36. Learning quantum Hamiltonians at any temperature in polynomial time with Chebyshev and bit complexity
Invited abstract in session TB-6: Advances in Semi-Definite Programming, stream Challenges in nonlinear programming.
Thursday, 10:05 - 11:20Room: M:H
Authors (first author is the speaker)
| 1. | Ales Wodecki
|
| Computer science, Czech Technical University in Prague | |
| 2. | Jakub Marecek
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| Dept. of Computer Science, Czech Technical University |
Abstract
We consider the problem of learning local quantum Hamiltonians given copies of their Gibbs state at a known inverse temperature, following Haah et al. [2108.04842] and Bakshi et al. [arXiv:2310.02243]. Our main technical contribution is a new flat polynomial approximation of the exponential function based on the Chebyshev expansion, which enables the formulation of learning quantum Hamiltonians as a polynomial optimization problem. This, in turn, can benefit from the use of moment/SOS relaxations, whose polynomial bit complexity requires careful analysis [O'Donnell, ITCS 2017]. Finally, we show that learning a k-local Hamiltonian, whose dual interaction graph is of bounded degree, runs in polynomial time under mild assumptions.
Keywords
- Conic and semidefinite optimization
- SS - Semidefinite Optimization
Status: accepted
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