In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying neural networks to identify the mapping between the inputs and the solution. This approach can be faster than traditional numerical methods when numerous instances are to be solved. Previous works that concentrate on solving the wave equation by neural networks consider either a single velocity model or multiple simple velocity models, which is restricted in practice. Instead, inspired by the idea of operator learning, this work leverages the Fourier neural operator (FNO) to effectively learn thefrequency domainseismic wavefields under the context ofvariable velocity models. We also propose a new frameworkparalleled Fourier neural operator(PFNO) for efficiently training the FNO-based solver given multiple source locations and frequencies. Numerical experiments demonstrate the high accuracy of both FNO and PFNO with complicated velocity models in the OpenFWI datasets. Furthermore, the cross-dataset generalization test verifies that PFNO adapts to out-of-distribution velocity models. Finally, PFNO admits higher computational efficiency on large-scale testing datasets than the traditional finite-difference method. The aforementioned advantages endow the FNO-based solver with the potential to build powerful models for research on seismic waves.

Various noise models have been developed in quantum computing study to describe the propagation and effect of the noise that is caused by imperfect implementation of hardware. Identifying parameters such as gate and readout error rates is critical to these models. We use a Bayesian inference approach to identify posterior distributions of these parameters such that they can be characterized more elaborately. By characterizing the device errors in this way, we can further improve the accuracy of quantum error mitigation. Experiments conducted on IBM’s quantum computing devices suggest that our approach provides better error mitigation performance than existing techniques used by the vendor. Also, our approach outperforms the standard Bayesian inference method in some scenarios.

As quantum computers evolve, simulations of quantum programs on classical computers will be essential in validating quantum algorithms, understanding the effect of system noise, and designing applications for future quantum computers. In this paper, we first propose a new multi-GPU programming methodology called MG-BSP which constructs a virtual BSP machine on top of modern multi-GPU platforms, and apply this methodology to build a multi-GPU density matrix quantum simulator called DM-Sim. We propose a new formulation that can significantly reduce communication overhead, and show that this formula transformation can conserve the semantics despite noise being introduced. We build the tool-chain for the simulator to run open standard quantum assembly code, execute synthesized quantum circuits, and perform ultra-deep and largescale simulations. We evaluated DM-Sim on several state-of-the-art multi-GPU platforms including NVIDIA's PascaUVolta DGX1, DGX-2, and ORNL's Summit supercomputer. In particular, we have demonstrated the simulation of one million general gates in 94 minutes on DGX-2, far deeper circuits than has been demonstrated in prior works. Our simulator is more than 10x faster with respect to the corresponding state-vector quantum simulators on GPUs and other platforms. The DM-Sim simulator is released at: http:llgithub.comlpnnllDM-Sim.

Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient analysis of variance-based stochastic circuit/microelectromechanical systems simulator to efficiently extract the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is efficiently simulated by our simulator at the cost of only 10min in MATLAB on a regular personal computer.