Nearly tight Trotterization of interacting electrons
We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and prior knowledge of the initial state. We achieve this using Trot...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2021-07-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2021-07-05-495/pdf/ |
| _version_ | 1819081666116714496 |
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| author | Yuan Su Hsin-Yuan Huang Earl T. Campbell |
| author_facet | Yuan Su Hsin-Yuan Huang Earl T. Campbell |
| author_sort | Yuan Su |
| collection | DOAJ |
| description | We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and prior knowledge of the initial state. We achieve this using Trotterization for a class of interacting electrons that encompasses various physical systems, including the plane-wave-basis electronic structure and the Fermi-Hubbard model. We estimate the simulation error by taking the transition amplitude of nested commutators of the Hamiltonian terms within the $\eta$-electron manifold. We develop multiple techniques for bounding the transition amplitude and expectation of general fermionic operators, which may be of independent interest. We show that it suffices to use $\left(\frac{n^{5/3}}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right)n^{o(1)}$ gates to simulate electronic structure in the plane-wave basis with $n$ spin orbitals and $\eta$ electrons, improving the best previous result in second quantization up to a negligible factor while outperforming the first-quantized simulation when $n=\eta^{2-o(1)}$. We also obtain an improvement for simulating the Fermi-Hubbard model. We construct concrete examples for which our bounds are almost saturated, giving a nearly tight Trotterization of interacting electrons. |
| first_indexed | 2024-12-21T20:04:24Z |
| format | Article |
| id | doaj.art-44ec6480e0e54b3fb68943c392ea412e |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-21T20:04:24Z |
| publishDate | 2021-07-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-44ec6480e0e54b3fb68943c392ea412e2022-12-21T18:51:53ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2021-07-01549510.22331/q-2021-07-05-49510.22331/q-2021-07-05-495Nearly tight Trotterization of interacting electronsYuan SuHsin-Yuan HuangEarl T. CampbellWe consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and prior knowledge of the initial state. We achieve this using Trotterization for a class of interacting electrons that encompasses various physical systems, including the plane-wave-basis electronic structure and the Fermi-Hubbard model. We estimate the simulation error by taking the transition amplitude of nested commutators of the Hamiltonian terms within the $\eta$-electron manifold. We develop multiple techniques for bounding the transition amplitude and expectation of general fermionic operators, which may be of independent interest. We show that it suffices to use $\left(\frac{n^{5/3}}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right)n^{o(1)}$ gates to simulate electronic structure in the plane-wave basis with $n$ spin orbitals and $\eta$ electrons, improving the best previous result in second quantization up to a negligible factor while outperforming the first-quantized simulation when $n=\eta^{2-o(1)}$. We also obtain an improvement for simulating the Fermi-Hubbard model. We construct concrete examples for which our bounds are almost saturated, giving a nearly tight Trotterization of interacting electrons.https://quantum-journal.org/papers/q-2021-07-05-495/pdf/ |
| spellingShingle | Yuan Su Hsin-Yuan Huang Earl T. Campbell Nearly tight Trotterization of interacting electrons Quantum |
| title | Nearly tight Trotterization of interacting electrons |
| title_full | Nearly tight Trotterization of interacting electrons |
| title_fullStr | Nearly tight Trotterization of interacting electrons |
| title_full_unstemmed | Nearly tight Trotterization of interacting electrons |
| title_short | Nearly tight Trotterization of interacting electrons |
| title_sort | nearly tight trotterization of interacting electrons |
| url | https://quantum-journal.org/papers/q-2021-07-05-495/pdf/ |
| work_keys_str_mv | AT yuansu nearlytighttrotterizationofinteractingelectrons AT hsinyuanhuang nearlytighttrotterizationofinteractingelectrons AT earltcampbell nearlytighttrotterizationofinteractingelectrons |