Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum Algorithms
The Quantum Fisher Information Matrix (QFIM) plays a crucial role in quantum optimization algorithms such as Variational Quantum Imaginary Time Evolution and Quantum Natural Gradient Descent. However, computing the full QFIM incurs a quadratic computational cost of $O(d^2)$ with respect to the numbe...
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-07-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-07-21-1798/pdf/ |
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| author | Mourad Halla |
| author_facet | Mourad Halla |
| author_sort | Mourad Halla |
| collection | DOAJ |
| description | The Quantum Fisher Information Matrix (QFIM) plays a crucial role in quantum optimization algorithms such as Variational Quantum Imaginary Time Evolution and Quantum Natural Gradient Descent. However, computing the full QFIM incurs a quadratic computational cost of $O(d^2)$ with respect to the number of parameters $d$, limiting its scalability for high-dimensional quantum systems. To address this limitation, stochastic methods such as the Simultaneous Perturbation Stochastic Approximation (SPSA) have been employed to reduce computational complexity to a constant (Quantum 5, 567 (2021)). In this work, we propose an alternative estimation framework based on Stein's identity that also achieves constant computational complexity. Furthermore, our method reduces the quantum resources required for QFIM estimation compared to the SPSA approach. We provide numerical examples using the transverse-field Ising model and the lattice Schwinger model to demonstrate the feasibility of applying our method to realistic quantum systems. |
| format | Article |
| id | doaj-art-3d0fd8ed0f814913bb0c1cee061b742a |
| institution | Matheson Library |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-3d0fd8ed0f814913bb0c1cee061b742a2025-07-21T11:25:38ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-07-019179810.22331/q-2025-07-21-179810.22331/q-2025-07-21-1798Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum AlgorithmsMourad HallaThe Quantum Fisher Information Matrix (QFIM) plays a crucial role in quantum optimization algorithms such as Variational Quantum Imaginary Time Evolution and Quantum Natural Gradient Descent. However, computing the full QFIM incurs a quadratic computational cost of $O(d^2)$ with respect to the number of parameters $d$, limiting its scalability for high-dimensional quantum systems. To address this limitation, stochastic methods such as the Simultaneous Perturbation Stochastic Approximation (SPSA) have been employed to reduce computational complexity to a constant (Quantum 5, 567 (2021)). In this work, we propose an alternative estimation framework based on Stein's identity that also achieves constant computational complexity. Furthermore, our method reduces the quantum resources required for QFIM estimation compared to the SPSA approach. We provide numerical examples using the transverse-field Ising model and the lattice Schwinger model to demonstrate the feasibility of applying our method to realistic quantum systems.https://quantum-journal.org/papers/q-2025-07-21-1798/pdf/ |
| spellingShingle | Mourad Halla Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum Algorithms Quantum |
| title | Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum Algorithms |
| title_full | Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum Algorithms |
| title_fullStr | Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum Algorithms |
| title_full_unstemmed | Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum Algorithms |
| title_short | Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum Algorithms |
| title_sort | estimation of quantum fisher information via stein s identity in variational quantum algorithms |
| url | https://quantum-journal.org/papers/q-2025-07-21-1798/pdf/ |
| work_keys_str_mv | AT mouradhalla estimationofquantumfisherinformationviasteinsidentityinvariationalquantumalgorithms |