Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/3/624 |
| _version_ | 1797441502344904704 |
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| author | Alessandro Carbone Davide Emilio Galli Mario Motta Barbara Jones |
| author_facet | Alessandro Carbone Davide Emilio Galli Mario Motta Barbara Jones |
| author_sort | Alessandro Carbone |
| collection | DOAJ |
| description | The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity. |
| first_indexed | 2024-03-09T12:24:00Z |
| format | Article |
| id | doaj.art-ad0df2dbee714ca6b941b5d1e1df623c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T12:24:00Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ad0df2dbee714ca6b941b5d1e1df623c2023-11-30T22:37:12ZengMDPI AGSymmetry2073-89942022-03-0114362410.3390/sym14030624Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum ComputersAlessandro Carbone0Davide Emilio Galli1Mario Motta2Barbara Jones3Theory and Simulation of Materials (THEOS), National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, SwitzerlandDipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, ItalyIBM Quantum, IBM Research Almaden, 650 Harry Road, San Jose, CA 95120, USAIBM Quantum, IBM Research Almaden, 650 Harry Road, San Jose, CA 95120, USAThe application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.https://www.mdpi.com/2073-8994/14/3/624quantum computingspin liquidseigenstatesquantum error mitigation |
| spellingShingle | Alessandro Carbone Davide Emilio Galli Mario Motta Barbara Jones Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers Symmetry quantum computing spin liquids eigenstates quantum error mitigation |
| title | Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers |
| title_full | Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers |
| title_fullStr | Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers |
| title_full_unstemmed | Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers |
| title_short | Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers |
| title_sort | quantum circuits for the preparation of spin eigenfunctions on quantum computers |
| topic | quantum computing spin liquids eigenstates quantum error mitigation |
| url | https://www.mdpi.com/2073-8994/14/3/624 |
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