Course description: After an introduction into the basics of quantum information and computation, we will to cover topics of current research such as: entanglement theory (including the concept of pseudo-entanglement), learning theory of quantum states and processes (hypothesis testing, (shadow) tomography); quantum communication in theory and practice (quantum repeaters, multipartite entanglement distribution, entanglement distillation); and noise in (random) quantum circuits (including the statistical mechanics model of random quantum circuits).
Lecture notes
- Jan. 21, 2025 — Introduction
- Jan. 23, 2025 — Quantum states
- Jan. 28, 2025 — Entanglement
- Jan. 30, 2025 — Entanglement (part II)
- Feb. 4, 2025 — Entanglement tests and measures
- Feb. 6, 2025 — Quantum circuits and computation
- Feb. 11, 2025 — Clifford gates and universal gate sets
- Feb. 13, 2025 — Universal gate sets (part II)
- Feb. 18, 2025 — Solovay-Kitaev theorem; quantum channels
- Mar. 4, 2025 — Quantum channels; noise in quantum computing
- Mar. 6, 2025 — Quantifying noise and errors
- Mar. 18, 2025 — Quantifying noise and errors (part II); estimating Pauli expectation values
- Mar. 20, 2025 — Haar measure for unitaries
- Mar. 25, 2025 — Haar measure for unitaries (part II); unitary k-designs
- Mar. 27, 2025 — (Noisy) random quantum circuits
- Apr. 1, 2025 — (Noisy) random quantum circuits (part II)
- Apr. 3, 2025 — (Noisy) random quantum circuits (part III)
- Apr. 8, 2025 — Quantum-state tomography
- Apr. 10, 2025 — Quantum-state tomography (part II); information-complete measurements
- Apr. 15, 2025 — Quantum-state tomography (part III)
- Apr. 17, 2025 — Quantum-state tomography (part IV)
- Apr. 22, 2025 — Quantum-state learning; shadow tomography
- Apr. 24, 2025 — Shadow tomography (part II)
Suggested papers for the final presentation
- Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits
- Adaptivity can help exponentially for shadow tomography
- Easy better quantum process tomography
- Most quantum states are too entangled to be useful as computational resources
- Learning k-body Hamiltonians via compressed sensing
- Learning quantum states prepared by shallow circuits in polynomial time
- Certifying almost all quantum states with few single-qubit measurements
- Adaptivity is not helpful for Pauli channel learning
- Learning shallow quantum circuits
- Improved Simulation of Stabilizer Circuits
- A polynomial-time classical algorithm for noisy random circuit sampling
- Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
- Zero-error communication under discrete-time Markovian dynamics (related: Capacities of quantum Markovian noise for large times)
- Two dimensional quantum repeaters
- Fast Scrambling in Classically Simulable Quantum Circuits
Sumeet Khatri 