Classical algorithm approximates fermionic energies beyond gaussian states
Improved classical optimization of fermionic Hamiltonians beyond Gaussian states
Data Structures and Algorithms
Summary
Finding the largest energy of complicated quantum particles called fermions is very hard. The authors created a classical algorithm that quickly finds a pretty good estimate of this largest energy for certain fermion systems. Their method either outputs a special kind of simple state called a Gaussian state or a state described with a small number of basic building blocks. This helps better understand fermionic systems using classical computers without needing quantum machines.
What this means in practice
- •For quantum software developers: Estimate energies of fermion systems efficiently on classical hardware to aid quantum algorithm design and testing.
- •For condensed matter simulation teams: Provide classical approximations of fermionic system energies to support simulation of materials without quantum resources.
Authors
Ojas Parekh
Abstract
We give a polynomial-time randomized classical algorithm that approximates the largest eigenvalue $λ_{\max}$ of a traceless quartic fermionic Hamiltonian $H$ on $n$ modes. The algorithm achieves energy at least $λ_{\max}/O(\sqrt n)$ and outputs either a fermionic Gaussian state or a polynomially sparse state in the Fock basis. This is achieved through a new upper bound on $λ_{\max}$ in terms of the maximum energy of a Gaussian state and $\sqrt{2^{-n}\operatorname{Tr}(H^2)}$.