Qudit-Basis Universal Quantum Computation using χ(2)\chi^{(2)} Interactions

We prove that universal quantum computation can be realized---using only linear optics and $\chi^{(2)}$ (three-wave mixing) interactions---in any $(n+1)$-dimensional qudit basis of the $n$-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that $\chi^{(2)}$ Hamiltonians and photon-number operators generate the full $\mathfrak{u}(3)$ Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-$Z$ gate can be implemented with only linear optics and $\chi^{(2)}$ interactions. We then use proof by induction to obtain our general qudit result. Our induction proof relies on coherent photon injection/subtraction, a technique enabled by $\chi^{(2)}$ interaction between the encoding modes and ancillary modes. Finally, we show that coherent photon injection is more than a conceptual tool in that it offers a route to preparing high-photon-number Fock states from single-photon Fock states.Comment: 9 pages, 3 figure

HOME: High-Order Mixed-Moment-based Embedding for Representation Learning

Minimum redundancy among different elements of an embedding in a latent space is a fundamental requirement or major preference in representation learning to capture intrinsic informational structures. Current self-supervised learning methods minimize a pair-wise covariance matrix to reduce the feature redundancy and produce promising results. However, such representation features of multiple variables may contain the redundancy among more than two feature variables that cannot be minimized via the pairwise regularization. Here we propose the High-Order Mixed-Moment-based Embedding (HOME) strategy to reduce the redundancy between any sets of feature variables, which is to our best knowledge the first attempt to utilize high-order statistics/information in this context. Multivariate mutual information is minimum if and only if multiple variables are mutually independent, which suggests the necessary conditions of factorized mixed moments among multiple variables. Based on these statistical and information theoretic principles, our general HOME framework is presented for self-supervised representation learning. Our initial experiments show that a simple version in the form of a three-order HOME scheme already significantly outperforms the current two-order baseline method (i.e., Barlow Twins) in terms of the linear evaluation on representation features

Sub-volume-based Denoising Diffusion Probabilistic Model for Cone-beam CT Reconstruction from Incomplete Data

Deep learning (DL) has emerged as a new approach in the field of computed tomography (CT) with many applicaitons. A primary example is CT reconstruction from incomplete data, such as sparse-view image reconstruction. However, applying DL to sparse-view cone-beam CT (CBCT) remains challenging. Many models learn the mapping from sparse-view CT images to the ground truth but often fail to achieve satisfactory performance. Incorporating sinogram data and performing dual-domain reconstruction improve image quality with artifact suppression, but a straightforward 3D implementation requires storing an entire 3D sinogram in memory and many parameters of dual-domain networks. This remains a major challenge, limiting further research, development and applications. In this paper, we propose a sub-volume-based 3D denoising diffusion probabilistic model (DDPM) for CBCT image reconstruction from down-sampled data. Our DDPM network, trained on data cubes extracted from paired fully sampled sinograms and down-sampled sinograms, is employed to inpaint down-sampled sinograms. Our method divides the entire sinogram into overlapping cubes and processes them in parallel on multiple GPUs, successfully overcoming the memory limitation. Experimental results demonstrate that our approach effectively suppresses few-view artifacts while preserving textural details faithfully

Wind power output prediction: a comparative study of extreme learning machine

This study aims to propose a wind power prediction method that achieves high accuracy in order to minimize the impact of wind power on the power system and reduce scheduling difficulties in systems incorporating wind power. The importance of developing renewable energy has been recognized by society due to the increasing severity of the energy crisis. Wind energy offers advantages such as efficiency, cleanliness, and ease of development. However, the random nature of wind energy poses challenges to power systems and complicates the scheduling process. Therefore, accurate wind power prediction is of utmost importance. A wind power prediction model was constructed based on an improved tunicate swarm algorithm–extreme learning machine (ITSA-ELM). The improved tunicate swarm algorithm (ITSA) optimizes the random parameters of extreme learning machine (ELM), resulting in the best prediction performance. ITSA is an enhancement of the tunicate swarm algorithm (TSA), which introduces a reverse learning mechanism, a non-linear self-learning factor, and a Cauchy mutation strategy to address the drawbacks of poor convergence and susceptibility to local optima in TSA. Two different scenarios were used to verify the effectiveness of ITSA-ELM. The results showed that ITSA-ELM has a decrease of 1.20% and 21.67% in MAPE, compared with TSA-ELM, in May and December, respectively. This study has significant implications for promoting the development of renewable energy and reducing scheduling difficulties in power systems