Improved algorithms for learning quantum Hamiltonians, via flat polynomials
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].
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Learning quantum Hamiltonians at any temperature in polynomial time with Chebyshev and bit complexity
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…
Learning quantum Hamiltonians at any temperature in polynomial time
We study the problem of learning a local quantum Hamiltonian $H$ given copies of its Gibbs state $\rho = e^{-\beta H}/\textrm{tr}(e^{-\beta H})$ at a known inverse temperature $\beta>0$. Anshu, Arunachalam, Kuwahara, and…
Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations
Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track st…
Meta-learning of Gibbs states for many-body Hamiltonians with applications to Quantum Boltzmann Machines
The preparation of quantum Gibbs states is a fundamental challenge in quantum computing, essential for applications ranging from modeling open quantum systems to quantum machine learning. Building on the Meta-Variational…
Quantum Machine LearningExponentially improved efficient machine learning for quantum many-body states with provable guarantees
Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical para…