scispace - formally typeset
Search or ask a question
Topic

Operator (computer programming)

About: Operator (computer programming) is a research topic. Over the lifetime, 40896 publications have been published within this topic receiving 671452 citations. The topic is also known as: operator symbol & operator name.


Papers
More filters
Journal ArticleDOI
TL;DR: In this article, a finite difference operator approximating second derivatives and satisfying a summation by parts rule was derived for the fourth, sixth and eighth order case by using the symbolic mathematics software Maple.

394 citations

Journal ArticleDOI
TL;DR: The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter.
Abstract: The next few years will be exciting as prototype universal quantum processors emerge, enabling implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation, and which have the potential to significantly expand the breadth of quantum computing applications. A leading candidate is Farhi et al.'s Quantum Approximate Optimization Algorithm, which alternates between applying a cost-function-based Hamiltonian and a mixing Hamiltonian. Here, we extend this framework to allow alternation between more general families of operators. The essence of this extension, the Quantum Alternating Operator Ansatz, is the consideration of general parametrized families of unitaries rather than only those corresponding to the time-evolution under a fixed local Hamiltonian for a time specified by the parameter. This ansatz supports the representation of a larger, and potentially more useful, set of states than the original formulation, with potential long-term impact on a broad array of application areas. For cases that call for mixing only within a desired subspace, refocusing on unitaries rather than Hamiltonians enables more efficiently implementable mixers than was possible in the original framework. Such mixers are particularly useful for optimization problems with hard constraints that must always be satisfied, defining a feasible subspace, and soft constraints whose violation we wish to minimize. More efficient implementation enables earlier experimental exploration of an alternating operator approach to a wide variety of approximate optimization, exact optimization, and sampling problems. Here, we introduce the Quantum Alternating Operator Ansatz, lay out design criteria for mixing operators, detail mappings for eight problems, and provide brief descriptions of mappings for diverse problems.

390 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the result of the measurement of an operator depends solely on the system being measured and not on the operator itself, and that if operators A and B commute, the result is the product of the results of separate measurements of A and of B.

389 citations

BookDOI
04 Feb 2011
TL;DR: This volume presents the state of the art of new developments, and some interesting and relevant applications of the OWA (ordered weighted averaging) operators.
Abstract: This volume presents the state of the art of new developments, and some interesting and relevant applications of the OWA (ordered weighted averaging) operators. The OWA operators were introduced in the early 1980s by Ronald R. Yager as a conceptually and numerically simple, easily implementable, yet extremely powerful general aggregation operator. That simplicity, generality and implementability of the OWA operators, combined with their intuitive appeal, have triggered much research both in the foundations and extensions of the OWA operators, and in their applications to a wide variety of problems in various fields of science and technology.Part I: Methods includes papers on theoretical foundations of OWA operators and their extensions. The papers in Part II: Applications show some more relevant applications of the OWA operators, mostly means, as powerful yet general aggregation operators. The application areas are exemplified by environmental modeling, social networks, image analysis, financial decision making and water resource management.

388 citations

Posted Content
TL;DR: The philosophy behind ITensor, a system for programming tensor network calculations with an interface modeled on tensor diagram notation, and examples of each part of the interface including Index objects, the ITensor product operator, Tensor factorizations, tensor storage types, algorithms for matrix product state (MPS) and matrix product operator (MPO) tensor networks, and the NDTensors library are discussed.
Abstract: 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 ITensor interface rules out common programming errors and enables rapid prototyping of tensor network algorithms. After discussing the philosophy behind the ITensor approach, we show examples of each part of the interface including Index objects, the ITensor product operator, tensor factorizations, tensor storage types, algorithms for matrix product state (MPS) and matrix product operator (MPO) tensor networks, quantum number conserving block-sparse tensors, and the NDTensors library. We also review publications that have used ITensor for quantum many-body physics and for other areas where tensor networks are increasingly applied. To conclude we discuss promising features and optimizations to be added in the future.

386 citations


Network Information
Related Topics (5)
Bounded function
77.2K papers, 1.3M citations
91% related
Eigenvalues and eigenvectors
51.7K papers, 1.1M citations
91% related
Differential equation
88K papers, 2M citations
89% related
Matrix (mathematics)
105.5K papers, 1.9M citations
88% related
Nonlinear system
208.1K papers, 4M citations
87% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202236
20212,210
20202,380
20192,310
20182,164
20171,834