Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Computing in Science & Engineering

Scientific computation and functional programming

L. Karczmarczuk

Published Jan 1, 1999• 12 citations
Publisher

Abstract

Modern functional programming languages and lazy functional techniques are useful for describing and implementing abstract mathematical objects in quantum mechanics. Scientists can use them both for pedagogical purposes and for real, not too computationally intensive, but conceptually and algorithmically difficult applications. This article shows how to perform simple abstract computations on state vectors and discusses the construction of lazy algorithms that enormously simplify manipulation of potentially infinite data structures or iterative processes. Lazy functional techniques can often replace the use of symbolic computer algebra packages, while also offering an interesting algorithmic complement to the manipulation of mathematical data. These techniques are more efficient than blindly used symbolic algebra and are easy to integrate with the numerical code.

DOI
10.1109/5992.764217

Related papers

Functional framework for representing and transforming quantum channels

Jarosław Adam Miszczak

We develop a framework which aims to simplify the analysis of quantum states and quantum operations by harnessing the potential of function programming paradigm. We show that the introduced framework allows a seamless manipulation of quantum channels, in particular to convert between different representations of quantum channels, and thus that the use of functional programming concepts facilitates the manipulation of abstract objects used in the language of quantum theory. For the purpose of our presentation we will use Mathematica computer algebra system. This choice is motivated twofold. First, it offers a rich programming language based on the functional paradigm. Second, this programming language is combined with powerful symbolic and numeric manipulation capabilities.

arXiv:1307.4906•Jul 18, 2013•1 citation

Extending scientific computing system with structural quantum programming capabilities

P. Gawron, J. Klamka, Jarosław Adam Miszczak +1 more

Abstract. We present the basic high-level structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudo-code based on QCL quantum programming language to describe them. We also present the implementation of introduced structures in GNU Octave language for scientific computing. Procedures used in the implementation are available as a package quantum-octave providing library of functions, which facilitates the simulation of quantum computing. This package allows also to incorporate high-level programming concepts into the simulation in GNU Octave and Matlab. As such it connects features unique for higl-level quantum programming languages, with the full palette of efficient computational routines commonly available in modern scientific computing systems. To present the major features of the described package we provide the implementation of selected quantum algorithms. We also show how quantum errors can be taken into account during the simulation of quantum algorithms using quantum-octave package. This is possible thanks to the ability to operate on density matrices implemented in quantum-octave. Key words: quantum information, quantum programming, models of quantum computation. 1.

•Jan 1, 2009•14 citations

Quantum Mechanics Using Computer Algebra

Willi-Hans Steeb

Solving problems in quantum mechanics is an essential skill and research activity for scientists, engineers and others. Nowadays, the labour of scientific computation has been greatly eased by the advent of computer algebra packages. These do not merely perform number-crunching, but enable users to manipulate algebraic expressions and equations symbolically. For example, differentiation and integration can now be carried out algebraically by the computer. This book collects standard and advanced methods in quantum mechanics and implements them using REDUCE, a popular computer algebra package. Throughout, sample programs and their output have been displayed alongside explanatory text, making the book easy to follow. Selected problems have also been implemented using two other popular packages, MATHEMATICA and MAPLE, and in the object-oriented programming language C++. Besides standard quantum mechanical techniques, modern developments in quantum theory are also covered. These include Fermi and Bose Operators, coherent states, gauge theory and quantum groups. All the special functions relevant to quantum mechanics (Hermite, Chebyshev, Legendre and more) are implemented. A careful balance is struck between practical computation and the underlying mathematical concepts, making the book well-suited for use with quantum mechanics courses.

WORLD SCIENTIFIC eBooks•May 1, 1994•7 citations

Simulation of Quantum Algorithms with a Symbolic Programming Language

Peter Nyman

This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational methods. The computational language will include formulations such as quantum state, superposition and quantum operator.

arXiv:0705.3333•May 23, 2007•9 citations

Extending scientific computing system with structural quantum programming capabilities

Piotr Gawron, J. Klamka, J. Miszczak +1 more

We present a basic high-level structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudo-code based on QCL quantum programming language to describe them. We also present the implementation of introduced structures in GNU Octave language for scientific computing. Procedures used in the implementation are available as a package quantum-octave, providing a library of functions, which facilitates the simulation of quantum computing. This package allows also to incorporate high-level programming concepts into the simulation in GNU Octave and Matlab. As such it connects features unique for high-level quantum programming languages, with the full palette of efficient computational routines commonly available in modern scientific computing systems. To present the major features of the described package we provide the implementation of selected quantum algorithms. We also show how quantum errors can be taken into account during the simulation of quantum algorithms using quantum-octave package. This is possible thanks to the ability to operate on density matrices.

arXiv:1006.1549•Bulletin of the Polish Academy of Sciences Technical Sciences•Jan 1, 2010•5 citations

QUANTUM MECHANICS USING COMPUTER ALGEBRA: INCLUDES SAMPLE PROGRAMS IN C++, SYMBOLICC++, MAXIMA, MAPLE, AND MATHEMATICA

Willi-Hans Steeb, Yorick Hardy

Solving problems in quantum mechanics is an essential skill and research activity for physicists, mathematicians, engineers and others. Nowadays, the labor of scientific computation has been greatly eased by the advent of computer algebra packages, which do not merely perform number crunching, but also enable users to manipulate algebraic expressions and equations symbolically. For example, the manipulations of noncommutative operators, differentiation and integration can now be carried out algebraically by the computer algebra package. This book collects standard and advanced methods in quantum mechanics and implements them using SymbolicC++ and Maxima, two popular computer algebra packages. Throughout, the sample programs and their outputs are accompanied with explanatory text of the underlying mathematics and physics explained in detail. Selected problems have also been implemented using two other popular packages Mathematica and Maple while some problems are implemented in C++. Modern developments in quantum theory are covered extensively, beyond the standard quantum mechanical techniques. The new research topics added to this second edition are: entanglement, teleportation, Berry phase, Morse oscillator, Magnus expansion, wavelets, Pauli and Clifford groups, coupled Bose Fermi systems, super-Lie algebras, etc.

•Mar 24, 2010•2 citations
Modern functional programming languages and lazy functional techniques are useful for describing and implementing abstract mathematical objects in quantum mechanics. Scientists can use them both for pedagogical purposes and for real, not too computationally intensive, but conceptually and algorithmically difficult applications. This article shows how to perform simple abstract computations on state vectors and discusses the construction of lazy algorithms that enormously simplify manipulation of potentially infinite data structures or iterative processes. Lazy functional techniques can often replace the use of symbolic computer algebra packages, while also offering an interesting algorithmic complement to the manipulation of mathematical data. These techniques are more efficient than blindly used symbolic algebra and are easy to integrate with the numerical code.
We develop a framework which aims to simplify the analysis of quantum states and quantum operations by harnessing the potential of function programming paradigm. We show that the introduced framework allows a seamless manipulation of quantum channels, in particular to convert between different representations of quantum channels, and thus that the use of functional programming concepts facilitates the manipulation of abstract objects used in the language of quantum theory. For the purpose of our presentation we will use Mathematica computer algebra system. This choice is motivated twofold. First, it offers a rich programming language based on the functional paradigm. Second, this programming language is combined with powerful symbolic and numeric manipulation capabilities.
Abstract. We present the basic high-level structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudo-code based on QCL quantum programming language to describe them. We also present the implementation of introduced structures in GNU Octave language for scientific computing. Procedures used in the implementation are available as a package quantum-octave providing library of functions, which facilitates the simulation of quantum computing. This package allows also to incorporate high-level programming concepts into the simulation in GNU Octave and Matlab. As such it connects features unique for higl-level quantum programming languages, with the full palette of efficient computational routines commonly available in modern scientific computing systems. To present the major features of the described package we provide the implementation of selected quantum algorithms. We also show how quantum errors can be taken into account during the simulation of quantum algorithms using quantum-octave package. This is possible thanks to the ability to operate on density matrices implemented in quantum-octave. Key words: quantum information, quantum programming, models of quantum computation. 1.
Solving problems in quantum mechanics is an essential skill and research activity for scientists, engineers and others. Nowadays, the labour of scientific computation has been greatly eased by the advent of computer algebra packages. These do not merely perform number-crunching, but enable users to manipulate algebraic expressions and equations symbolically. For example, differentiation and integration can now be carried out algebraically by the computer. This book collects standard and advanced methods in quantum mechanics and implements them using REDUCE, a popular computer algebra package. Throughout, sample programs and their output have been displayed alongside explanatory text, making the book easy to follow. Selected problems have also been implemented using two other popular packages, MATHEMATICA and MAPLE, and in the object-oriented programming language C++. Besides standard quantum mechanical techniques, modern developments in quantum theory are also covered. These include Fermi and Bose Operators, coherent states, gauge theory and quantum groups. All the special functions relevant to quantum mechanics (Hermite, Chebyshev, Legendre and more) are implemented. A careful balance is struck between practical computation and the underlying mathematical concepts, making the book well-suited for use with quantum mechanics courses.
We present a basic high-level structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudo-code based on QCL quantum programming language to describe them. We also present the implementation of introduced structures in GNU Octave language for scientific computing. Procedures used in the implementation are available as a package quantum-octave, providing a library of functions, which facilitates the simulation of quantum computing. This package allows also to incorporate high-level programming concepts into the simulation in GNU Octave and Matlab. As such it connects features unique for high-level quantum programming languages, with the full palette of efficient computational routines commonly available in modern scientific computing systems. To present the major features of the described package we provide the implementation of selected quantum algorithms. We also show how quantum errors can be taken into account during the simulation of quantum algorithms using quantum-octave package. This is possible thanks to the ability to operate on density matrices.
Solving problems in quantum mechanics is an essential skill and research activity for physicists, mathematicians, engineers and others. Nowadays, the labor of scientific computation has been greatly eased by the advent of computer algebra packages, which do not merely perform number crunching, but also enable users to manipulate algebraic expressions and equations symbolically. For example, the manipulations of noncommutative operators, differentiation and integration can now be carried out algebraically by the computer algebra package. This book collects standard and advanced methods in quantum mechanics and implements them using SymbolicC++ and Maxima, two popular computer algebra packages. Throughout, the sample programs and their outputs are accompanied with explanatory text of the underlying mathematics and physics explained in detail. Selected problems have also been implemented using two other popular packages Mathematica and Maple while some problems are implemented in C++. Modern developments in quantum theory are covered extensively, beyond the standard quantum mechanical techniques. The new research topics added to this second edition are: entanglement, teleportation, Berry phase, Morse oscillator, Magnus expansion, wavelets, Pauli and Clifford groups, coupled Bose Fermi systems, super-Lie algebras, etc.