Improved Complexity Estimation for Hamiltonian Simulation with Trotter Formula

Explore a 39-minute conference talk on improved complexity estimation for Hamiltonian simulation using the Trotter formula. Delve into Dong An's presentation at IPAM's Quantum Numerical Linear Algebra Workshop, covering two specific scenarios: simulating the Schrödinger equation with time-dependent effective mass and near adiabatic dynamics. Discover how measuring error in vector norm can potentially reduce computational costs, and learn about the efficiency of first-order Trotter formula in discrete near adiabatic evolution operators. Gain insights into the poly-logarithmic scaling of complexity under certain conditions and understand the implications for quantum numerical linear algebra.

Introduction
Hamiltonian simulation
Highorder method
Arrow bounds
First application
Comparison
Numerical test
Adiabatic computing
Discrete evolution
Limitations