Update fys3415.md

Author: mhjensen

doc/Admin/ContentFYS3415/fys3415.md

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-# Quantum Computing and Quantum Machine Learning 
-
-The first part of the course (project 1 and till mid march) has its focus on studies of
-quantum-mechanical many-particle systems using quantum computing
-algorithms and quantum computers. The second part is optional and
-depends on the interests and backgrounds of the participants. Two main
-themes can be covered:
-- Quantum machine learning algorithms, implementations and studies
-- Realization and studies of entanglement in physical systems
-- Advanced VQE and hamiltonian systems
-### Possible  textbooks:
-- Maria Schuld and Francesco Petruccione, Machine Learning with Quantum Computers, see https://link.springer.com/book/10.1007/978-3-030-83098-4
-- Wolfgang Scherer, Mathematics of Quantum Computing, see https://link.springer.com/book/10.1007/978-3-030-12358-1
-- Robert Hundt, Quantum Computing for Programmers, https://www.cambridge.org/core/books/quantum-computing-for-programmers/BA1C887BE4AC0D0D5653E71FFBEF61C6
-- Robert Loredo, Learn Quantum Computing with Python and IBM Quantum Experience, see https://github.com/PacktPublishing/Learn-Quantum-Computing-with-Python-and-IBM-Quantum-Experience
-
-
-### Interesting online courses and software:
-- IBM's Quantum Computer Programming: Hands-On Workshop at https://quantgates.com/learn-quantum
-- QuTip at https://github.com/qutip
-- QisKit at https://www.ibm.com/quantum/qiskit
-- PySCF for traditional quantum mechanical methods at https://pyscf.org/user/install.html#how-to-install-pyscf. This library can be integrated with QisKit for quantum computing simulations.
-- Qbraid at https://www.qbraid.com
-
-### Time: Each Wednesday at 215pm-4pm CET and exercise sessions 4pm-5pm (The lecture sessions will be recorded)
--Permanent Zoom link for the whole semester is https://uio.zoom.us/my/mortenhj
-
-
-## January 20-24, 2025. Overview of first week, Basic Notions of Quantum Mechanics
+# FYS3415 Tentative content
+
+
+## Basic Notions of Quantum Mechanics
 - Definitions, Linear Algebra reminder, Hilbert Space, Operators on Hilbert Spaces, Composite Systems
-  - Definitions
-  - Mathematical notation, Hilbert spaces and operators
+  - Definitions and reminders on linear algebra
+  - Mathematical notation, Hilbert spaces and operators, computational basis and change of basis
+  - Functions of operators
+  - Measurements and statistics of measurements
   - Description of Quantum Systems and one-qubit systems 
   - States in Hilbert Space, pure and mixed states
-  - Video of lecture at https://youtu.be/YRobDADb63E
-- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week1
-  - _Reading recommendation_: Scherer chapter 2 
-
-## January 27 - January 31, 2025. Composite Systems and Tensor Products
-  - Spectral decomposition and measurements
+  - Composite Systems and Tensor Products
+
+## More basic quantum mechanics
+  - Observables
+  - Composite systems
+  - Unitary trasformations
+  - Time evolution of quantum states, generalized Born rule, Trotter approximation and other
+    mathematical details
+  - Examples of simple Hamiltonians and unitary transformations
+
+## General state of a qubit, no-cloning theorem, entanglement and Bell states
+  - General qubit states
+  - Bloch sphere representation
+  - No-cloning theorem 
+  - Entanglement and Bell states 
+
+## Einstein-Podolsky-Rosen (EPR), Bell’s inequalities, and Local Realism
+   - An EPR Experiment
+   - Bells’ Inequality
+
+## Spectral decomposition, measurements and simple quantum operations
   - Density matrices
-  - Entanglement, pure and mixed states
-v- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week2  
-  - _Reading recommendation_: Scherer chapter 2 and sections 3.1-3.3. Hundt, Quantum Computing for Programmers, chapter 2.1-2.5. Hundt's text is relevant for the programming part where we build from scratch the ingredients we will need.
-  - Video of lecture at https://youtu.be/T7l-rciM0N0
-  - Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesJanuary29.pdf 
-
-## February 3-7, 2025. Density matrices and Measurements
-  - Discussion of gates and project 1
+  - Change in the density matrix under a unitary transformation
+  - More on Entanglement, pure and mixed states
+  - Density matrix of a system in a well defined state 
+  - Density matrix of a subsystem when the combined system is in a well defined state
+  - Entanglement and Schmidt decomposition 
+  - Entropy as a measurement of entanglement
   - Quantum gates and circuits
-  - Developing our own codes for Bell states and comparing with qiskit
-- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week3  
-
-## February 10-14, 2025. Entanglement and entropies
-  - Reminder from last week on gates and circuits
   - One-qubit and two-qubit gates, background and realizations
   - Simple Hamiltonian systems
-- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week4  
-  - _Reading recommendation_: For the discussion of one-qubit, two-qubit and other gates, sections 2.6-2.11 and 3.1-3.4 of Hundt's book Quantum Computing for Programmers, contain most of the relevant information.
-  - Video of lecture at https://youtu.be/UcfOVvFyw2E
-  - Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf
-  
 
-## February 17-21, 2025.
-  - Entanglement and Schmidt decomposition 
-  - Entropy as a measurement of entanglement
-  - Simple one-qubit and two-qubit Hamiltonians
-- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week5  
-  - _Reading recommendation_: For the discussion of one-qubit, two-qubit and other gates, sections 2.6-2.11, 3.1-3.4 and 6.11.1-.6.11.3 of Hundt's book Quantum Computing for Programmers, contain most of the relevant information.
-- Video of lecture at https://youtu.be/caR8AQM6Rwo
-- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary19.pdf
+## Generating and measuring Bell States
+  - Discussion on coding and how to implement qubits and various gates
+
+## Quantum Functions and Quantum Parallelism
 
-## February 24-28, 2025. Quantum gates and circuits and Quantum Fourier Transform and Hamiltonians
+## Simple algorithms
+  - Deutsch’s Algorithm
+  - Identities in quantum circuits
+  - The Bernstein-Vazirani Algorithm
+  - Simon’s Algorithm 
+
+## Quantum Fourier transforms
   - Quantum gates and operations and simple quantum algorithms
-  - Discussion of the VQE algorithm and discussions of project 1
-  - Video of lecture at https://youtu.be/13JyMS50beg/
-  - Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary26.pdf
-- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week6
-
-##  March 3-7, 2025. Algorithms for solving quantum mechanical problems.
-  - VQE and adaptive VQE, Variational Quantum Eigensolver and discussion of codes
-  - Simulations of  of Hamiltonians, focus on the one- and two-qubit Hamiltonians
-  - Start discussions of Lipkin model
-  - Video of lecture at https://youtu.be/jGtcEc85VbE
-  - Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesMarch5.pdf
-  
-- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week7
-
-
-##  March 10-14, 2025. Solving quantum mechanical problems
-  - Lipkin model and VQE
-  - Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week8
-  - Video of lecture at https://youtu.be/hdUnJcJGigw
-  - Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesMarch12.pdf
-
-
-## March 17-21, 2025. Discussions of project 1 and work on the VQE
-  - Lipkin model and VQE
-  - Discussion of project 1 and work on finalizing project
-- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week9
-
-## March 24-28, 2025
+  - Fourier transforms, from discrete to fast Fourier transform
   - Quantum Fourier Transforms, algorithm and implementation
   - Quantum phase estimation algorithm
-  - Video of lecture at https://youtu.be/UHqBk1eQT6E
-  - Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesMarch26.pdf
-- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week10
-
-
-
-## March 31-April 4, 2025
-  - Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT)
-  - Quantum Fourier transforms (QFTs), reminder from last week
-  - Setting up circuits for QFTs
-  - Quantum phase estimation algorithm (QPE)
-- Reading recommendation Hundt, Quantum Computing for Programmers, sections 6.1-6.4 on QFT and QPE.
-
-## April 7-11, 2025
-  - Setting up circuits for QFTs
-  - Quantum phase estimation algorithm (QPE)
-- Reading recommendation Hundt, Quantum Computing for Programmers, sections 6.1-6.4 on QFT and QPE.
 
+## Finding eigenvalues of simple Hamiltonians
+  - Implementing the QPE for finding eigenvalues
+  - Discussions and implementations of the Variational Quantum Eigenvolver
 
-## April 14-18, 2025, Public holidays in Norway no classes
+## Physical realization and how to make quantum components (gates and circuits)
+  Discussion of quantum platforms such as
+  - Nuclear magnetic resonance
+  - Trapped ions and quantum dots
+  - Superconducting circuits
+  - Optics
 
-## April 21-15, 2025
-  - Quantum Machine Learning
+## Possible additional topics
+  - Shor’s Algorithm and factorization 
+  - Quantum Error Correction
+  - Grover’s Search Algorithm
 
 
-## April 28-May 2, 2025
-  - Quantum machine learning
 
-## May 5-9, 2025
-  - Quantum machine learning
+# Advanced topics, at master level
 
-## May 12-16, 2025
-  - Quantum machine learning
-  - Summary of course
+## Quantum sensing, module of 5 ECTS
+## Building Quantum computers