{"citation":{"mla":"Buhrman, Harry, et al. “Beating Grover Search for Low-Energy Estimation and State Preparation.” <i>ArXiv:2407.03073</i>, 2024.","bibtex":"@article{Buhrman_Gharibian_Landau_Gall_Schuch_Tamaki_2024, title={Beating Grover search for low-energy estimation and state preparation}, journal={arXiv:2407.03073}, author={Buhrman, Harry and Gharibian, Sevag and Landau, Zeph and Gall, François Le and Schuch, Norbert and Tamaki, Suguru}, year={2024} }","chicago":"Buhrman, Harry, Sevag Gharibian, Zeph Landau, François Le Gall, Norbert Schuch, and Suguru Tamaki. “Beating Grover Search for Low-Energy Estimation and State Preparation.” <i>ArXiv:2407.03073</i>, 2024.","ama":"Buhrman H, Gharibian S, Landau Z, Gall FL, Schuch N, Tamaki S. Beating Grover search for low-energy estimation and state preparation. <i>arXiv:240703073</i>. Published online 2024.","apa":"Buhrman, H., Gharibian, S., Landau, Z., Gall, F. L., Schuch, N., &#38; Tamaki, S. (2024). Beating Grover search for low-energy estimation and state preparation. In <i>arXiv:2407.03073</i>.","ieee":"H. Buhrman, S. Gharibian, Z. Landau, F. L. Gall, N. Schuch, and S. Tamaki, “Beating Grover search for low-energy estimation and state preparation,” <i>arXiv:2407.03073</i>. 2024.","short":"H. Buhrman, S. Gharibian, Z. Landau, F.L. Gall, N. Schuch, S. Tamaki, ArXiv:2407.03073 (2024)."},"title":"Beating Grover search for low-energy estimation and state preparation","user_id":"71541","date_created":"2024-07-04T09:02:42Z","publication":"arXiv:2407.03073","abstract":[{"lang":"eng","text":"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."}],"year":"2024","status":"public","type":"preprint","_id":"55037","external_id":{"arxiv":["2407.03073"]},"author":[{"full_name":"Buhrman, Harry","first_name":"Harry","last_name":"Buhrman"},{"orcid":"0000-0002-9992-3379","full_name":"Gharibian, Sevag","last_name":"Gharibian","first_name":"Sevag","id":"71541"},{"full_name":"Landau, Zeph","first_name":"Zeph","last_name":"Landau"},{"first_name":"François Le","last_name":"Gall","full_name":"Gall, François Le"},{"full_name":"Schuch, Norbert","first_name":"Norbert","last_name":"Schuch"},{"last_name":"Tamaki","first_name":"Suguru","full_name":"Tamaki, Suguru"}],"date_updated":"2024-07-04T09:03:23Z","language":[{"iso":"eng"}]}