Academic literature on the topic 'Bra-Ket Notation'

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Journal articles on the topic "Bra-Ket Notation"

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Royer, Antoine. "Antilinear operators in Dirac’s bra–ket notation." American Journal of Physics 62, no. 8 (August 1994): 730–32. http://dx.doi.org/10.1119/1.17506.

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Stafford, Randall B., M. Louis Lauzon, Mohammad Sabati, Richard Frayne, and Robert I. Thompson. "A tutorial on the precessional behaviour of hydrogen nuclei in external magnetic fields." Canadian Journal of Physics 88, no. 7 (July 2010): 465–77. http://dx.doi.org/10.1139/p10-033.

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The purpose of this tutorial is to derive the precessional characteristics of the magnetic moments of hydrogen nuclei in the presence of a constant external magnetic field using the Dirac bra-ket formulation of quantum mechanics (QM). This behaviour has many applications, most notably in nuclear magnetic resonance (NMR) and magnetic resonance (MR) imaging. Many NMR and MR imaging textbooks claim that the QM expectation value of the magnetic moment of a proton in a magnetic field reduces to the classical picture of a precessing magnetic dipole. This paper validates this conclusion by reducing the cumbersome QM integrals using Dirac notation and matrix algebra, and then comparing this result with the classical picture. It illustrates the connections between the quantum and classical pictures and demonstrates quantitatively how they differ and how they are similar. This tutorial targets students and researchers interested in the fundamental physics behind the MR phenomenon and assumes that the reader has a basic understanding of QM. This may be helpful for undergraduate QM students learning about spin angular momentum and Dirac notation.
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Muñoz, J. L. Gómez, and F. Delgado. "QUANTUM: A WolframMathematicaadd-on for Dirac Bra-Ket Notation, Non-Commutative Algebra, and Simulation of Quantum Computing Circuits." Journal of Physics: Conference Series 698 (March 2016): 012019. http://dx.doi.org/10.1088/1742-6596/698/1/012019.

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Evans, Daniel. "Quick Quantum Circuit Simulation." Journal of Computer Science Research 3, no. 4 (September 23, 2021). http://dx.doi.org/10.30564/jcsr.v3i4.3567.

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Quick Quantum Circuit Simulation (QQCS) is a software system for computing the result of a quantum circuit using a notation that derives directly from the circuit, expressed in a single input line. Quantum circuits begin with an initial quantum state of one or more qubits, which are the quantum analog to classical bits. The initial state is modified by a sequence of quantum gates, quantum machine language instructions, to get the final state. Measurements are made of the final state and displayed as a classical binary result. Measurements are postponed to the end of the circuit because a quantum state collapses when measured and produces probabilistic results, a consequence of quantum uncertainty. A circuit may be run many times on a quantum computer to refine the probabilistic result. Mathematically, quantum states are 2n -dimensional vectors over the complex number field, where n is the number of qubits. A gate is a 2n ×2n unitary matrix of complex values. Matrix multiplication models the application of a gate to a quantum state. QQCS is a mathematical rendering of each step of a quantum algorithm represented as a circuit, and as such, can present a trace of the quantum state of the circuit after each gate, compute gate equivalents for each circuit step, and perform measurements at any point in the circuit without state collapse. Output displays are in vector coefficients or Dirac bra-ket notation. It is an easy-to-use educational tool for students new to quantum computing.
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Dissertations / Theses on the topic "Bra-Ket Notation"

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Katabira, Joseph. "Groverův algoritmus v kvantovém počítání a jeho aplikace." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445458.

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Kvantová výpočetní technika je rychle rostoucí obor informatiky, který přenáší principy kvantových jevu do našeho každodenního života. Díky své kvantové podstatě získávají kvantové počítače převahu nad klasickými počítači. V této práci jsme se zaměřili na vysvětlení základů kvantového počítání a jeho implementaci na kvantovém počítači. Zejména se zaměřujeme na popis fungování, konstrukci a implementaci Groverova algoritmu jako jednoho ze základních kvantových algoritmů. Demonstrovali jsme sílu tohoto kvantového algoritmu při prohledávání databáze a porovnávali ho s klasickými nekvantovými algoritmy pomocí implementace prostřednictvím simulačního prostředí QISKit. Pro simulaci jsme použili QASM Simulator a State vector Simulator Aer backends a ukázali, že získané výsledky korelují s dříve diskutovanými teoretickými poznatky. Toto ukazuje, že Groverův algoritmus umožňuje kvadratické zrychlení oproti klasickému nekvantovému vyhledávacímu algoritmu, Použitelnost algoritmu stejně jako ostatních kvantových algoritmů je ale stále omezena několika faktory, mezi které patří vysoké úrovně dekoherence a chyby hradla.
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Books on the topic "Bra-Ket Notation"

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Horing, Norman J. Morgenstern. Dirac Notation and Transformation Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0001.

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Chapter 1 opens with a brief review of some basic features of quantum mechanics, including the Schrödinger equation, linear and angular momentum and the theory of the hydrogenic atom: It also includes complete orthonormal sets of eigenfunctions, the translation operator, current, spin, equation of continuity, gauge transformation, determinant & permanent multiparticle energy eigenfunctions for noninteracting particles and the Pauli exclusion principle. Attention is then focused on Dirac bra-ket notation and complete sets of commuting observables. In this connection, representations and transformation among representations are discussed in detail for the Schrödinger system state vector and the eigenstates, as well as bra-ket matrix elements of operators. Finally, Schwinger’s interpretation of ket-bra matrix operator structures (Schwinger “Measurement Symbols”) in terms of annihilation and creation of systems in eigenstates is introduced.
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Book chapters on the topic "Bra-Ket Notation"

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Nguyen-Schäfer, Hung, and Jan-Philip Schmidt. "General Basis and Bra–Ket Notation." In Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers, 1–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-46132-7_1.

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Nguyen-Schäfer, Hung, and Jan-Philip Schmidt. "General Basis and Bra–Ket Notation." In Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers, 1–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-43444-4_1.

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Nguyen-Schäfer, Hung, and Jan-Philip Schmidt. "General Basis and Bra-Ket Notation." In Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers, 1–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-48497-5_1.

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Kasirajan, Venkateswaran. "Dirac’s Bra-ket Notation and Hermitian Operators." In Fundamentals of Quantum Computing, 35–73. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-63689-0_2.

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Dick, Rainer. "Notions from Linear Algebra and Bra-Ket Notation." In Graduate Texts in Physics, 57–74. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-8077-9_4.

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Nguyen-Schäfer, Hung, and Jan-Philip Schmidt. "Tensors and Bra-Ket Notation in Quantum Mechanics." In Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers, 249–311. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-48497-5_6.

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Dick, Rainer. "Notions from Linear Algebra and Bra-Ket Notation." In Graduate Texts in Physics, 63–85. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-57870-1_4.

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Dick, Rainer. "Notions from Linear Algebra and Bra-Ket Notation." In Graduate Texts in Physics, 63–83. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-25675-7_4.

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"Bra-ket Notation." In Quantum Chemistry, 629–30. Elsevier, 2006. http://dx.doi.org/10.1016/b978-012457551-6/50026-3.

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"BRA—KET NOTATION." In Quantum Chemistry, 643–44. Elsevier, 1993. http://dx.doi.org/10.1016/b978-0-08-051554-0.50030-8.

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