properties/approximate_qecc.yml @@ -81,6 +81,8 @@ protection: | \end{align} is the output state of the complementary noise channel \(\mathcal{E}^C = \Lambda+B\), and the Bures distance \(d(\Lambda+B,\Lambda)\le\epsilon\)~\cite{arxiv:0907.5391}. An alternative measure, the \textit{AQEC relative entropy}, measures the relative entropy between \(\Lambda + B\) and \(\Lambda\) \cite{arxiv:2312.16991}. + The non-correctable contributions \(B_{ij}\) can be arranged in a signature vector \cite{arxiv:2410.07983}. + The Frobenius norm of the matrix \(B_{ij}\) bounds the difference between the two \hyperref[topic:quantum-weight-enumerator]{quantum weight enumerators} \cite{arxiv:2108.04434}. In addition to the necessary and sufficient error correction conditions, there exist sufficient conditions for AQECCs. diff --git a/codes/quantum/properties/qecc_finite.yml b/codes/quantum/properties/qecc_finite.yml index 447bc2df7..becfe99ef 100644 --- a/codes/quantum/properties/qecc_finite.yml +++ b/codes/quantum/properties/qecc_finite.yml @@ -39,7 +39,6 @@ protection: | The Knill-Laflamme conditions can alternatively be expressed in terms of the \hyperref[topic:complementary-channel]{complementary channel}, or in an information-theoretic way via a data processing inequality \cite{arxiv:quant-ph/9604022,arxiv:quant-ph/9702031}\cite[Eq. (29)]{arxiv:quant-ph/9604034}. They motivate higher-rank numerical ranges, which are generalizations of the numerical range of an operator \cite{arxiv:quant-ph/0511101,arXiv:math/0511278}. They have been extended to sequences of multiple errors and rounds of correction \cite{arxiv:2405.17567}. - The non-correctable contributions to the conditions can be arranged in a signature vector \cite{arxiv:2410.07983}. \begin{defterm}{Degeneracy} \label{topic:degeneracy}