Search

The solving of linear systems provides a rich area to investigate the use of nearer-term, noisy, intermediate-scale quantum computers. In this work, we discuss hybrid quantum-classical algorithms for skewed linear systems for over-determined and under-determined cases. Our input model is such that the columns or rows of the matrix defining the linear system are given via quantum circuits of poly-logarithmic depth and the number of circuits is much smaller than their Hilbert space dimension. Our algorithms have poly-logarithmic dependence on the dimension and polynomial dependence in other natural quantities. In addition, we present an algorithm for the special case of a factorized linear system with run time poly-logarithmic in the respective dimensions. At the core of these algorithms is the Hadamard test and in the second part of this paper we consider the optimization of the circuit depth of this test. Given an $n$-qubit and $d$-depth quantum circuit $\mathcal{C}$, we can approximate $\langle 0|\mathcal{C}|0\rangle$ using $(n + s)$ qubits and $O\left(\log s + d\log (n/s) + d\right)$-depth quantum circuits, where $s\leq n$. In comparison, the standard implementation requires $n+1$ qubits and $O(dn)$ depth. Lattice geometries underlie recent quantum supremacy experiments with superconducting devices. We also optimize the Hadamard test for an $(l_1\times l_2)$ lattice with $l_1 \times l_2 = n$, and can approximate $\langle 0|\mathcal{C} |0\rangle$ with $(n + 1)$ qubits and $O\left(d \left(l_1 + l_2\right)\right)$-depth circuits. In comparison, the standard depth is $O\left(d n^2\right)$ in this setting. Both of our optimization methods are asymptotically tight in the case of one-depth quantum circuits $\mathcal{C}$., Comment: 28+16 pages, 6 figures

In many real-world datasets, like WebVision, the performance of DNN based classifier is often limited by the noisy labeled data. To tackle this problem, some image related side information, such as captions and tags, often reveal underlying relationships across images. In this paper, we present an efficient weakly supervised learning by using a Side Information Network (SINet), which aims to effectively carry out a large scale classification with severely noisy labels. The proposed SINet consists of a visual prototype module and a noise weighting module. The visual prototype module is designed to generate a compact representation for each category by introducing the side information. The noise weighting module aims to estimate the correctness of each noisy image and produce a confidence score for image ranking during the training procedure. The propsed SINet can largely alleviate the negative impact of noisy image labels, and is beneficial to train a high performance CNN based classifier. Besides, we released a fine-grained product dataset called AliProducts, which contains more than 2.5 million noisy web images crawled from the internet by using queries generated from 50,000 fine-grained semantic classes. Extensive experiments on several popular benchmarks (i.e. Webvision, ImageNet and Clothing-1M) and our proposed AliProducts achieve state-of-the-art performance. The SINet has won the first place in the classification task on WebVision Challenge 2019, and outperformed other competitors by a large margin., Comment: Accepted by ECCV 2020

In this article, we will derive the differential equations considering the concentration polarization (\textsc{cp}) in membrane separations and purifications, which involve convective-diffusive equations of the concentration polarization layer and the Spiegler-Kedem-Katchalsky (\textsc{skk}) model of the membrane layer. Analytical solutions of these differential equations are straightforward and given. The film theory coupled \textsc{skk} model can be used to evaluate the degree of concentration polarization, and predict flux and rejection rates., Comment: There is an error in Eq. (8) on the page 8

Prominent features of simulated moving bed (SMB) chromatography processes in the downstream processing is based on the determination of operating conditions. However, effects of different types of uncertainties have to be studied and analysed whenever the triangle theory or numerical optimization approaches are applied. In this study, a Bayesian inference based method is introduced to consider the uncertainty of operating conditions on the performance assessment, of a glucose-fructose SMB unit under linear condition. A multiple chain Markov Chain Monte Carlo (MCMC) algorithm (i.e., Metropolis algorithm with delayed rejection and adjusted Metropolis) is applied to generate samples. The proposed method renders versatile information by constructing from the MCMC samples, e.g., posterior distributions, uncertainties, credible intervals of the operating conditions, and posterior predictive check and Pareto fronts between each pair of the performance indicators. Additionally, the MCMC samples can be mapped onto the $(m_\text{II}, m_\text{III})$ and $(m_\text{IV}, m_\text{I})$ plains to show the actually complete separation region under uncertainties. The proposed method is a convenient tool to find both optimal values and uncertainties of the operating conditions. Moreover, it is not limited to SMB processes under the linear isotherm; and it should be more powerful in the nonlinear scenarios., Comment: 32 pages, 8 figures, 4 tables

Model-based process design of ion-exchange simulated moving bed (IEX-SMB) chromatography for center-cut separation of proteins is studied. Use of nonlinear binding models that describe more accurate adsorption behaviours of macro-molecules could make it impossible to utilize triangle theory to obtain operating parameters. Moreover, triangle theory provides no rules to design salt profiles in IEX-SMB. In the modelling study here, proteins (i.e., ribonuclease, cytochrome and lysozyme) on the chromatographic columns packed with strong cation-exchanger SP Sepharose FF is used as an example system. The general rate model with steric mass-action kinetics was used; two closed-loop IEX-SMB network schemes were investigated (i.e., cascade and eight-zone schemes). Performance of the IEX-SMB schemes was examined with respect to multi-objective indicators (i.e., purity and yield) and productivity, and compared to a single column batch system with the same amount of resin utilized. A multi-objective sampling algorithm, Markov Chain Monte Carlo (MCMC), was used to generate samples for constructing the Pareto optimal fronts. MCMC serves on the sampling purpose, which is interested in sampling the Pareto optimal points as well as those near Pareto optimal. Pareto fronts of the three schemes provide the full information of trade-off between the conflicting indicators of purity and yield. The results indicate the cascade IEX-SMB scheme and the integrated eight-zone IEX-SMB scheme have the similar performance that both outperforms the single column batch system., Comment: 26 pages, 14 figures, 7 tables

Efficiently processing basic linear algebra subroutines is of great importance for a wide range of computational problems. In this paper, we consider techniques to implement matrix functions on a quantum computer, which are composed of basic matrix operations on a set of matrices. These matrix operations include addition, multiplication, Kronecker sum, tensor product, Hadamard product, and single-matrix functions. We discuss the composed matrix functions in terms of the estimation of scalar quantities such as inner products, trace, determinant and Schatten p-norms. We thus provide a framework for compiling instructions for linear algebraic computations into gate sequences on actual quantum computers.

In this work, we propose the first quantum Ans\"atze for the statistical relational learning on knowledge graphs using parametric quantum circuits. We introduce two types of variational quantum circuits for knowledge graph embedding. Inspired by the classical representation learning, we first consider latent features for entities as coefficients of quantum states, while predicates are characterized by parametric gates acting on the quantum states. For the first model, the quantum advantages disappear when it comes to the optimization of this model. Therefore, we introduce a second quantum circuit model where embeddings of entities are generated from parameterized quantum gates acting on the pure quantum state. The benefit of the second method is that the quantum embeddings can be trained efficiently meanwhile preserving the quantum advantages. We show the proposed methods can achieve comparable results to the state-of-the-art classical models, e.g., RESCAL, DistMult. Furthermore, after optimizing the models, the complexity of inductive inference on the knowledge graphs might be reduced with respect to the number of entities.