Institute for Pure & Applied Mathematics (IPAM) Courses

Classical Topology and Quantum Complexity - IPAM at UCLA

Explore the intersection of classical topology and quantum complexity, focusing on computational challenges in determining homology groups and their implications for quantum mechanics and data analysis.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Hamiltonian Simulation Meets Holographic Duality - IPAM at UCLA

Explore connections between Hamiltonian simulation and AdS/CFT duality, uncovering universal quantum Hamiltonians and extending toy models to include energy scales and dynamics in quantum gravity.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Making the Leap to Quantum PCPs - IPAM at UCLA

Explore quantum PCPs, NLTS conjecture, and quantum error-correcting codes. Discover connections to quantum complexity theory and future research directions in this intuition-focused talk.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Fast Erasure Decoder for a Class of Quantum LDPC Codes - IPAM at UCLA

Explore fast erasure decoding for quantum LDPC codes, focusing on hypergraph product codes and their potential to reduce qubit count in fault-tolerant quantum computers.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

Layer Codes - IPAM at UCLA

Explore topological defect networks in quantum error correction, focusing on a novel construction method for 3D codes with optimal scaling parameters and low-weight stabilizers.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

High-Dimensional Sipser-Spielman Codes - IPAM at UCLA

Exploration of high-dimensional Sipser-Spielman codes, extending expander codes to cell complexes and cellular sheaves, with applications in quantum error correction and coding theory.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Fault Tolerant Quantum Computation Using Majorana-Based Topological Qubits

Explore fault-tolerant quantum computation using Majorana-based topological qubits, focusing on tetron qubits and scalable error correction in semiconductor-superconductor heterostructures.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Topological Defects in Toric Code and Sequential Quantum Circuit - IPAM at UCLA

Explore topological defects in toric code and sequential quantum circuits, focusing on the Cheshire string and its implications for understanding higher-dimensional topological orders and quantum error correction.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Categorical Landau Paradigm and the SymTFT - IPAM at UCLA

Explore advanced concepts in quantum physics with Oxford researcher Sakura Schafer-Nameki, focusing on the Categorical Landau Paradigm and SymTFT in relation to quantum error correction and gravity.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

Global Unitaries and Local Measurements - IPAM at UCLA

Explore quantum cellular automata, local unitary circuits, and measurement-induced locality-preserving unitaries in this advanced talk on quantum information theory and topology.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Entanglement of Sections - IPAM at UCLA

Explore quantum information in parameter families through examples, presented by Microsoft Research's Michael Freedman at IPAM's workshop on topology and quantum error correction.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

The Development of Quantum Error Correction - Green Family Lecture at IPAM at UCLA

Explore the evolution of quantum error correction with Peter Shor, overcoming the Heisenberg Uncertainty Principle to enable fault-tolerant quantum computing. Gain insights into early developments and their impact.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Circuit-to-Hamiltonian from Tensor Networks and Fault Tolerance - IPAM at UCLA

Explore a novel approach to mapping quantum circuits to local Hamiltonians using tensor networks, avoiding clock registers and incorporating fault tolerance for robust quantum computation.

• YouTube
• 37 minutes
• Self-Paced
• Free Video

Topology of Moduli Spaces of Topological Theories and Applications to Codes

Explore moduli spaces of topological theories, their homotopy types, and applications to Hastings-Haah floquet codes in quantum error correction and quantum gravity.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Quantum Error Correcting for Gravity in the Large-N Limit - IPAM at UCLA

Explore quantum error correcting codes for large-N limit theories, focusing on gravitational duals and emerging features. Covers asymptotic operator algebra results and information theoretic constraints.

• YouTube
• 55 minutes
• Self-Paced
• Free Video