Related papers: The Syntax and Semantics of einsum
Simulation is essential for developing quantum hardware and algorithms. However, simulating quantum circuits on classical hardware is challenging due to the exponential scaling of quantum state space. While factorized tensors can greatly…
The physics community relies on index notation to effectively manipulate types of tensors. This paper introduces the first formally verified implementation of index notation in the interactive theorem prover Lean 4. By integrating index…
We introduce a new logic programming language T-PRISM based on tensor embeddings. Our embedding scheme is a modification of the distribution semantics in PRISM, one of the state-of-the-art probabilistic logic programming languages, by…
We consider the problem of automatically decomposing operations over tensors or arrays so that they can be executed in parallel on multiple devices. We address two, closely-linked questions. First, what programming abstraction should…
(To appear in Theory and Practice of Logic Programming (TPLP)) ESmodels is designed and implemented as an experiment platform to investigate the semantics, language, related reasoning algorithms, and possible applications of epistemic…
We present trainsum, a versatile Python package for doing computations with multidimensional quantics tensor trains: https://github.com/fh-igd-iet/trainsum. Using the Array API standard together with opt_einsum, trainsum allows the…
The paper presents a REDUCE program for the simplification of tensor expressions that are considered as formal indexed objects. The proposed algorithm is based on the consideration of tensor expressions as vectors in some linear space. This…
We extend the recently introduced notion of tensor enumerator to the circuit enumerator. We provide a mathematical framework that offers a novel method for analyzing circuits and error models without resorting to Monte Carlo techniques. We…
ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagram notation, which allows users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The…
The quantum assembly language (QASM) is a popular intermediate representation used in many quantum compilation and simulation tools to describe quantum circuits. Currently, multiple different dialects of QASM are used in different quantum…
This paper introduces ENFrame, a unified data processing platform for querying and mining probabilistic data. Using ENFrame, users can write programs in a fragment of Python with constructs such as bounded-range loops, list comprehension,…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
Mathematical notation makes up a large portion of STEM literature, yet finding semantic representations for formulae remains a challenging problem. Because mathematical notation is precise, and its meaning changes significantly with small…
This paper shows how to optimize sparse tensor algebraic expressions by introducing temporary tensors, called workspaces, into the resulting loop nests. We develop a new intermediate language for tensor operations called concrete index…
Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by dense tensor algebra and the algorithmic efficiency that…
Neural networks can be regarded as a new programming paradigm, i.e., instead of building ever-more complex programs through (often informal) logical reasoning in the programmers' mind, complex 'AI' systems are built by optimising generic…
We introduce a new OpenMath content dictionary, named tensor1, containing symbols for the expression of tensor formulas. These symbols support the expression of non-Cartesian coordinates and invariant, multilinear expressions in the context…
We introduce Qunity, a new quantum programming language designed to treat quantum computing as a natural generalization of classical computing. Qunity presents a unified syntax where familiar programming constructs can have both quantum and…
We provide a systematic approach to quantum mechanics from an information-theoretic perspective using the language of tensor networks. Our formulation needs only a single kind of object, so-called positive *-tensors. Physical models…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…