Exploring Entanglement and Parameter Sensitivity in QAOA through Quantum Fisher Information

• URL: http://arxiv.org/abs/2507.18844v1
• Date: Thu, 24 Jul 2025 22:59:53 GMT
• Title: Exploring Entanglement and Parameter Sensitivity in QAOA through Quantum Fisher Information
• Authors: Brian García Sarmina, Jorge Saavedra Benavides, Guo-Hua Sun, Shi-Hai Dong,
• Abstract summary: Quantum Fisher Information (QFI) can be used to quantify how sensitive a quantum state reacts to changes in its variational parameters.<n>We propose a QFI-Informed Mutation (QIm) that sets mutation probabilities and step sizes from the normalized diagonal QFI.<n>On 7- and 10-qubit instances, QIm attains higher mean and lower variance than equal-probability and random-restart baselines over 100 runs.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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