Classical and Quantum Approaches
Description: This is a graduate-level course that explores the classical and quantum algorithmic foundations of machine learning and data science, with a focus on techniques that provide provable guarantees. The course is divided into two parts. The first half introduces a number of classical techniques for algorithm design, including tensor methods, Sum-of-Squares (SoS), spectral analysis, MCMC, and diffusion. The second half presents a self-contained introduction to quantum algorithms for optimization and machine learning, including quantum linear algebra, quantum sampling, and learning from quantum data. Throughout the course, we will cover applications across a range of domains, including but not limited to robust statistics, generative modeling, statistical and quantum physics. We aim to provide a unified perspective on how advanced algorithmic techniques—both classical and quantum—can be applied to address key challenges in high-dimensional data analysis.
Time/Location: TTH 9:00 am, SCHM 116
Instructor: Ruizhe Zhang (rzzhang@purdue.edu)
Office hours: By appointment
Course information: Here
Course feedback: Here
Assignments will be posted below and in Brightspace when they become available.
The schedule will be updated as we progress through the course.
| Date | Topic | Materials | Resources |
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| Aug 26 | Introduction; Quantum supremacy and classical spoofing | [slides] |
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| Aug 28 | Tensors (I): Jennrich's algorithm | [slides] |
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| Sep 2 | Tensor (II): Iterative methods | [slides] |
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| Sep 6 | Tensors (III): Overcomplete tensor decomposition | [slides] |
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| Sep 9 | Tensors (IV.I): Tensor networks: basics | [slides] |
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| Sep 11 | Tensors (IV.II): Tensor networks: applications in quantum (quantum circuit simulation and DMRG) | [slides] |
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| Sep 16 - 18 | Tensors (V): Tensor networks: applications in cryo-EM (orbit recovery) | [slides] |
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| Sep 23 | Super-resolution (I) | [slides] |
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| Sep 25 | Super-resolution (II) | [slides] |
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| Sep 30 | Sum-of-Squares (I) | [slides] |
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| Oct 2 | Sum-of-Squares (II) | [slides] |
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| Oct 7 | Sum-of-Squares (III) | [slides] |
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| Oct 9 - 16 | Sampling (I): Variational inference | [slides] |
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| Oct 21 | Sampling (II): Stochastic calculus | [slides] |
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| Oct 23 | Sampling (III): Diffusion model | [slides] |
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| Oct 28 | Quantum eigenvalue problems (I): Quantum phase estimation | ||
| Oct 30 | Quantum eigenvalue problems (II): Early fault-tolerant phase estimation | ||
| Nov 4 | Quantum linear algebra (I) | ||
| Nov 6 | Quantum linear algebra (II) | ||
| Nov 11 | Quantum linear algebra (III) | ||
| Nov 13 | Quantum linear algebra (IV) | ||
| Nov 18 | Quantum sampling: Quantum walk | ||
| Nov 20 | Quantum sampling: Quantum Gibbs sampling; Intro to open quantum systems | ||
| Nov 25 | Quantum learning theory: Shadow tomography | ||
| Dec 2 | Quantum learning theory: Hamiltonian learning | ||
| Dec 4 | Project presentation | ||
| Dec 9 | Project presentation | ||
| Dec 11 | Project presentation |