Andrew Eddins, Tanvi Gujarati, et al.
APS March Meeting 2021
We discuss classical algorithms for approximating the largest eigenvalue of quantum spin and fermionic Hamiltonians based on semidefinite programming relaxation methods. First, we consider traceless 2-local Hamiltonians H describing a system of n qubits. We give an efficient algorithm that outputs a separable state whose energy is at least λ max /O(log n), where λ max is the maximum eigenvalue of H. We also give a simplified proof of a theorem due to Lieb that establishes the existence of a separable state with energy at least λ max /9. Second, we consider a system of n fermionic modes and traceless Hamiltonians composed of quadratic and quartic fermionic operators. We give an efficient algorithm that outputs a fermionic Gaussian state whose energy is at least λ max /O(n log n). Finally, we show that Gaussian states can vastly outperform Slater determinant states commonly used in the Hartree-Fock method. We give a simple family of Hamiltonians for which Gaussian states and Slater determinants approximate λ max within a fraction 1 − O(n −1 ) and O(n −1 ), respectively.
Andrew Eddins, Tanvi Gujarati, et al.
APS March Meeting 2021
Sergey Bravyi, Robert König
Commun. Math. Phys.
Sergey Bravyi, Anirban Chowdhury, et al.
QIP 2022
Sergey Bravyi, David Gosset, et al.
STOC 2024