Library
Books, lecture notes, and surveys I keep returning to, in quantum computing, machine learning, and the mathematics underneath both. Short by design.
Quantum computing
Algorithms, learning, complexity, error correction, and open systems.
Algorithms
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Lecture notes on quantum algorithms
The standard toolkit from quantum walks to Hamiltonian simulation.
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Quantum computing: lecture notes
Compact, with exercises; strong on query complexity and lower bounds.
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Lecture notes on quantum algorithms for scientific computation
Linear systems, simulation, and block encodings.
Learning
- A survey of quantum learning theory
- A survey on the complexity of learning quantum states
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The randomized measurement toolbox
Classical shadows and their relatives.
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Introduction to Haar measure tools in quantum information
Weingarten calculus and unitary designs, written for use.
Complexity
- The quantum PCP conjecture
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Quantum proofs
QMA and its variants.
Error correction
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Surviving as a quantum computer in a classical world
A textbook on error correction and fault tolerance, in draft.
- Lecture notes on quantum error correction
Information theory and open systems
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The theory of quantum information
The rigorous reference for channels, distinguishability, and semidefinite programming.
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Lecture notes on the theory of open quantum systems
Master equations and the Lindblad form, derived carefully.
Machine learning
Learning theory, deep learning, and statistical learning.
Theory
Deep learning
Statistical learning
Mathematics
Graphs, Markov chains, analysis, concentration, and optimization.
Graphs and Markov chains
- Spectral and algebraic graph theory
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Markov chains and mixing times
Mixing times, coupling, and spectral methods.
Analysis and concentration
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Analysis of Boolean functions
Fourier analysis on the Boolean cube.
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An introduction to matrix concentration inequalities
Matrix Bernstein and its relatives, with proofs.
Optimization
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Introduction to online convex optimization
Regret bounds from first principles.