# Improved Hardness Results for the Guided Local Hamiltonian Problem

@article{Gharibian2022ImprovedHR, title={Improved Hardness Results for the Guided Local Hamiltonian Problem}, author={Sevag Gharibian and Ryunosuke Hayakawa and Franccois Le Gall and Tomoyuki Morimae}, journal={ArXiv}, year={2022}, volume={abs/2207.10250} }

Estimating the ground state energy of a local Hamiltonian is a central problem in quantum chemistry. In order to further investigate its complexity and the potential of quantum algorithms for quantum chemistry, Gharibian and Le Gall (STOC 2022) recently introduced the guided local Hamiltonian problem (GLH) , which is a variant of the local Hamiltonian problem where an approximation of a ground state (which is called a guiding state) is given as an additional input. Gharibian and Le Gall showed…

## 4 Citations

### Complexity of the Guided Local Hamiltonian Problem: Improved Parameters and Extension to Excited States

- ChemistryArXiv
- 2022

Recently it was shown that the so-called guided local Hamiltonian problem – estimating the smallest eigenvalue of a k -local Hamiltonian when provided with a description of a quantum state (‘guiding…

### Parameterized Complexity of Weighted Local Hamiltonian Problems and the Quantum Exponential Time Hypothesis

- PhysicsArXiv
- 2022

We study a parameterized version of the local Hamiltonian problem, called the weighted local Hamiltonian problem, where the relevant quantum states are superpositions of computational basis states of…

### Spectral estimation for Hamiltonians: a comparison between classical imaginary-time evolution and quantum real-time evolution

- PhysicsNew Journal of Physics
- 2022

We consider the task of spectral estimation of local quantum Hamiltonians. The spectral estimation is performed by estimating the oscillation frequencies or decay rates of signals representing the…

### Generating Approximate Ground States of Molecules Using Quantum Machine Learning

- Computer Science
- 2022

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