相关论文: Physics0.01 : Object-Oriented Programming for Exac…
This article introduces Newton, a specification language for notating the analytic form, units of measure, and sensor signal properties for physical-object-specific invariants and general physical laws. We designed Newton to provide a means…
Optimization techniques play an important role in several scientific and real-world applications, thus becoming of great interest for the community. As a consequence, a number of open-source libraries are available in the literature, which…
In this paper we give a framework for describing how abstract systems can be used to compute if no randomness or error is involved. Using this we describe a class of classical "physical" computation systems whose computational capabilities…
Certain simplicial complexes are used to construct a subset $D$ of $\mathbb{F}_{2^n}^m$ and $D$, in turn, defines the linear code $C_{D}$ over $\mathbb{F}_{2^n}$ that consists of $(v\cdot d)_{d\in D}$ for $v\in \mathbb{F}_{2^n}^m$. Here we…
The universal object oriented languages made programming more simple and efficient. In the article is considered possibilities of using similar methods in computer algebra. A clear and powerful universal language is useful if particular…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential…
Every algorithm which can be executed on a computer can at least in principle be realized in hardware, i.e. by a discrete physical system. The problem is that up to now there is no programming language by which physical systems can…
Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…
We present a code modularization approach to design efficient and massively parallel cubic and linear-scaling solvers for electronic structure calculations using atomic orbitals. The modular implementation of the orbital minimization…
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
With the growth of machine learning algorithms with geometry primitives, a high-efficiency library with differentiable geometric operators are desired. We present an optimized Differentiable Geometry Algorithm Library (DGAL) loaded with…
Exact diagonalization (ED) is one of the most reliable and established numerical methods of quantum many-body theory. The main limiting factor of the method is the exponential scaling of Hilbert space dimension with system size.…
The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Recently, Zhu et al. (PLDI 2020) have formulated differentiable quantum programming with bounded…
In order to gain a better understanding of the state space of programs, with the aim of making their verification more tractable, models based on directed topological spaces have been introduced, allowing to take in account equivalence…
Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of…
Q# is a standalone domain-specific programming language from Microsoft for writing and running quantum programs. Like most industrial languages, it was designed without a formal specification, which can naturally lead to ambiguity in its…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
Numerical software in computational science and engineering often relies on highly-optimized building blocks from libraries such as BLAS and LAPACK, and while such libraries provide portable performance for a wide range of computing…
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…