Exploring Entanglement and Parameter Sensitivity in QAOA through Quantum Fisher Information
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| Format: | Preprint |
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2025
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| _version_ | 1866910194934480896 |
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| author | Sarmina, Brian García Benavides, Jorge Saavedra Sun, Guo-Hua Dong, Shi-Hai |
| author_facet | Sarmina, Brian García Benavides, Jorge Saavedra Sun, Guo-Hua Dong, Shi-Hai |
| contents | Quantum Fisher Information (QFI) can be used to quantify how sensitive a quantum state reacts to changes in its variational parameters, making it a natural diagnostic for algorithms such as the Quantum Approximate Optimization Algorithm (QAOA). We perform a systematic QFI analysis of QAOA for Max-Cut on cyclic and complete graphs with $N = 4 - 10$ qubits. Two mixer families are studied, RX-only and hybrid RX-RY, with depths $p = 2, 4, 6$ and $p = 3, 6, 9$, respectively, and with up to three entanglement stages implemented through cyclic- or complete-entangling patterns. Complete graphs consistently yield larger QFI eigenvalues than cyclic graphs; none of the settings reaches the Heisenberg limit ($4N^2$), but several exceed the linear bound ($4N$). Introducing entanglement primarily redistributes QFI from diagonal to off-diagonal entries: non-entangled circuits maximize per-parameter (diagonal) sensitivity, whereas entangling layers increase the covariance fraction and thus cross-parameter correlations, with diminishing returns beyond the first stage. Leveraging these observations, we propose, as a proof of concept, a QFI-Informed Mutation (QIm) heuristic that sets mutation probabilities and step sizes from the normalized diagonal QFI. On 7- and 10-qubit instances, QIm attains higher mean energies and lower variance than equal-probability and random-restart baselines over 100 runs, underscoring QFI as a lightweight, problem-aware preconditioner for QAOA and other variational quantum algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_18844 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring Entanglement and Parameter Sensitivity in QAOA through Quantum Fisher Information Sarmina, Brian García Benavides, Jorge Saavedra Sun, Guo-Hua Dong, Shi-Hai Quantum Physics Emerging Technologies 81P68, 68Q09, 68Q12 I.m; H.m Quantum Fisher Information (QFI) can be used to quantify how sensitive a quantum state reacts to changes in its variational parameters, making it a natural diagnostic for algorithms such as the Quantum Approximate Optimization Algorithm (QAOA). We perform a systematic QFI analysis of QAOA for Max-Cut on cyclic and complete graphs with $N = 4 - 10$ qubits. Two mixer families are studied, RX-only and hybrid RX-RY, with depths $p = 2, 4, 6$ and $p = 3, 6, 9$, respectively, and with up to three entanglement stages implemented through cyclic- or complete-entangling patterns. Complete graphs consistently yield larger QFI eigenvalues than cyclic graphs; none of the settings reaches the Heisenberg limit ($4N^2$), but several exceed the linear bound ($4N$). Introducing entanglement primarily redistributes QFI from diagonal to off-diagonal entries: non-entangled circuits maximize per-parameter (diagonal) sensitivity, whereas entangling layers increase the covariance fraction and thus cross-parameter correlations, with diminishing returns beyond the first stage. Leveraging these observations, we propose, as a proof of concept, a QFI-Informed Mutation (QIm) heuristic that sets mutation probabilities and step sizes from the normalized diagonal QFI. On 7- and 10-qubit instances, QIm attains higher mean energies and lower variance than equal-probability and random-restart baselines over 100 runs, underscoring QFI as a lightweight, problem-aware preconditioner for QAOA and other variational quantum algorithms. |
| title | Exploring Entanglement and Parameter Sensitivity in QAOA through Quantum Fisher Information |
| topic | Quantum Physics Emerging Technologies 81P68, 68Q09, 68Q12 I.m; H.m |
| url | https://arxiv.org/abs/2507.18844 |