Recent Advances in Quantum Simulation with Applications to Chemistry and Field Theory

Explore recent advancements in quantum simulation and their applications to chemistry and field theory in this 45-minute lecture by Nathan Wiebe from the University of Washington. Delve into the mathematics of time-dependent Hamiltonians and examine various simulation techniques, including Linear Combinations of Unitaries, QDRIFT, and Truncated Dyson Series. Investigate the complexities of different simulation methods and learn about the Interaction Picture Simulation. Analyze Trotter Formulas and Multi-Product Formulas, understanding their performance and practical applications. Discover the implementation of these techniques in simulating the Schwinger Model, with insights into actual gate counts. Gain a comprehensive understanding of quantum algorithms and their potential impact on chemistry and field theory research.

Intro
Overview
Time-Dependent Hamiltonians
Mathematics of Time-Dependent H
Problems
Linear Combinations of Unitaries / QDRIFT
Simplest Case: QDRIFT
What's the complexity?
Truncated Dyson Series Simulation
Complexity of simulation
Interaction Picture Simulation
Simulating Hamiltonians
Trotter Formulas
Main Result
Technique
Multi-Product Formulas
How does it work?
Performance
Simulation of Schwinger Model
Actual Gate Counts
Conclusion