Two-Gate Extensions of Free Axis and Free Quaternion Selection for Sequential Optimization of Parameterized Quantum Circuits

Quantum Physics [Submitted on 26 Mar 2026] Two-Gate Extensions of Free Axis and Free Quaternion Selection for Sequential Optimization of Parameterized Quantum Circuits Joona V. Pankkonen We propose two-gate extensions of the sequential single-qubit optimizers, Free Axis Selection (Fraxis) and Free Quaternion Selection (FQS), termed Two-Gate Fraxis (TGF) and Two-Gate FQS (TGFQS), respectively. In contrast to Fraxis and FQS, which update one single-qubit gate at a time via quadratic local cost function and matrix diagonalization, TGF and TGFQS optimize two parameterized single-qubit gates simultaneously by constructing an exact quartic local cost function and optimizing it using classical optimizers. We further investigate how different gate pairing strategies affect optimization performance. Using numerical experiments on spin Hamiltonians, molecular Hamiltonians, and quantum state preparation tasks, we find that TGF and TGFQS frequently achieve a lower final relative error to the ground state energy or infidelity than their single gate counterparts. We observe that the random and half-shifted gate pairing strategies for TGF and TGFQS perform best in many of the tested settings. In the additional finite-shot experiments on Fermi-Hubbard and transverse-field Ising model Hamiltonians, the best gate pairing strategies retain their advantage across the tested shot counts in shallow circuits. These improvements come at the cost of increased circuit evaluations per gate update, highlighting a trade-off between the power of local optimization and measurement overhead. Comments: 17 pages, 11 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.25876 [quant-ph]   (or arXiv:2603.25876v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.25876 Focus to learn more Submission history From: Joona Pankkonen [view email] [v1] Thu, 26 Mar 2026 20:06:11 UTC (538 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)