Related papers: Automatic differentiation for coupled cluster meth…
The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to…
Algorithmic Differentiation (AD) can be used to automate the generation of derivatives in arbitrary software projects. This will generate maintainable derivatives, that are always consistent with the computation of the software. If a domain…
We describe an algorithm for the automated deduction of many $d_2$ differentials in the Adams spectral sequence. We discuss our implementation and the results of the computation.
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
Slater determinants have underpinned quantum chemistry for nearly a century, yet their full potential has remained challenging to exploit. In this work, we show that a variational wavefunction composed of a few hundred optimized…
Optimization of beamlines and lattices is a common problem in accelerator physics, which is usually solved with semi-analytical methods and numerical optimization routines. However, these are usually of the gradient-free or…
We give a gentle introduction to using various software tools for automatic differentiation (AD). Ready-to-use examples are discussed, and links to further information are presented. Our target audience includes all those who are looking…
The compensated quotient-difference (Compqd) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard quotient-difference (qd) algorithm can be numerically unstable. The Compqd algorithm…
Autonomous synthesis and characterization of inorganic materials requires the automatic and accurate analysis of X-ray diffraction spectra. For this task, we designed a probabilistic deep learning algorithm to identify complex multi-phase…
Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered…
Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded…
The coupled cluster method is considered a gold standard in quantum chemistry, reliably giving energies that are exact within chemical accuracy (1.6 mHartree). However, even in the CCSD approximation, where the cluster operator is truncated…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
The foundational theory of differentiation was developed as part of the original release of ACL2(r). In work reported at the last ACL2 Workshop, we presented theorems justifying the usual differentiation rules, including the chain rule and…
The Dirichlet process (DP) is a fundamental mathematical tool for Bayesian nonparametric modeling, and is widely used in tasks such as density estimation, natural language processing, and time series modeling. Although MCMC inference…
In this tutorial-style review we discuss basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the…
We propose to apply several gradient estimation techniques to enable the differentiation of programs with discrete randomness in High Energy Physics. Such programs are common in High Energy Physics due to the presence of branching processes…
The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to…