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

Explore a 33-minute lecture on Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers, presented by Yu Tong from the University of California, Berkeley. Delve into an alternative method to quantum phase estimation (QPE) that achieves Heisenberg-limited precision scaling using a simple quantum circuit with one ancilla qubit and classical post-processing. Discover how this approach not only estimates ground state energy but also produces an approximate cumulative distribution function of the spectral measure. Learn about the algorithm's components, including simplified circuits, random evolution time, and Fourier approximation. Compare this method to traditional QPE and examine its potential for quantum chemistry applications. Gain insights into observables, unbiased time evolution, and the control-free version of the algorithm.

Intro
Useful quantum advantage for quantum chemistry
Assumption: a good initial guess
Hardness with a good initial guess
Three goals of our work
A simplified circuit
Introducing additional randomness
Random evolution time
The cumulative distribution function
The CDF: the numerical result
Summary of the algorithm
Ground state energy estimation
Comparison with QPE
Fourier approximation
The control-free version
Observables and unbiased time evolution
Conclusions