Circuit Complexity Courses and Certifications

Simons Institute

Recent Structure Lemmas for Depth-Two Threshold Circuits

Explore recent advancements in structure lemmas for depth-two threshold circuits, focusing on Boolean devices and their implications in computational complexity theory.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Simons Institute

Top-Down Lower Bounds for Depth-Four Circuits

Explores new proof techniques for depth-4 boolean circuit complexity, applying robust sunflowers and block unpredictability to demonstrate exponential lower bounds for the parity function.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Association for Computing Machinery (ACM)

Strong Average-Case Circuit Lower Bounds from Non-trivial Derandomization

Explore circuit lower bounds and derandomization, focusing on AC circuits, algorithmic methods, and pseudorandom generators. Learn about recent developments in average-case circuit analysis.

• YouTube
• 21 minutes
• On-Demand
• Free Video

Institute for Advanced Study

The Orthogonal Vectors Conjecture and Nonuniform Circuit Lower Bounds

Explore advanced connections between circuit analysis algorithms and nonuniform lower bounds, revealing new win-win results that could refute the Orthogonal Vectors Conjecture.

• YouTube
• 2 hours 4 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Proof and Circuit Complexity - Robert Robere

Explore proof and circuit complexity with Robert Robere, delving into Boolean circuits, monotone circuits, slice functions, and the Click function to understand computational limitations.

• YouTube
• 24 minutes
• On-Demand
• Free Video

IEEE

Lifting with Simple Gadgets and Applications to Circuit and Proof Complexity

Explore lifting techniques in circuit and proof complexity, focusing on Cutting Planes measures, communication complexity, and applications to monotone circuits and formulas.

• YouTube
• 21 minutes
• On-Demand
• Conference Talk

Simons Institute

The Parallelism Tradeoff: Understanding Transformer Expressivity Through Circuit Complexity

Explore transformer neural nets' computational power and limitations through circuit complexity analysis, revealing insights into parallelism tradeoffs in large-scale model architectures.

• YouTube
• 45 minutes
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

Circuit Complexity of Code States in Topological Quantum Computing - Part 3

Delve into advanced quantum code theory, focusing on surface codes, dimensional limitations, and circuit complexity in quantum computing systems for practical applications and topological phases.

• YouTube
• 56 minutes
• On-Demand
• Free Video

ICTP-SAIFR

Krylov Complexity from Circuit Complexity and from Instantons

Explore Krylov complexity through circuit complexity and instantons in quantum field theory and condensed matter physics applications.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Centre for Quantum Technologies

NLTS Hamiltonians from Good Quantum Codes - Understanding Low-Energy States and Circuit Complexity

Delve into the complexity of NLTS conjecture, quantum LDPC codes, and their connection to local Hamiltonians, exploring circuit lower bounds and many-body entanglement principles.

• YouTube
• 42 minutes
• On-Demand
• Free Video

IIT Kanpur;  NPTEL

Circuit Complexity Theory

Explore Boolean circuit complexity, proving upper and lower bounds on circuit resources. Delve into mathematical concepts, theorems, and advanced topics in theoretical computer science.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

Kolmogorov-Seminar

Computing Majority of N Using Majority-K Circuits with Logarithmic Depth

Delve into probabilistic constructions and computational complexity, exploring Valiant's theorem on majority functions using Maj-k circuits and their depth analysis.

• YouTube
• 1 hour 50 minutes
• On-Demand
• Free Video

Ryan O'Donnell

Algebraic Circuit Complexity

Explore algebraic circuit complexity, including models, formulas, and NP connections in computational complexity theory.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Krylov Complexity and Trotter Transitions in Unitary Circuit Dynamics

Explore Krylov complexity and Trotter transitions in unitary circuit dynamics, examining mechanisms constraining many-body quantum systems and their implications for non-equilibrium physics.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Institute for Advanced Study

From Classical to Quantum Circuit Complexity - The Tale of QAC0

Explore quantum circuit complexity in the NISQ era, focusing on QAC0 circuits' power, limitations, and learnability through Fourier concentration techniques and computational bounds.

• YouTube
• 1 hour 19 minutes
• On-Demand
• Free Video