Quantum Circuits for partial differential equations via Schrödingerisation
Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian simulation, which is directly applicable only to Schrödinger-type equ...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2024-12-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2024-12-12-1563/pdf/ |
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| _version_ | 1850061142090579968 |
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| author | Junpeng Hu Shi Jin Nana Liu Lei Zhang |
| author_facet | Junpeng Hu Shi Jin Nana Liu Lei Zhang |
| author_sort | Junpeng Hu |
| collection | DOAJ |
| description | Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian simulation, which is directly applicable only to Schrödinger-type equations. To address this limitation, Schrödingerisation techniques have been developed, employing the warped transformation to convert general linear PDEs into Schrödinger-type equations. However, despite the development of Schrödingerisation techniques, the explicit implementation of the corresponding quantum circuit for solving general PDEs remains to be designed. In this paper, we present detailed implementation of a quantum algorithm for general PDEs using Schrödingerisation techniques. We provide examples of the heat equation, and the advection equation approximated by the upwind scheme, to demonstrate the effectiveness of our approach. Complexity analysis is also carried out to demonstrate the quantum advantages of these algorithms in high dimensions over their classical counterparts. |
| format | Article |
| id | doaj-art-bec3fec9cb4f43cb8924a40e29a200b6 |
| institution | DOAJ |
| issn | 2521-327X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-bec3fec9cb4f43cb8924a40e29a200b62025-08-20T02:50:20ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-12-018156310.22331/q-2024-12-12-156310.22331/q-2024-12-12-1563Quantum Circuits for partial differential equations via SchrödingerisationJunpeng HuShi JinNana LiuLei ZhangQuantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian simulation, which is directly applicable only to Schrödinger-type equations. To address this limitation, Schrödingerisation techniques have been developed, employing the warped transformation to convert general linear PDEs into Schrödinger-type equations. However, despite the development of Schrödingerisation techniques, the explicit implementation of the corresponding quantum circuit for solving general PDEs remains to be designed. In this paper, we present detailed implementation of a quantum algorithm for general PDEs using Schrödingerisation techniques. We provide examples of the heat equation, and the advection equation approximated by the upwind scheme, to demonstrate the effectiveness of our approach. Complexity analysis is also carried out to demonstrate the quantum advantages of these algorithms in high dimensions over their classical counterparts.https://quantum-journal.org/papers/q-2024-12-12-1563/pdf/ |
| spellingShingle | Junpeng Hu Shi Jin Nana Liu Lei Zhang Quantum Circuits for partial differential equations via Schrödingerisation Quantum |
| title | Quantum Circuits for partial differential equations via Schrödingerisation |
| title_full | Quantum Circuits for partial differential equations via Schrödingerisation |
| title_fullStr | Quantum Circuits for partial differential equations via Schrödingerisation |
| title_full_unstemmed | Quantum Circuits for partial differential equations via Schrödingerisation |
| title_short | Quantum Circuits for partial differential equations via Schrödingerisation |
| title_sort | quantum circuits for partial differential equations via schrodingerisation |
| url | https://quantum-journal.org/papers/q-2024-12-12-1563/pdf/ |
| work_keys_str_mv | AT junpenghu quantumcircuitsforpartialdifferentialequationsviaschrodingerisation AT shijin quantumcircuitsforpartialdifferentialequationsviaschrodingerisation AT nanaliu quantumcircuitsforpartialdifferentialequationsviaschrodingerisation AT leizhang quantumcircuitsforpartialdifferentialequationsviaschrodingerisation |