---
res:
bibo_abstract:
- "Estimating ground state energies of many-body Hamiltonians is a central task\r\nin
many areas of quantum physics. In this work, we give quantum algorithms\r\nwhich,
given any $k$-body Hamiltonian $H$, compute an estimate for the ground\r\nstate
energy and prepare a quantum state achieving said energy, respectively.\r\nSpecifically,
for any $\\varepsilon>0$, our algorithms return, with high\r\nprobability, an
estimate of the ground state energy of $H$ within additive\r\nerror $\\varepsilon
M$, or a quantum state with the corresponding energy. Here,\r\n$M$ is the total
strength of all interaction terms, which in general is\r\nextensive in the system
size. Our approach makes no assumptions about the\r\ngeometry or spatial locality
of interaction terms of the input Hamiltonian and\r\nthus handles even long-range
or all-to-all interactions, such as in quantum\r\nchemistry, where lattice-based
techniques break down. In this fully general\r\nsetting, the runtime of our algorithms
scales as $2^{cn/2}$ for $c<1$, yielding\r\nthe first quantum algorithms for low-energy
estimation breaking the natural\r\nbound based on Grover search. The core of our
approach is remarkably simple,\r\nand relies on showing that any $k$-body Hamiltonian
has a low-energy subspace\r\nof exponential dimension.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Harry
foaf_name: Buhrman, Harry
foaf_surname: Buhrman
- foaf_Person:
foaf_givenName: Sevag
foaf_name: Gharibian, Sevag
foaf_surname: Gharibian
foaf_workInfoHomepage: http://www.librecat.org/personId=71541
orcid: 0000-0002-9992-3379
- foaf_Person:
foaf_givenName: Zeph
foaf_name: Landau, Zeph
foaf_surname: Landau
- foaf_Person:
foaf_givenName: François Le
foaf_name: Gall, François Le
foaf_surname: Gall
- foaf_Person:
foaf_givenName: Norbert
foaf_name: Schuch, Norbert
foaf_surname: Schuch
- foaf_Person:
foaf_givenName: Suguru
foaf_name: Tamaki, Suguru
foaf_surname: Tamaki
dct_date: 2024^xs_gYear
dct_language: eng
dct_title: Beating Grover search for low-energy estimation and state preparation@
...