Institute for Pure & Applied Mathematics (IPAM) Courses

Quantum Approximate Optimization Algorithm and Local Max-Cut - IPAM at UCLA

Explore quantum optimization algorithms, focusing on QAOA's application to LocalMaxCut. Discover insights on quantum supremacy and the performance comparison between local algorithms and QAOA on various graph instances.

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

Variational Quantum Architectures for Linear Algebra Applications

Explore variational quantum algorithms for linear algebra applications, including singular value decomposition, linear system solving, and generative models, with focus on NISQ-era implementations and real-world examples.

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

Classical and Quantum Algorithms for Isogeny Problems

Explore classical and quantum algorithms for isogeny problems in post-quantum cryptography, focusing on computational challenges, path finding in isogeny graphs, and reductions to other problems in elliptic curve cryptography.

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

Heisenberg-Limited Ground State Energy Estimation for Early Fault-Tolerant Quantum Computers

Explore Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers, featuring a simplified circuit and classical post-processing for improved efficiency.

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

Sophia Economou - Problem-Tailored Variational Quantum Algorithms - IPAM at UCLA

Explore problem-tailored variational quantum algorithms, including symmetry-preserving circuits, ADAPT-VQE, and ctrl-VQE, for improved performance in quantum simulations.

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

Arithmetic Tensor Networks and Integration - IPAM at UCLA

Explore arithmetic tensor networks and their applications in function integration, with insights on exact and approximate contraction methods and their implications for various mathematical problems.

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

Optimal Scaling Quantum Linear Systems Solver via Discrete Adiabatic Theorem

Explore optimal quantum linear systems solver using discrete adiabatic theorem, achieving linear complexity in condition number and precision, with simplified implementation and constant factor analysis.

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

Improved Complexity Estimation for Hamiltonian Simulation with Trotter Formula

Explore improved complexity estimation for Hamiltonian simulation using Trotter formula, focusing on time-dependent effective mass and near adiabatic dynamics scenarios with potential for enhanced efficiency.

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

On Quantum Linear Algebra for Machine Learning - IPAM at UCLA

Explore quantum singular value transformation for machine learning, its applications, limitations, and connections to classical algorithms in this technical talk on quantum linear algebra.

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

Dequantization and Quantum Advantage in Learning from Experiments - IPAM at UCLA

Explore quantum advantage in data processing, learning from experiments, and dequantization. Discover how quantum technology can revolutionize experimental data acquisition and analysis in various scientific tasks.

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

The Quantum Linear Systems Problem - IPAM at UCLA

Explore quantum algorithms for solving linear systems, including improved methods and complexity analysis, with a focus on potential exponential speedups and verification challenges.

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

Fast Algorithms for Quantum Signal Processing - IPAM at UCLA

Explore fast algorithms for quantum signal processing, focusing on optimization techniques, energy landscapes, and phase factor structures in quantum singular value transformation.

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

Quantum Algorithms for Quantum Information Processing Tasks

Explore quantum linear algebra methods for efficient quantum information processing, including block-encoding, singular value transformation, and applications in estimation, testing, and tomography tasks.

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

Time-Dependent Hamiltonian Simulation of Highly Oscillatory Dynamics - IPAM at UCLA

Explore highly oscillatory dynamics in quantum systems, focusing on efficient simulation algorithms for time-dependent Hamiltonians with applications in various scientific fields.

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

Efficient Quantum Algorithm for Dissipative Nonlinear Differential Equations

Explore efficient quantum algorithms for nonlinear differential equations, overcoming limitations through Carleman linearization. Discover potential applications in biology, fluid dynamics, and plasma physics.

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