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

Journal of Knot Theory and Its Ramifications

Quantum mechanics for quantum computing

Robert Owczarek

Published Jan 4, 2016• 2 citations
Publisher

Abstract

Quantum computing is a field of great interest, attracting, among others, the attention of many mathematicians. Although not all quantum mechanics is needed to successfully engage in research on quantum computing, the somewhat superficial approach usually applied by non-physicists is, in the opinion of the author of the lectures, not feasible. The following notes from lectures given at the mathematics department of George Washington University are meant to be a partial remedy to the situation, offering a very brief and slightly unorthodox introduction to one-particle quantum mechanics, and even shorter discussion of passage to multi-particle quantum mechanics, as needed for quantum computing.

DOI
10.1142/s0218216516400095

Related papers

A short survey of quantum computing

Uwe Kaiser

Quantum computing is closely related to [Formula: see text]-dimensional topological quantum field theory through its approach in topological quantum computation. The following are notes based on lectures given by the author at the Mathematics Department of George Washington University. The idea is to give a brief introduction and survey of a few basic facts of quantum computing to an audience of non-experts interested in taking a quick look at some of the most important concepts of quantum computing. The author is a topologist with strong interest in the general ideas of quantum computing. The notes touch on how quantum topology enters the field but emphasizes the general ideas of quantum computing in the first place.

Journal of Knot Theory and Its Ramifications•Dec 22, 2016•1 citation

Introduction to Quantum Mechanics

Eduardo J. S. Villaseñor, Rui Loja Fernandes, Roger Picken

The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.

arXiv:0804.3728•AIP conference proceedings•Jan 1, 2008•52 citations

Lectures on Quantum Mechanics

Philip L. Bowers

Quantum mechanics is one of the principle pillars of modern physics. It also remains a topic of great interest to mathematicians. Since its discovery it has inspired and been inspired by many topics within modern mathematics, including functional analysis and operator algebras, Lie groups, Lie algebras and their representations, principle bundles, distribution theory, and much more. Written with beginning graduate students in mathematics in mind, this book provides a thorough treatment of (nonrelativistic) quantum mechanics in a style that is leisurely, without the usual theorem-proof grammar of pure mathematics, while remaining mathematically honest. The author takes the time to fully develop the required mathematics and employs a consistent mathematical presentation to clarify the often-confusing notation of physics texts. Along the way the reader encounters several topics requiring more advanced mathematics than found in many discussions of the subject, making for a fascinating course in how mathematics and physics interact.

Cambridge University Press eBooks•Aug 27, 2020•185 citations

Quantum to Quantum Computing

V K Gupta

Quantum theory and quantum computing in recent years, has raised more and more increasing interest within the scientific community because of various reasons. First, the highly interdisciplinary nature of the subject which involves diverse topics such as, on the theoretical side, information theory and foundational issues of quantum mechanics and on the experimental side, the physics of quantum, optical, atomic and solid state systems. Secondly, the field is extremely promising for revolutionary technological implications in the near future. It is now perfectly clear that one can use quantum mechanics to process and transmit information in a way which does not have a classical analogue, and that using quantum techniques one can implement fully secure cryptographic systems. Recent breakthroughs, such as quantum teleportation, have led to extremely rapid progresses in a fascinating new field and, as a consequence, have attracted the interest of many scientists from varied disciplines. The purpose of this article is to provide a comprehensive overview about the deep involvement of quantum theory in quantum computation to young researchers and newcomers in the field.

IETE Technical Review•Sep 1, 2002•4 citations

A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation

Samuel J. Lomonaco, Jr. .

The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief introduction to quantum computation, covering such topics as elementary quantum computing devices, wiring diagrams, the no-cloning theorem, quantum teleportation, Shor's algorithm, Grover's algorithm. Many examples are given. A table of contents as well as an index are provided for readers who wish to "pick and choose." Since this paper is intended for a diverse audience, it is written in an informal style at varying levels of difficulty and sophistication from the very elementary to the more advanced.

arXiv:quant-ph/0007045•Jul 17, 2000•1 citation

Introduction to dissipation and decoherence in quantum systems

Florian Marquardt, Annett Püttmann

These lecture notes address an audience of physicists or mathematicians who have been exposed to a first course in quantum mechanics. We start with a brief discussion of the general "system-bath" paradigm of quantum dissipative systems, analyze in some detail the simplest example of "pure dephasing" of a two-level system, and review the basic concept of the density matrix. We then treat the general dissipative time-evolution, introducing completely positive maps, their relation to entanglement theory, and their Kraus decomposition. Restricting ourselves to Markovian evolution, we discuss the Lindblad form of master equations. The notes conclude with an overview of topics of current interest that go beyond Lindblad Markov master equations. (These notes were prepared for lectures delivered by F. Marquardt in October 2007 at the Langeoog workshop of the SFB/TR 12, "Symmetries and Universality in Mesoscopic Systems")

arXiv:0809.4403•Sep 25, 2008•12 citations
Quantum computing is a field of great interest, attracting, among others, the attention of many mathematicians. Although not all quantum mechanics is needed to successfully engage in research on quantum computing, the somewhat superficial approach usually applied by non-physicists is, in the opinion of the author of the lectures, not feasible. The following notes from lectures given at the mathematics department of George Washington University are meant to be a partial remedy to the situation, offering a very brief and slightly unorthodox introduction to one-particle quantum mechanics, and even shorter discussion of passage to multi-particle quantum mechanics, as needed for quantum computing.
Quantum computing is closely related to [Formula: see text]-dimensional topological quantum field theory through its approach in topological quantum computation. The following are notes based on lectures given by the author at the Mathematics Department of George Washington University. The idea is to give a brief introduction and survey of a few basic facts of quantum computing to an audience of non-experts interested in taking a quick look at some of the most important concepts of quantum computing. The author is a topologist with strong interest in the general ideas of quantum computing. The notes touch on how quantum topology enters the field but emphasizes the general ideas of quantum computing in the first place.
Quantum mechanics is one of the principle pillars of modern physics. It also remains a topic of great interest to mathematicians. Since its discovery it has inspired and been inspired by many topics within modern mathematics, including functional analysis and operator algebras, Lie groups, Lie algebras and their representations, principle bundles, distribution theory, and much more. Written with beginning graduate students in mathematics in mind, this book provides a thorough treatment of (nonrelativistic) quantum mechanics in a style that is leisurely, without the usual theorem-proof grammar of pure mathematics, while remaining mathematically honest. The author takes the time to fully develop the required mathematics and employs a consistent mathematical presentation to clarify the often-confusing notation of physics texts. Along the way the reader encounters several topics requiring more advanced mathematics than found in many discussions of the subject, making for a fascinating course in how mathematics and physics interact.
Quantum theory and quantum computing in recent years, has raised more and more increasing interest within the scientific community because of various reasons. First, the highly interdisciplinary nature of the subject which involves diverse topics such as, on the theoretical side, information theory and foundational issues of quantum mechanics and on the experimental side, the physics of quantum, optical, atomic and solid state systems. Secondly, the field is extremely promising for revolutionary technological implications in the near future. It is now perfectly clear that one can use quantum mechanics to process and transmit information in a way which does not have a classical analogue, and that using quantum techniques one can implement fully secure cryptographic systems. Recent breakthroughs, such as quantum teleportation, have led to extremely rapid progresses in a fascinating new field and, as a consequence, have attracted the interest of many scientists from varied disciplines. The purpose of this article is to provide a comprehensive overview about the deep involvement of quantum theory in quantum computation to young researchers and newcomers in the field.
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief introduction to quantum computation, covering such topics as elementary quantum computing devices, wiring diagrams, the no-cloning theorem, quantum teleportation, Shor's algorithm, Grover's algorithm. Many examples are given. A table of contents as well as an index are provided for readers who wish to "pick and choose." Since this paper is intended for a diverse audience, it is written in an informal style at varying levels of difficulty and sophistication from the very elementary to the more advanced.
These lecture notes address an audience of physicists or mathematicians who have been exposed to a first course in quantum mechanics. We start with a brief discussion of the general "system-bath" paradigm of quantum dissipative systems, analyze in some detail the simplest example of "pure dephasing" of a two-level system, and review the basic concept of the density matrix. We then treat the general dissipative time-evolution, introducing completely positive maps, their relation to entanglement theory, and their Kraus decomposition. Restricting ourselves to Markovian evolution, we discuss the Lindblad form of master equations. The notes conclude with an overview of topics of current interest that go beyond Lindblad Markov master equations. (These notes were prepared for lectures delivered by F. Marquardt in October 2007 at the Langeoog workshop of the SFB/TR 12, "Symmetries and Universality in Mesoscopic Systems")