Quantum Matrix-Product Codes: CSS-T Characterization and Maximality
本文通过扩展CSS-T码的代数特征至矩阵积码,特别是对于循环子码使用定义的分圆集进行显式刻画,从而构建新的更长CSS-T码以纠正量子计算中的错误。
本文通过扩展CSS-T码的代数特征至矩阵积码,特别是对于循环子码使用定义的分圆集进行显式刻画,从而构建新的更长CSS-T码以纠正量子计算中的错误。
本文通过调整深度神经网络模型,利用众包注释进行星系形态分类,探讨了不同训练方法对准确性和效率的影响。
Long-term electricity-consumption profiles exhibit several simultaneous periodic structures, including daily, weekly, and annual cycles. This work introduces Calendar-SPCA, a calendar-structured sparse principal component method that incorporates this known multi-periodic geometry directly into low-dimensional representation learning. The feature domain is represented as the Cartesian product of cyclic calendar axes, and a low-rank factorization is estimated using an L1 loading penalty together with graph total variation over the resulting calendar graph. The method therefore produces sparse and locally coherent loading patterns that remain directly readable in their original temporal coordinates. Calendar-SPCA is evaluated on two independent smart-meter datasets with different sample sizes and temporal resolutions: GoiEner and Low Carbon London. A factorial experiment characterizes the complementary effects of sparsity and calendar coherence and examines robustness across sample size, latent dimensionality, and repeated fits. At rank 15, Calendar-SPCA retains 96.92% and 82.90% of the explained variance of rank-matched PCA in GoiEner and Low Carbon London, respectively, while producing mean loading sparsities of 61.95% and 81.50%. Comparisons with classical sparse PCA and SPCA-TV further show that Calendar-SPCA adds a systematic organization of the latent factors in the original calendar coordinates while preserving substantial low-rank information. The resulting components form coherent and complementary daily, weekly, seasonal, and jointly localized calendar patterns, with dataset-specific geometries across the two datasets.
This work addresses a critical gap in robust optimization theory: the lack of understanding regarding the expected survival time of fixed solutions in dynamic environments, particularly its dependence on environmental dynamics, deployment quality, and problem structure. Focusing on isotropic Gaussian dynamics, the paper models survival time as a discrete first-exit-time problem and, within the ROOT framework, derives for the first time a rigorous lower bound and a computable multi-step upper bound. Theoretical analysis reveals that in slowly varying environments, survival time scales as Θ(σ⁻²), while in high dimensions it approaches the minimal value of one. Extensive experiments combining stochastic process analysis and Monte Carlo simulations validate the proposed bounds, demonstrating their practical utility in guiding deployment decisions by clearly classifying target durations as guaranteed, excluded, or uncertain.
This work addresses decoherence in general qubit systems induced by mixed longitudinal and transverse noise, particularly anisotropic noise, by proposing a suppression strategy based on continuous dynamical decoupling (CDD). Through the introduction of a tailored unitary transformation, the noise is mapped onto an effective stochastic term dependent on driving parameters. By integrating this framework with a noisy Landau–Zener model, the impact of linearly ramped control fields on dressed states is analyzed. The study systematically uncovers, for the first time, the robustness mechanism of CDD under mixed and anisotropic noise environments and elucidates how control parameters modulate the effective noise spectrum. Proper optimization of these parameters significantly enhances decoherence suppression, demonstrating the strong adaptability and efficacy of the proposed approach in realistic quantum systems.
本文通过扩展CSS-T码的代数特征至矩阵积码,特别是对于循环子码使用定义的分圆集进行显式刻画,从而构建新的更长CSS-T码以纠正量子计算中的错误。
本文通过调整深度神经网络模型,利用众包注释进行星系形态分类,探讨了不同训练方法对准确性和效率的影响。
Long-term electricity-consumption profiles exhibit several simultaneous periodic structures, including daily, weekly, and annual cycles. This work introduces Calendar-SPCA, a calendar-structured sparse principal component method that incorporates this known multi-periodic geometry directly into low-dimensional representation learning. The feature domain is represented as the Cartesian product of cyclic calendar axes, and a low-rank factorization is estimated using an L1 loading penalty together with graph total variation over the resulting calendar graph. The method therefore produces sparse and locally coherent loading patterns that remain directly readable in their original temporal coordinates. Calendar-SPCA is evaluated on two independent smart-meter datasets with different sample sizes and temporal resolutions: GoiEner and Low Carbon London. A factorial experiment characterizes the complementary effects of sparsity and calendar coherence and examines robustness across sample size, latent dimensionality, and repeated fits. At rank 15, Calendar-SPCA retains 96.92% and 82.90% of the explained variance of rank-matched PCA in GoiEner and Low Carbon London, respectively, while producing mean loading sparsities of 61.95% and 81.50%. Comparisons with classical sparse PCA and SPCA-TV further show that Calendar-SPCA adds a systematic organization of the latent factors in the original calendar coordinates while preserving substantial low-rank information. The resulting components form coherent and complementary daily, weekly, seasonal, and jointly localized calendar patterns, with dataset-specific geometries across the two datasets.
This work addresses a critical gap in robust optimization theory: the lack of understanding regarding the expected survival time of fixed solutions in dynamic environments, particularly its dependence on environmental dynamics, deployment quality, and problem structure. Focusing on isotropic Gaussian dynamics, the paper models survival time as a discrete first-exit-time problem and, within the ROOT framework, derives for the first time a rigorous lower bound and a computable multi-step upper bound. Theoretical analysis reveals that in slowly varying environments, survival time scales as Θ(σ⁻²), while in high dimensions it approaches the minimal value of one. Extensive experiments combining stochastic process analysis and Monte Carlo simulations validate the proposed bounds, demonstrating their practical utility in guiding deployment decisions by clearly classifying target durations as guaranteed, excluded, or uncertain.
This work addresses decoherence in general qubit systems induced by mixed longitudinal and transverse noise, particularly anisotropic noise, by proposing a suppression strategy based on continuous dynamical decoupling (CDD). Through the introduction of a tailored unitary transformation, the noise is mapped onto an effective stochastic term dependent on driving parameters. By integrating this framework with a noisy Landau–Zener model, the impact of linearly ramped control fields on dressed states is analyzed. The study systematically uncovers, for the first time, the robustness mechanism of CDD under mixed and anisotropic noise environments and elucidates how control parameters modulate the effective noise spectrum. Proper optimization of these parameters significantly enhances decoherence suppression, demonstrating the strong adaptability and efficacy of the proposed approach in realistic quantum systems.