{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-generalized-circuit-for-the-hamiltonian","title":"A Generalized Circuit for the Hamiltonian Dynamics Through the Truncated Series","arxiv_id":"1801.09720","date":"2018-01-29","proceeding":null,"authors":["Ammar Daskin","Sabre Kais"],"abstract":"In this paper, we present a method for the Hamiltonian simulation in the\ncontext of eigenvalue estimation problems which improves earlier results\ndealing with Hamiltonian simulation through the truncated Taylor series. In\nparticular, we present a fixed-quantum circuit design for the simulation of the\nHamiltonian dynamics, $H(t)$, through the truncated Taylor series method\ndescribed by Berry et al. \\cite{berry2015simulating}. The circuit is general\nand can be used to simulate any given matrix in the phase estimation algorithm\nby only changing the angle values of the quantum gates implementing the time\nvariable $t$ in the series. The circuit complexity depends on the number of\nsummation terms composing the Hamiltonian and requires $O(Ln)$ number of\nquantum gates for the simulation of a molecular Hamiltonian. Here, $n$ is the\nnumber of states of a spin orbital, and $L$ is the number of terms in the\nmolecular Hamiltonian and generally bounded by $O(n^4)$. We also discuss how to\nuse the circuit in adaptive processes and eigenvalue related problems along\nwith a slight modified version of the iterative phase estimation algorithm. In\naddition, a simple divide and conquer method is presented for mapping a matrix\nwhich are not given as sums of unitary matrices into the circuit. The\ncomplexity of the circuit is directly related to the structure of the matrix\nand can be bounded by $O(poly(n))$ for a matrix with $poly(n)-$sparsity.","url_abs":"http://arxiv.org/abs/1801.09720v3","url_pdf":"http://arxiv.org/pdf/1801.09720v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-generalized-circuit-for-the-hamiltonian","repo_url":"https://github.com/adaskin/circuitforTaylorseries","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}