Beating Grover search for low-energy estimation and state preparation

Autor(en)

Harry Buhrman, Sevag Gharibian, Zeph Landau, François Le Gall, Norbert Schuch, Suguru Tamaki

Abstrakt

Estimating ground state energies of many-body Hamiltonians is a central task in many areas of quantum physics. In this work, we give quantum algorithms which, given any $k$-body Hamiltonian $H$, compute an estimate for the ground state energy and prepare a quantum state achieving said energy, respectively. Specifically, for any $\varepsilon>0$, our algorithms return, with high probability, an estimate of the ground state energy of $H$ within additive error $\varepsilon M$, or a quantum state with the corresponding energy. Here, $M$ is the total strength of all interaction terms, which in general is extensive in the system size. Our approach makes no assumptions about the geometry or spatial locality of interaction terms of the input Hamiltonian and thus handles even long-range or all-to-all interactions, such as in quantum chemistry, where lattice-based techniques break down. In this fully general setting, the runtime of our algorithms scales as $2^{cn/2}$ for $c

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation, Institut für Mathematik

Externe Organisation(en)

Quantinuum, Qusoft – Research center for Quantum software & technology, Universität Paderborn, University of California, Berkeley, Nagoya University, University of Hyogo

Seiten

1-8

DOI

https://doi.org/10.48550/arXiv.2407.03073

Publikationsdatum

07-2024

ÖFOS 2012

101028 Mathematische Modellierung, 103025 Quantenmechanik, 103036 Theoretische Physik

Schlagwörter

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/0c3b5bb8-441b-4364-9700-b87a16965b85