Topic
Quantum process
About: Quantum process is a research topic. Over the lifetime, 13818 publications have been published within this topic receiving 501360 citations.
Papers published on a yearly basis
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Papers
TL;DR: This paper introduces the basic concepts of quantum computation and quantum simulation and presents quantum algorithms that are known to be much faster than the available classic algorithms and provides a statistical framework for the analysis of quantum algorithms and quantum Simulation.
Abstract: Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. As the theory of quantum physics is fundamentally stochastic, randomness and uncertainty are deeply rooted in quantum computation, quantum simulation and quantum information. Consequently quantum algorithms are random in nature, and quantum simulation utilizes Monte Carlo techniques extensively. Thus statistics can play an important role in quantum computation and quantum simulation, which in turn offer great potential to revolutionize computational statistics. While only pseudo-random numbers can be generated by classical computers, quantum computers are able to produce genuine random numbers; quantum computers can exponentially or quadratically speed up median evaluation, Monte Carlo integration and Markov chain simulation. This paper gives a brief review on quantum computation, quantum simulation and quantum information. We introduce the basic concepts of quantum computation and quantum simulation and present quantum algorithms that are known to be much faster than the available classic algorithms. We provide a statistical framework for the analysis of quantum algorithms and quantum simulation.
9,491 citations
TL;DR: In this paper, the notion of a quantum dynamical semigroup is defined using the concept of a completely positive map and an explicit form of a bounded generator of such a semigroup onB(ℋ) is derived.
Abstract: The notion of a quantum dynamical semigroup is defined using the concept of a completely positive map. An explicit form of a bounded generator of such a semigroup onB(ℋ) is derived. This is a quantum analogue of the Levy-Khinchin formula. As a result the general form of a large class of Markovian quantum-mechanical master equations is obtained.
8,228 citations
Book•
29 Aug 2002
TL;DR: Probability in classical and quantum physics has been studied in this article, where classical probability theory and stochastic processes have been applied to quantum optical systems and non-Markovian dynamics in physical systems.
Abstract: PREFACE ACKNOWLEDGEMENTS PART 1: PROBABILITY IN CLASSICAL AND QUANTUM MECHANICS 1. Classical probability theory and stochastic processes 2. Quantum Probability PART 2: DENSITY MATRIX THEORY 3. Quantum Master Equations 4. Decoherence PART 3: STOCHASTIC PROCESSES IN HILBERT SPACE 5. Probability distributions on Hilbert space 6. Stochastic dynamics in Hilbert space 7. The stochastic simulation method 8. Applications to quantum optical systems PART 4: NON-MARKOVIAN QUANTUM PROCESSES 9. Projection operator techniques 10. Non-Markovian dynamics in physical systems PART 5: RELATIVISTIC QUANTUM PROCESSES 11. Measurements in relativistic quantum mechanics 12. Open quantum electrodynamics
8,079 citations
TL;DR: In this article, the linearity of quantum mechanics has been shown to prevent the replication of a photon of definite polarization in the presence of an excited atom, and the authors show that this conclusion holds for all quantum systems.
Abstract: If a photon of definite polarization encounters an excited atom, there is typically some nonvanishing probability that the atom will emit a second photon by stimulated emission. Such a photon is guaranteed to have the same polarization as the original photon. But is it possible by this or any other process to amplify a quantum state, that is, to produce several copies of a quantum system (the polarized photon in the present case) each having the same state as the original? If it were, the amplifying process could be used to ascertain the exact state of a quantum system: in the case of a photon, one could determine its polarization by first producing a beam of identically polarized copies and then measuring the Stokes parameters1. We show here that the linearity of quantum mechanics forbids such replication and that this conclusion holds for all quantum systems.
5,874 citations
TL;DR: In the mid-1990s, theorists devised methods to preserve the integrity of quantum bits\char22{}techniques that may become the key to practical quantum computing on a large scale.
Abstract: In the mid-1990s, theorists devised methods to preserve the integrity of quantum bits---techniques that may become the key to practical quantum computing on a large scale.
4,912 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 4 |
| 2025 | 91 |
| 2024 | 32 |
| 2023 | 77 |
| 2022 | 352 |
| 2021 | 92 |