相关论文: Fast numerical evaluation of time-derivative nonad…

In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general…

We extend the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), a semiclassical method for computing real-time correlation functions, to electronically nonadiabatic systems using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian…

In this paper, we propose and analyze ETD-Multistep-Pad\'{e} (ETD-MS-Pad\'{e}) and ETD Implicit Multistep-Pad\'{e} (ETD-IMS-Pad\'{e}) for semilinear parabolic delay differential equations with smooth solutions. In our previous work [15], we…

In this paper, we derive universal nonadiabatic passages in a general $M+N$-dimensional discrete system, where $M$ and $N$ denote the degrees of freedom for the assistant and working subspaces, respectively, that could be separated by…

First-order nonadiabatic coupling matrix elements (fo-NACMEs) are the basic quantities in theoretical descriptions of electronically nonadiabatic processes that are ubiquitous in molecular physics and chemistry. Given the large size of…

In the paper an efficient semi-analytical approach based on the method of steps and differential transformation is proposed for numerical approximation of solutions of retarded logistic models of delayed and neutral type, including models…

A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…

Adiabatic quantum computing (AQC) is a promising approach for discrete and often NP-hard optimization problems. Current AQCs allow to implement problems of research interest, which has sparked the development of quantum representations for…

Understanding how non-adiabatic terms affect quantum dynamics is fundamental to improving various protocols for quantum technologies. We present a novel approach to computing the Adiabatic Gauge Potential (AGP), which gives information on…

As a highly expressive generative model, diffusion models have demonstrated exceptional success across various domains, including image generation, natural language processing, and combinatorial optimization. However, as data distributions…

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…

We propose Stochastic Weight Averaging in Parallel (SWAP), an algorithm to accelerate DNN training. Our algorithm uses large mini-batches to compute an approximate solution quickly and then refines it by averaging the weights of multiple…

Time Series Classification (TSC) is an important problem with numerous applications in science and technology. Dissimilarity-based approaches, such as Dynamic Time Warping (DTW), are classical methods for distinguishing time series when…

The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…

We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative…

Solving optimization problems is a key task for which quantum computers could possibly provide a speedup over the best known classical algorithms. Particular classes of optimization problems including semi-definite programming (SDP) and…

A three-level explicit time-split MacCormack scheme is proposed for solving the two-dimensional nonlinear reaction-diffusion equations. The computational cost is reduced thank to the splitting and the explicit MacCormack scheme. Under the…

In the rapidly evolving internet-of-things (IoT) ecosystem, effective data analysis techniques are crucial for handling distributed data generated by sensors. Addressing the limitations of existing methods, such as the sub-gradient…

We lay the foundation for a benchmarking methodology for assessing current and future quantum computers. We pose and begin addressing fundamental questions about how to fairly compare computational devices at vastly different stages of…

Temporal difference (TD) methods constitute a class of methods for learning predictions in multi-step prediction problems, parameterized by a recency factor lambda. Currently the most important application of these methods is to temporal…