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8.321 Quantum Theory I (MIT) 8.321 Quantum Theory I (MIT)

Description

8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement. 8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Subjects

eigenstates | eigenstates | uncertainty relation | uncertainty relation | observables | observables | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamics

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8.322 Quantum Theory II (MIT) 8.322 Quantum Theory II (MIT)

Description

8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation. 8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subjects

uncertainty relation | uncertainty relation | observables | observables | eigenstates | eigenstates | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | quantization | quantization | EM radiation field | EM radiation field | electromagnetic radiation field | electromagnetic radiation field | adiabatic theorem | adiabatic theorem | Berry?s phase | Berry?s phase | many-particle systems | many-particle systems | Dirac equation | Dirac equation | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamics

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MAS.865J Quantum Information Science (MIT) MAS.865J Quantum Information Science (MIT)

Description

This is an advanced graduate course on quantum computation and quantum information, for which prior knowledge of quantum mechanics is required. Topics include quantum computation, advanced quantum error correction codes, fault tolerance, quantum algorithms beyond factoring, properties of quantum entanglement, and quantum protocols and communication complexity. This is an advanced graduate course on quantum computation and quantum information, for which prior knowledge of quantum mechanics is required. Topics include quantum computation, advanced quantum error correction codes, fault tolerance, quantum algorithms beyond factoring, properties of quantum entanglement, and quantum protocols and communication complexity.

Subjects

quantum computation | quantum computation | quantum error correction codes | quantum error correction codes | fault tolerance | fault tolerance | quantum algorithms | quantum algorithms | quantum entanglement | quantum entanglement | quantum protocols | quantum protocols | communication complexity | communication complexity | quantum cryptography | quantum cryptography | adiabatic quantum computation | adiabatic quantum computation | MAS.865 | MAS.865 | 6.443 | 6.443 | 8.371 | 8.371

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6.453 Quantum Optical Communication (MIT) 6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola

Subjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | number states | coherent states | coherent states | and squeezed states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | heterodyne detection | heterodyne detection | and homodyne detection. Second-order nonlinear optics: phasematched interactions | and homodyne detection. Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | generation of squeezed states | photon-twin beams | photon-twin beams | non-classical fourth-order interference | non-classical fourth-order interference | and polarization entanglement. Quantum systems theory: optimum binary detection | and polarization entanglement. Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | and quantum teleportation. | and quantum teleportation.

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6.453 Quantum Optical Communication (MIT) 6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following.  Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields.  Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&a This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following.  Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields.  Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&a

Subjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | coherent states | and squeezed states | number states | coherent states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields | P-representation and classical fields | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers | phase-insensitive and phase-sensitive amplifiers | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Second-order nonlinear optics: phasematched interactions | Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | Quantum systems theory: optimum binary detection | Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | quantum teleportation | quantum teleportation

License

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18.435J Quantum Computation (MIT) 18.435J Quantum Computation (MIT)

Description

This course provides an introduction to the theory and practice of quantum computation. Topics covered include: physics of information processing, quantum logic, quantum algorithms including Shor's factoring algorithm and Grover's search algorithm, quantum error correction, quantum communication, and cryptography. This course provides an introduction to the theory and practice of quantum computation. Topics covered include: physics of information processing, quantum logic, quantum algorithms including Shor's factoring algorithm and Grover's search algorithm, quantum error correction, quantum communication, and cryptography.

Subjects

quantum computation | quantum computation | physics of information processing | physics of information processing | quantum logic | quantum logic | quantum algorithms including Shor's factoring algorithm and Grover's search algorithm | quantum algorithms including Shor's factoring algorithm and Grover's search algorithm | quantum error correction | quantum error correction | quantum communication | quantum communication | cryptography | cryptography | 18.345 | 18.345 | 2.111 | 2.111 | ESD.79 | ESD.79

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6.453 Quantum Optical Communication (MIT) 6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola

Subjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | number states | coherent states | coherent states | and squeezed states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | heterodyne detection | heterodyne detection | and homodyne detection. Second-order nonlinear optics: phasematched interactions | and homodyne detection. Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | generation of squeezed states | photon-twin beams | photon-twin beams | non-classical fourth-order interference | non-classical fourth-order interference | and polarization entanglement. Quantum systems theory: optimum binary detection | and polarization entanglement. Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | and quantum teleportation. | and quantum teleportation.

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8.321 Quantum Theory I (MIT)

Description

8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Subjects

eigenstates | uncertainty relation | observables | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

License

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8.322 Quantum Theory II (MIT)

Description

8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subjects

uncertainty relation | observables | eigenstates | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | quantization | EM radiation field | electromagnetic radiation field | adiabatic theorem | Berry?s phase | many-particle systems | Dirac equation | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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8.321 Quantum Theory I (MIT)

Description

8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Subjects

eigenstates | uncertainty relation | observables | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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8.322 Quantum Theory II (MIT)

Description

8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subjects

uncertainty relation | observables | eigenstates | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | quantization | EM radiation field | electromagnetic radiation field | adiabatic theorem | Berry?s phase | many-particle systems | Dirac equation | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

License

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6.845 Quantum Complexity Theory (MIT) 6.845 Quantum Complexity Theory (MIT)

Description

This course is an introduction to quantum computational complexity theory, the study of the fundamental capabilities and limitations of quantum computers. Topics include complexity classes, lower bounds, communication complexity, proofs, advice, and interactive proof systems in the quantum world. The objective is to bring students to the research frontier. This course is an introduction to quantum computational complexity theory, the study of the fundamental capabilities and limitations of quantum computers. Topics include complexity classes, lower bounds, communication complexity, proofs, advice, and interactive proof systems in the quantum world. The objective is to bring students to the research frontier.

Subjects

quantum computational complexity theory | quantum computational complexity theory | quantum computers | quantum computers | complexity classes | complexity classes | lower bounds | lower bounds | communication complexity | communication complexity | interactive proof systems | interactive proof systems | BQP | BQP | quantum algorithms | quantum algorithms | QMA | QMA | quantum Merlin Arthur | quantum Merlin Arthur

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18.238 Geometry and Quantum Field Theory (MIT) 18.238 Geometry and Quantum Field Theory (MIT)

Description

Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory. Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory.

Subjects

perturbative quantum field theory | perturbative quantum field theory | classical field theory | classical field theory | free quantum theories | free quantum theories | Feynman diagrams | Feynman diagrams | Renormalization theory | Renormalization theory | Local operators | Local operators | Operator product expansion | Operator product expansion | Renormalization group equation | Renormalization group equation | classical | classical | field | field | theory | theory | Feynman | Feynman | diagrams | diagrams | free | free | quantum | quantum | theories | theories | local | local | operators | operators | product | product | expansion | expansion | perturbative | perturbative | renormalization | renormalization | group | group | equations | equations | functional | functional | function | function | intergrals | intergrals | operator | operator | QFT | QFT | string | string | physics | physics | mathematics | mathematics | geometry | geometry | geometric | geometric | algebraic | algebraic | topology | topology | number | number | 0-dimensional | 0-dimensional | 1-dimensional | 1-dimensional | d-dimensional | d-dimensional | supergeometry | supergeometry | supersymmetry | supersymmetry | conformal | conformal | stationary | stationary | phase | phase | formula | formula | calculus | calculus | combinatorics | combinatorics | matrix | matrix | mechanics | mechanics | lagrangians | lagrangians | hamiltons | hamiltons | least | least | action | action | principle | principle | limits | limits | formalism | formalism | Feynman-Kac | Feynman-Kac | current | current | charges | charges | Noether?s | Noether?s | theorem | theorem | path | path | integral | integral | approach | approach | divergences | divergences | functional integrals | functional integrals | fee quantum theories | fee quantum theories | renormalization theory | renormalization theory | local operators | local operators | operator product expansion | operator product expansion | renormalization group equation | renormalization group equation | mathematical language | mathematical language | string theory | string theory | 0-dimensional QFT | 0-dimensional QFT | Stationary Phase Formula | Stationary Phase Formula | Matrix Models | Matrix Models | Large N Limits | Large N Limits | 1-dimensional QFT | 1-dimensional QFT | Classical Mechanics | Classical Mechanics | Least Action Principle | Least Action Principle | Path Integral Approach | Path Integral Approach | Quantum Mechanics | Quantum Mechanics | Perturbative Expansion using Feynman Diagrams | Perturbative Expansion using Feynman Diagrams | Operator Formalism | Operator Formalism | Feynman-Kac Formula | Feynman-Kac Formula | d-dimensional QFT | d-dimensional QFT | Formalism of Classical Field Theory | Formalism of Classical Field Theory | Currents | Currents | Noether?s Theorem | Noether?s Theorem | Path Integral Approach to QFT | Path Integral Approach to QFT | Perturbative Expansion | Perturbative Expansion | Renormalization Theory | Renormalization Theory | Conformal Field Theory | Conformal Field Theory | algebraic topology | algebraic topology | algebraic geometry | algebraic geometry | number theory | number theory

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MAS.865J Quantum Information Science (MIT)

Description

This is an advanced graduate course on quantum computation and quantum information, for which prior knowledge of quantum mechanics is required. Topics include quantum computation, advanced quantum error correction codes, fault tolerance, quantum algorithms beyond factoring, properties of quantum entanglement, and quantum protocols and communication complexity.

Subjects

quantum computation | quantum error correction codes | fault tolerance | quantum algorithms | quantum entanglement | quantum protocols | communication complexity | quantum cryptography | adiabatic quantum computation | MAS.865 | 6.443 | 8.371

License

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22.51 Quantum Theory of Radiation Interactions (MIT) 22.51 Quantum Theory of Radiation Interactions (MIT)

Description

This subject introduces the key concepts and formalism of quantum mechanics and their relevance to topics in current research and to practical applications. Starting from the foundation of quantum mechanics and its applications in simple discrete systems, it develops the basic principles of interaction of electromagnetic radiation with matter. Topics covered are composite systems and entanglement, open system dynamics and decoherence, quantum theory of radiation, time-dependent perturbation theory, scattering and cross sections. Examples are drawn from active research topics and applications, such as quantum information processing, coherent control of radiation-matter interactions, neutron interferometry and magnetic resonance. This subject introduces the key concepts and formalism of quantum mechanics and their relevance to topics in current research and to practical applications. Starting from the foundation of quantum mechanics and its applications in simple discrete systems, it develops the basic principles of interaction of electromagnetic radiation with matter. Topics covered are composite systems and entanglement, open system dynamics and decoherence, quantum theory of radiation, time-dependent perturbation theory, scattering and cross sections. Examples are drawn from active research topics and applications, such as quantum information processing, coherent control of radiation-matter interactions, neutron interferometry and magnetic resonance.

Subjects

quantum mechanics | quantum mechanics | closed system dynamics | closed system dynamics | composite systems | composite systems | entanglement | entanglement | mixed states | mixed states | open quantum systems | open quantum systems | quantum harmonic oscillator | quantum harmonic oscillator | perturbation theory | perturbation theory | scattering | scattering | interaction with matter | interaction with matter

License

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6.728 Applied Quantum and Statistical Physics (MIT) 6.728 Applied Quantum and Statistical Physics (MIT)

Description

6.728 covers concepts in elementary quantum mechanics and statistical physics. The course introduces applied quantum physics and  emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger's equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others. 6.728 covers concepts in elementary quantum mechanics and statistical physics. The course introduces applied quantum physics and  emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger's equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others.

Subjects

applied quantum physics | applied quantum physics | quantum physics | quantum physics | statistical physics | statistical physics | quantum mechanics | quantum mechanics | Schrodinger | Schrodinger | tunneling | tunneling | harmonic oscillator | harmonic oscillator | hydrogen atom | hydrogen atom | variational methods | variational methods | Fermi-Dirac | Fermi-Dirac | Bose-Einstein | Bose-Einstein | Boltzmann | Boltzmann | distribution function | distribution function | electron microscope | electron microscope | scanning tunneling microscope | scanning tunneling microscope | thermonic emitter | thermonic emitter | atomic force microscope | atomic force microscope

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6.728 Applied Quantum and Statistical Physics (MIT) 6.728 Applied Quantum and Statistical Physics (MIT)

Description

6.728 is offered under the department's "Devices, Circuits, and Systems" concentration. The course covers concepts in elementary quantum mechanics and statistical physics, introduces applied quantum physics, and emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger's equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others. 6.728 is offered under the department's "Devices, Circuits, and Systems" concentration. The course covers concepts in elementary quantum mechanics and statistical physics, introduces applied quantum physics, and emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger's equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others.

Subjects

applied quantum physics | applied quantum physics | quantum physics | quantum physics | statistical physics | statistical physics | quantum mechanics | quantum mechanics | Schrodinger | Schrodinger | tunneling | tunneling | harmonic oscillator | harmonic oscillator | hydrogen atom | hydrogen atom | variational methods | variational methods | Fermi-Dirac | Fermi-Dirac | Bose-Einstein | Bose-Einstein | Boltzmann | Boltzmann | distribution function | distribution function | electron microscope | electron microscope | scanning tunneling microscope | scanning tunneling microscope | thermonic emitter | thermonic emitter | atomic force microscope | atomic force microscope

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18.177 Universal Random Structures in 2D (MIT) 18.177 Universal Random Structures in 2D (MIT)

Description

This graduate-level course introduces students to some fundamental 2D random objects, explains how they are related to each other, and explores some open problems in the field. This graduate-level course introduces students to some fundamental 2D random objects, explains how they are related to each other, and explores some open problems in the field.

Subjects

continuum random tree | continuum random tree | stable Levy tree | stable Levy tree | stable looptree | stable looptree | Gaussian free field | Gaussian free field | Schramm-Loewner evolution | Schramm-Loewner evolution | percolation | percolation | uniform spanning tree | uniform spanning tree | loop-erased random walk | loop-erased random walk | Ising model | Ising model | FK cluster model | FK cluster model | conformal loop ensemble | conformal loop ensemble | Brownian loop soup | Brownian loop soup | random planar map | random planar map | Liouville | Liouville | quantum gravity | quantum gravity | Brownian map | Brownian map | Brownian snake | Brownian snake | diffusion limited aggregation | diffusion limited aggregation | first passage percolation | first passage percolation | and dielectric breakdown model | and dielectric breakdown model | imaginary geometry | imaginary geometry | quantum zipper | quantum zipper | peanosphere | peanosphere | quantum Loewner evolution | quantum Loewner evolution

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6.050J Information and Entropy (MIT) 6.050J Information and Entropy (MIT)

Description

6.050J / 2.110J presents the unified theory of information with applications to computing, communications, thermodynamics, and other sciences. It covers digital signals and streams, codes, compression, noise, and probability, reversible and irreversible operations, information in biological systems, channel capacity, maximum-entropy formalism, thermodynamic equilibrium, temperature, the Second Law of Thermodynamics, and quantum computation. Designed for MIT freshmen as an elective, this course has been jointly developed by MIT's Departments of Electrical Engineering and Computer Science and Mechanical Engineering. There is no known course similar to 6.050J / 2.110J offered at any other university.  6.050J / 2.110J presents the unified theory of information with applications to computing, communications, thermodynamics, and other sciences. It covers digital signals and streams, codes, compression, noise, and probability, reversible and irreversible operations, information in biological systems, channel capacity, maximum-entropy formalism, thermodynamic equilibrium, temperature, the Second Law of Thermodynamics, and quantum computation. Designed for MIT freshmen as an elective, this course has been jointly developed by MIT's Departments of Electrical Engineering and Computer Science and Mechanical Engineering. There is no known course similar to 6.050J / 2.110J offered at any other university. 

Subjects

information and entropy | information and entropy | computing | computing | communications | communications | thermodynamics | thermodynamics | digital signals and streams | digital signals and streams | codes | codes | compression | compression | noise | noise | probability | probability | reversible operations | reversible operations | irreversible operations | irreversible operations | information in biological systems | information in biological systems | channel capacity | channel capacity | aximum-entropy formalism | aximum-entropy formalism | thermodynamic equilibrium | thermodynamic equilibrium | temperature | temperature | second law of thermodynamics quantum computation | second law of thermodynamics quantum computation | maximum-entropy formalism | maximum-entropy formalism | second law of thermodynamics | second law of thermodynamics | quantum computation | quantum computation | biological systems | biological systems | unified theory of information | unified theory of information | digital signals | digital signals | digital streams | digital streams | bits | bits | errors | errors | processes | processes | inference | inference | maximum entropy | maximum entropy | physical systems | physical systems | energy | energy | quantum information | quantum information | 6.050 | 6.050 | 2.110 | 2.110

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6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola

Subjects

Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | number states | coherent states | and squeezed states | radiation field quantization and quantum field propagation | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | heterodyne detection | and homodyne detection. Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement. Quantum systems theory: optimum binary detection | quantum precision measurements | quantum cryptography | and quantum teleportation.

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18.435J Quantum Computation (MIT)

Description

This course provides an introduction to the theory and practice of quantum computation. Topics covered include: physics of information processing, quantum logic, quantum algorithms including Shor's factoring algorithm and Grover's search algorithm, quantum error correction, quantum communication, and cryptography.

Subjects

quantum computation | physics of information processing | quantum logic | quantum algorithms including Shor's factoring algorithm and Grover's search algorithm | quantum error correction | quantum communication | cryptography | 18.345 | 2.111 | ESD.79

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6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following.  Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields.  Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&a

Subjects

Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | number states | coherent states | and squeezed states | radiation field quantization and quantum field propagation | P-representation and classical fields | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | phase-insensitive and phase-sensitive amplifiers | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | Quantum systems theory: optimum binary detection | quantum precision measurements | quantum cryptography | quantum teleportation

License

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6.453 Quantum Optical Communication (MIT)

Description

6.453 Quantum Optical Communication is one of a collection of MIT classes that deals with aspects of an emerging field known as quantum information science. This course covers Quantum Optics, Single-Mode and Two-Mode Quantum Systems, Multi-Mode Quantum Systems, Nonlinear Optics, and Quantum System Theory.

Subjects

Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | number states | coherent states | and squeezed states | radiation field quantization and quantum field propagation | Prepresentation and classical fields | Linear loss and linear amplification: Commutator preservation and the Uncertainty Principle | beam splitters | phase-insensitive and phase-sensitive amplifiers | Quantum photodetection: Direct detection | heterodyne detection | and homodyne detection | Second-order nonlinear optics: Phasematched interactions | optical parametric amplifiers | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | Quantum systems theory: optimum binary detection | quantum precision measurements | quantum cryptography | and quantum teleportation

License

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5.74 Introductory Quantum Mechanics II (MIT) 5.74 Introductory Quantum Mechanics II (MIT)

Description

5.74 explores time-dependent quantum mechanics and spectroscopy. Topics covered include: perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy. The instructor would like to acknowledge Anne Hudson for assisting in preparation of the 5.74 notes. 5.74 explores time-dependent quantum mechanics and spectroscopy. Topics covered include: perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy. The instructor would like to acknowledge Anne Hudson for assisting in preparation of the 5.74 notes.

Subjects

introductory quantum mechanics | introductory quantum mechanics | time-dependent quantum mechanics | time-dependent quantum mechanics | spectroscopy | spectroscopy | perturbation theory | perturbation theory | two-level systems | two-level systems | light-matter interactions | light-matter interactions | correlation functions | correlation functions | linear response theory | linear response theory | nonlinear spectroscopy | nonlinear spectroscopy

License

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5.61 Physical Chemistry (MIT) 5.61 Physical Chemistry (MIT)

Description

This course presents an introduction to quantum mechanics. It begins with an examination of the historical development of quantum theory, properties of particles and waves, wave mechanics and applications to simple systems -- the particle in a box, the harmonic oscillator, the rigid rotor and the hydrogen atom. The lectures continue with a discussion of atomic structure and the Periodic Table. The final lectures cover applications to chemical bonding including valence bond and molecular orbital theory, molecular structure, spectroscopy.AcknowledgementsThe material for 5.61 has evolved over a period of many years, and, accordingly, several faculty members have contributed to the development of the course contents. The original version of the lecture notes that are available on OCW was prepa This course presents an introduction to quantum mechanics. It begins with an examination of the historical development of quantum theory, properties of particles and waves, wave mechanics and applications to simple systems -- the particle in a box, the harmonic oscillator, the rigid rotor and the hydrogen atom. The lectures continue with a discussion of atomic structure and the Periodic Table. The final lectures cover applications to chemical bonding including valence bond and molecular orbital theory, molecular structure, spectroscopy.AcknowledgementsThe material for 5.61 has evolved over a period of many years, and, accordingly, several faculty members have contributed to the development of the course contents. The original version of the lecture notes that are available on OCW was prepa

Subjects

physical chemistry | physical chemistry | quantum mechanics | quantum mechanics | quantum chemistry | quantum chemistry | particles and waves; wave mechanics | particles and waves; wave mechanics | atomic structure | atomic structure | valence orbital | valence orbital | molecular orbital theory | molecular orbital theory | molecular structure | molecular structure | photochemistry | photochemistry | particles and waves | wave mechanics | particles and waves | wave mechanics

License

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