Improved algorithms for learning quantum Hamiltonians, via flat polynomials
Abstract
We give an improved algorithm for learning a quantum Hamiltonian given copies of its Gibbs state, that can succeed at any temperature. Specifically, we improve over the work of Bakshi, Liu, Moitra, and Tang [BLMT24], by reducing the sample complexity and runtime dependence to singly exponential in the inverse-temperature parameter, as opposed to doubly exponential. Our main technical contribution is a new flat polynomial approximation to the exponential function, with significantly lower degree than the flat polynomial approximation used in [BLMT24].
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.04540
- arXiv:
- arXiv:2407.04540
- Bibcode:
- 2024arXiv240704540N
- Keywords:
-
- Quantum Physics;
- Computer Science - Data Structures and Algorithms;
- Computer Science - Machine Learning
- E-Print:
- 26 pages