SMS: Spiking marching scheme for efficient long time integration of differential equations
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We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.
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An overview of the hardware and software developed for the Source Term Analysis of Xenon (STAX) project is presented which includes the data collection from two stack monitoring systems installed at medical isotope production facilities, infrastructure to transfer data to a central repository, and methods for sharing data from the repository with users. STAX is an experiment to collect radioxenon emission data from industrial nuclear facilities with the goal of developing a better understanding of the global radioxenon background and the effect industrial radioxenon releases have on nuclear explosion monitoring. The final goal of this work is to utilize collected data along with atmospheric transport modeling to calculate the contribution of a peak or set of peaks detected by the International Monitoring System (IMS) to provide desired discriminating information to the International Data Centre (IDC) and National Data Centers (NDCs). Types of data received from the STAX equipment are shown and collected data was used for a case study to predict radioxenon concentrations at two IMS stations closest to the Institute for RadioElements (IRE) in Belgium. The initial evaluation of results indicate that the data is very valuable to the nuclear explosion monitoring community.
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Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has affected the lives and livelihood of millions of individuals around the world. It has mutated several times after its first inception, with an estimated two mutations occurring every month. Although we have been successful in developing vaccines against the virus, the emergence of variants has enabled it to escape therapy. Few of the generated variants are also reported to be more infectious than the wild-type (WT). In this study, we analyze the attributes of all RBD/ACE2 complexes for the reported VOCs, namely, Alpha, Beta, Gamma, and Delta through computer simulations. Results indicate differences in orientation and binding energies of the VOCs from the WT. Overall, it was observed that electrostatic interactions play a major role in the binding of the complexes. Detailed residue level energetics revealed that the most prominent changes in interaction energies were seen particularly at the mutated residues which were present at RBD/ACE2 interface. We found that the Delta variant is one of the most tightly bound variants of SARS-CoV-2 with dynamics similar to WT. The high binding affinity of RBD towards ACE2 is indicative of an increase in viral transmission and infectivity. The details presented in our study provide additional information for the design and development of effective therapeutic strategies for the emerging variants of the virus in the future.
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The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging datasets of the combinatorial structures of interest drawn from some distribution of problem instances. Reinforcement learning has also been employed to find such structures. Here, in this paper, we propose a different approach in that no data is required for training the neural networks that produce the solution. In this sense, what we present is not a machine learning solution, but rather one that is dependent on neural networks and where backpropagation is applied to a loss function defined by the structure of the neural network architecture as opposed to a training dataset. In particular, we reduce the popular combinatorial optimization problem of finding a maximum independent set to a neural network and employ a dataless training scheme to refine the parameters of the network such that those parameters yield the structure of interest. Additionally, we propose a universal graph reduction procedure to handle large-scale graphs. The reduction exploits community detection for graph partitioning and is applicable to any graph type and/or density. Experimental results on both real and synthetic graphs demonstrate that our proposed method performs on par or outperforms state-of-the-art learning-based methods in terms of the size of the found set without requiring any training data.
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