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Digital quantum simulation (DQS) of continuous-variable quantum systems in the position basis requires efficient implementation of diagonal unitaries approximating the time evolution operator generated by the potential energy function. In this work, we provide efficient implementations suitable for potential functions approximable by piecewise polynomials, with either uniform or adaptively chosen subdomains. For a fixed precision of approximation, we show how adaptive grids can significantly reduce the total gate count at the cost of introducing a small number of ancillary qubits. We demonstrate the circuit construction with both physically motivated and artificially designed potential functions, and discuss their generalizations to higher dimensions.

This paper is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourier transform of a time-dependent source whose radiating period in the time domain is known. The time-dependent source is supposed to be stationary in the sense that its compact support does not vary along the time variable. Via a multi-frequency direct sampling method, we show that the smallest strip containing the source support and perpendicular to the observation direction can be recovered from far-field patterns at a fixed observation angle. With multiple but sparse observation directions, the shape of the convex hull of the source support can be recovered. The frequency-domain analysis performed here can be used to handle inverse time-dependent source problems. Our algorithm has low computational overhead and is robust against noise. Numerical experiments in both two and three dimensions have proved our theoretical findings.

The quantum circuits that declare quantum supremacy, such as Google Sycamore [Nature \textbf{574}, 505 (2019)], raises a paradox in building reliable result references. While simulation on traditional computers seems the sole way to provide reliable verification, the required run time is doomed with an exponentially-increasing compute complexity. To find a way to validate current ``quantum-supremacy" circuits with more than $50$ qubits, we propose a simulation method that exploits the ``classical advantage" (the inherent ``store-and-compute" operation mode of von Neumann machines) of current supercomputers, and computes uncorrelated amplitudes of a random quantum circuit with an optimal reuse of the intermediate results and a minimal memory overhead throughout the process. Such a reuse strategy reduces the original linear scaling of the total compute cost against the number of amplitudes to a sublinear pattern, with greater reduction for more amplitudes. Based on a well-optimized implementation of this method on a new-generation Sunway supercomputer, we directly verify Sycamore by computing three million exact amplitudes for the experimentally generated bitstrings, obtaining an XEB fidelity of $0.191\%$ which closely matches the estimated value of $0.224\%$. Our computation scales up to $41,932,800$ cores with a sustained single-precision performance of $84.8$ Pflops, which is accomplished within $8.5$ days. Our method has a far-reaching impact in solving quantum many-body problems, statistical problems as well as combinatorial optimization problems where one often needs to contract many tensor networks which share a significant portion of tensors in common.

Collective decision-making is vital for recent information and communications technologies. In our previous research, we mathematically derived conflict-free joint decision-making that optimally satisfies players' probabilistic preference profiles. However, two problems exist regarding the optimal joint decision-making method. First, as the number of choices increases, the computational cost of calculating the optimal joint selection probability matrix explodes. Second, to derive the optimal joint selection probability matrix, all players must disclose their probabilistic preferences. Now, it is noteworthy that explicit calculation of the joint probability distribution is not necessarily needed; what is necessary for collective decisions is sampling. This study examines several sampling methods that converge to heuristic joint selection probability matrices that satisfy players' preferences. We show that they can significantly reduce the above problems of computational cost and confidentiality. We analyze the probability distribution each of the sampling methods converges to, as well as the computational cost required and the confidentiality secured. In particular, we introduce two conflict-free joint sampling methods through quantum interference of photons. The first system allows the players to hide their choices while satisfying the players' preferences almost perfectly when they have the same preferences. The second system, where the physical nature of light replaces the expensive computational cost, also conceals their choices under the assumption that they have a trusted third party. This paper has been published in Phys. Rev. Applied 18, 064018 (2022) (DOI: 10.1103/PhysRevApplied.18.064018).

Accomplishing safe and efficient driving is one of the predominant challenges in the controller design of connected automated vehicles (CAVs). It is often more convenient to address these goals separately and integrate the resulting controllers. In this study, we propose a controller integration scheme to fuse performance-based controllers and safety-oriented controllers safely for the longitudinal motion of a CAV. The resulting structure is compatible with a large class of controllers, and offers flexibility to design each controller individually without affecting the performance of the others. We implement the proposed safe integration scheme on a connected automated truck using an optimal-in-energy controller and a safety-oriented connected cruise controller. We validate the premise of the safe integration through experiments with a full-scale truck in two scenarios: a controlled experiment on a test track and a real-world experiment on a public highway. In both scenarios, we achieve energy efficient driving without violating safety.

Reinforcement-learning agents seek to maximize a reward signal through environmental interactions. As humans, our contribution to the learning process is through designing the reward function. Like programmers, we have a behavior in mind and have to translate it into a formal specification, namely rewards. In this work, we consider the reward-design problem in tasks formulated as reaching desirable states and avoiding undesirable states. To start, we propose a strict partial ordering of the policy space. We prefer policies that reach the good states faster and with higher probability while avoiding the bad states longer. Next, we propose an environment-independent tiered reward structure and show it is guaranteed to induce policies that are Pareto-optimal according to our preference relation. Finally, we empirically evaluate tiered reward functions on several environments and show they induce desired behavior and lead to fast learning.

We study the problem of designing worst-case to average-case reductions for quantum algorithms. For all linear problems, we provide an explicit and efficient transformation of quantum algorithms that are only correct on a small (even sub-constant) fraction of their inputs into ones that are correct on all inputs. This stands in contrast to the classical setting, where such results are only known for a small number of specific problems or restricted computational models. En route, we obtain a tight $\Omega(n^2)$ lower bound on the average-case quantum query complexity of the Matrix-Vector Multiplication problem. Our techniques strengthen and generalise the recently introduced additive combinatorics framework for classical worst-case to average-case reductions (STOC 2022) to the quantum setting. We rely on quantum singular value transformations to construct quantum algorithms for linear verification in superposition and learning Bogolyubov subspaces from noisy quantum oracles. We use these tools to prove a quantum local correction lemma, which lies at the heart of our reductions, based on a noise-robust probabilistic generalisation of Bogolyubov's lemma from additive combinatorics.

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.