Lecture notes for the video “Quantum mechanics essentials: Everything you need for quantum computation”

Here you can find the pdf copy of the notes I wrote during the video

The essentials of quantum mechanicsDownload

Introduction to general relativity

This summer semester (2021) I am giving a course on General Relativity (GR). This course is intended for theorists with familiarity with special relativity (a must) and basic physics.

I will be making the lecture notes produced during these videos available here:

Introduction to general relativity prerelativity gravitationDownload

Introduction to general relativity The equivalence principle and Mach’s principleDownload

Introduction to general relativity manifoldsDownload

Introduction to general relativity tangent spaceDownload

Introduction to general relativity flows and tensorsDownload

Introduction to general relativity tensors continuedDownload

Introduction to general relativity abstract index notation curvatureDownload

Introduction to general relativity derivative operators and parallel transportDownload

A note on da as a covariant derivativeDownload

Introduction to general relativity parallel transport continuedDownload

Introduction to general relativity Geodesics cont. curvatureDownload

Introduction to general relativity curvature contDownload

general-relativityDownload

introduction-to-general-relativity-einsteins-field-equations-linearised-solutionsDownload

introduction-to-general-relativity-lie-derivatives-newtonian-limitDownload

introduction-to-general-relativity-gravitational-radiationDownload

Introduction to general relativity homogeneity and isotropy contDownload

Introduction to general relativity homogeneity and isotropy cont 2Download

Introduction to general relativity FLRW contDownload

Introduction to general relativity FLRW cont 2Download

Introduction to general relativity the Schwarzschild solutionDownload

Introduction to general relativity the Schwarzschild solution contDownload

Introduction to general relativity geodesics in SchwarzschildDownload

Introduction to general relativity trajectories of null geodesics in SchwarzschildDownload

You can find the videos for this course at the following playlist:

Mathematical methods of quantum information theory

In 2017 Reinhard Werner gave a series of lectures on the mathematical methods of quantum information theory at the Leibniz Universität Hannover. These lectures were recorded and I have the pleasure of hosting these videos on my youtube channel. Over the coming weeks I’ll be posting these lectures there. The playlist of all of these videos can be found here.

The prerequisites for these lectures are a standard course on quantum mechanics and some familiarity with mathematical analysis, e.g., Hilbert space, operators, etc., although these topics are reviewed in the first lectures.

The material covered in these lectures covered a range of topics in quantum information theory, a partial list is given below:

Lecture 1: Hilbert spaces, scalar product, bra, ket, operators.

Lecture 2: operators, diagonalization, functional calculus, qubit, composite systems, tensor product.

Lecture 3: composition, tensor product, channels, Heisenberg picture, Schrödinger picture, complete positivity, channel examples: unitary, depolarizing, von Neumann measurement.

Lecture 4: state space, probabilites, composition positivity, geometry of cones.

Lecture 5: geometry, extremal points, pure states, POVM, effect operators.

Lecture 6: Choi-Jamiokowski isomorphism, Kraus operators.

Lecture 7: Wigner’s theorem, anti unitary operators, symmetry groups, one-parameter groups, irreducible representations

Lecture 8: How to construct a Hilbert space, positive kernel, kolmogorov dilation, completion, going to the larger Hilbert space.

Lecture 9: Stinespring dilation Theorem and proof, Example: Naimark dilation, GNS representation, comparison theorem.

Lecture 10: Corollary of Stinespring, Kraus Form.

Lecture 11: Instrument, statistical structure; entanglement, Choi isomorphism and channels, classical models, Bell correlation.

Lecture 12: Mixed state entanglement, Bell inequalites, Tsirelsons inequality, pure state entanglement, Schmidt decomposition, maximally entangled states.

Lecture 13: Dispersion-free preparation, Joint measurement, measurement uncertainty relation, copying, transmitting a quantum state via a classical channel, signalling on correlations, teleportation.

Lecture 14: quantum teleportation; dense coding

Lecture 15: teleportation vs. dense coding, star trek

Lecture 16: norms and fidelities, operator norms, Schatten norms, trace norm, diamond norm, cb norm.

Lecture 17: some semidefinite tasks in QI SDPs, examples: unambiguous state discrimination, entanglement detection, code optimization, dual SDP, optimization on a convex cone (interior point method).

Lecture 18: noisy resources and conversion rates classical-quantum information transmission, two-step encoding inequality.

Lecture notes and exercises will not be distributed.

Symplectic geometry & classical mechanics, Problem sheet 6

For winter semester 2017-18 I am giving a course on symplectic geometry and classical mechanics. This course is intended for anyone with a familiarity with classical mechanics and basic differential geometry. You can find the Youtube playlist here.

Problem sheets are being prepared by Terry Farrelly and will be made available here on my blog, however solutions will *not* be distributed.

Here you can find last problem sheet 6.

Symplectic geometry & classical mechanics, Problem sheet 5

For winter semester 2017-18 I am giving a course on symplectic geometry and classical mechanics. This course is intended for anyone with a familiarity with classical mechanics and basic differential geometry. You can find the Youtube playlist here.

Problem sheets are being prepared by Terry Farrelly and will be made available here on my blog, however solutions will *not* be distributed.

Here you can find problem sheet 5.

Symplectic geometry & classical mechanics, Problem sheet 4

For winter semester 2017-18 I am giving a course on symplectic geometry and classical mechanics. This course is intended for anyone with a familiarity with classical mechanics and basic differential geometry. You can find the Youtube playlist here.

Problem sheets are being prepared by Terry Farrelly and will be made available here on my blog, however solutions will *not* be distributed.

Here you can find problem sheet 4.

Symplectic geometry & classical mechanics, Problem sheet 3

For winter semester 2017-18 I am giving a course on symplectic geometry and classical mechanics. This course is intended for anyone with a familiarity with classical mechanics and basic differential geometry. You can find the Youtube playlist here.

Problem sheets are being prepared by Terry Farrelly and will be made available here on my blog, however solutions will *not* be distributed.

Here you can find problem sheet 3.

Symplectic geometry & classical mechanics, Problem sheet 2

For winter semester 2017-18 I am giving a course on symplectic geometry and classical mechanics. This course is intended for anyone with a familiarity with classical mechanics and basic differential geometry. You can find the Youtube playlist here.

Problem sheets are being prepared by Terry Farrelly and will be made available here on my blog, however solutions will *not* be distributed.

Here you can find problem sheet 2.

Symplectic geometry & classical mechanics, Problem sheet 1

For winter semester 2017-18 I am giving a course on symplectic geometry and classical mechanics. This course is intended for anyone with a familiarity with classical mechanics and basic differential geometry. You can find the Youtube playlist here.

Problem sheets are being prepared by Terry Farrelly and will be made available here on my blog, however solutions will *not* be distributed.

Here you can find problem sheet 1.

A QIG seminar on “the Polynomial Hierarchy” by Friederike Dziemba

In this post I’d like to share a video we’ve uploaded of a recent talk in the quantum information group seminar series by Friederike Dziemba where she presents a physicist-friendly overview of the polynomial hierarchy, a central idea in computational complexity theory:

If you’d like to see more content like this then please do hit the like button. And if you’d like to keep up to date with content from the quantum information group, Hannover, then please don’t hesitate to subscribe to our channel and my own channel.