|
This is an introductory course on quantum machine learning meant for Ph.D students. Others are free to audit and attend the course. Only the Ph.D students can credit this course.
This website will have all the updates for this course. |
|
║ prelimnaries ║ |
|
|
Some questions about quantum machine learning Artificial intelligence and machine learning for quantum technologies, Phys, Rev. X (2023) |
| Keep visiting this page for updates to this course. |
|
║ 6.9.2023 ║ Lecture 1 ║ |
|
|
Introductory ideas about Turing machine, computational complexity. Introduction to different strands of quantum machine learning. Ref : Chapter 3 of Ref [2], and Chapter 1 of Ref [1] Basic ideas about P and NP complexity classes |
|
|
║ 7.9.2023 ║ Lecture 2 ║ |
|
|
A toy quantum machine learning problem. Introduces feature vector, data encoding, some general property of Hadamard operation, measuring output. Ref : Section 1.2 of Ref [1]. Ref : EPL 119, 60002 (2017). arXiv version:1703.10793 |
|
|
║ 13.9.2023 ║ Lecture 3 ║ |
|
|
Classical machine learning basics -- part 1. Data, feature vectors, models, loss functions. Definitions and examples. Ref : Sections 2.1 and 2.2 of Ref [1]. |
|
|
║ 14.9.2023 ║ Lecture 4 ║ |
|
|
Classical machine learning basics -- part 2. Risk minimisation, overfitting, optimisation by gradient descent method, stochastic gradient descent. A simple linear model. Ref : Sections 2.3 of Ref [1]. Overfitting and regularisation |
|
|
║ 21.9.2023 ║ Lecture 5 ║ |
|
|
Classical machine learning basics -- part 3. Linear regression, perceptron as linear classifier, feed-forward neural network, recurrent neural network. Ref : Sections 2.5.1 and 2.5.2 of Ref [1]. Pseudo-inverse of a matrix Perceptron |
|
|
║ 5.10.2023 ║ Lecture 6 ║ |
|
|
Classical machine learning basics -- part 4. Recurrent neural network, Hopfield networks, Boltzmann machines Ref : Sections 2.5.2.3 and 2.5.2.4 of Ref [1]. Hopfield networks Boltzmann machines |
|
|
║ 10.10.2023 ║ Lecture 7 ║ |
|
|
Schemes for data encoding on quantum computer, quantum speed-up Ref : Sections 3.4 and 3.5 of Ref [1]. Basis and amplitude encoding |
|
|
║ 18.10.2023 ║ Lecture 8 ║ |
|
|
Algorithm for basis state encoding of data in superposition Ref : Sections 4.1.1 and 4.1.2 of Ref [1]. Quantum associative memory |
|
|
║ 25.10.2023 ║ Lecture 9 ║ |
|
|
Algorithm for amplitude encoding of data in superposition, quantum random access memory (QRAM) Ref : Sections 4.2, 4.2.1 and 4.2.2.1 of Ref [1]. See Quantum Inform. Comput. 5, 467 (2005) or its arXiv version for creating arbitrary amplitude encoded states. First proposal for QRAM, A simple exposition about QRAM One another QRAM resource |
|
|
║ 27.10.2023 ║ Lecture 10 ║ |
|
|
Variational quantum algorithm, quantum variational eigensolver (VQE), quantum variational circuits (VQC) Ref : Sections 3.6.5 and 5.1 of Ref [1]. Video : General intro to quantum circuits for ML See section 2 in Phys. Rep. 986, 1 (2022) or its arXiv version for a review of VQE. One more review on VQE : Nature Physics 3 625, (2021). An example of VQC, and one more example. |
|
|
║1.11.2023 ║ Lecture 11 ║ |
|
|
quantum variational circuits (VQC) Ref : Sections 5.1.4, 5.2.1 and 5.2.2 of Ref [1]. See also generative VQC (arXiv:1801.07686) Barren plateaus in VQC |
|
|
║8.11.2023 ║ Lecture 12 ║ |
|
|
Towards quantum support vector machine (SVM), Basics of classical SVM Ref : Section 16.5 in Numerical Recipes. You can download the PDF file. Ref : Section 2.5.4 of Ref [1] for kernels, and the kernel trick. See also : SVM with an application and SVM lecture Lagrange multipliers : A simple intro A short intro to kernel methods (video) |
|
|
║10.11.2023 ║ Lecture 13 ║ |
|
|
Dual formalism, Least-squares version of SVM, and qSVM Ref : LS-SVM : Neural Processing Lett. 9, 293 (1999). You can also download the paper from here. See also : LS-SVM and Lagrange multiplier and dual formalism Ref : qSVM paper : Phys. Rev. Lett. 113, 130503 (2014) and a simpler exposition of basic ideas. qSVM requires : QRAM (see lecture 9 above), swap test and quantum phase estimation algorithm in section 5.2 of Ref [2] |
|
|
║15.11.2023 ║ Lecture 14 ║ |
|
|
HHL algorithm Ref : Phys. Rev. Lett. 103, 150502 (2008). arXiv version. See also : Step-by-step walk through HHL Ref: For quantum phase estimation algorithm : section 5.2 and 5.2.1 of Ref [2]. |
|
|
║ Postscript : Some additional readings ║ |
|
|
Scott Aaronson on QML. This is somewhat old, but still worth reading and thinking about it. Opportunities and challenges in QML (2022). This is somewhat biased towards quantum neural networks. Implementations of some QML algorithms. |
|
|
References : [1] Machine Learning with Quantum Computers, Maria Schuld, Francesco Petruccione, (Springer, 2021) [2] Quantum Computation and Quantum Information, Michael Nielsen and Isaac Chuang, (Cambridge Univ Press, 2010) |