Year: 2023
Type: article
Abstract: We consider the problem of approximating the ground state energy of a fermionic Hamiltonian using a Gaussian state. In sharp contrast to the dense case [1, 2], we prove that strictly q -local sparse fermionic Hamiltonians have a constant Gaussian approximation ratio; the result holds for any connectivity and interaction strengths. Sparsity means that each fermion participates in a bounded number of interactions, and strictly q -local means that each term involves exactly q fermionic (Majorana) operators. We extend our proof to give a constant Gaussian approximation ratio for sparse fermionic Hamiltonians with both quartic and quadratic terms. With additional work, we also prove a constant Gaussian approximation ratio for the so-called sparse SYK model with strictly 4 -local interactions (sparse SYK- 4 model). In each setting we show that the Gaussian state can be efficiently determined. Finally, we prove that the O(n−1/2) Gaussian approximation ratio for the normal (dense) SYK- 4 model extends to SYK- q for even q>4 , with an approximation ratio of O(n1/2–q/4) . Our results identify non-sparseness as the prime reason that the SYK- 4 model can fail to have a constant approximation ratio [1, 2].
Source: Quantum
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $215
OpenAlex ID: W4385719952