Quantum Simulation of Non-unitary Dynamics via Contour-based Matrix Decomposition

• URL: http://arxiv.org/abs/2511.10267v1
• Date: Fri, 14 Nov 2025 01:42:24 GMT
• Title: Quantum Simulation of Non-unitary Dynamics via Contour-based Matrix Decomposition
• Authors: Chao Wang, Huan-Yu Liu, Cheng Xue, Xi-Ning Zhuang, Menghan Dou, Zhao-Yun Chen, Guo-Ping Guo,
• Abstract summary: We introduce contour-based matrix decomposition (CBMD), a framework for scalable simulation of non-unitary dynamics.<n>CBMD generalizes Cauchy's residue theorem to matrix-valued functions and directly decomposes a non-Hermitian function into a linear combination of Hermitian ones.
• Score: 6.538464633253838
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce contour-based matrix decomposition (CBMD), a framework for scalable simulation of non-unitary dynamics. Unlike existing methods that follow the ``integrate-then-discretize" paradigm and rely heavily on numerical quadrature, CBMD generalizes Cauchy's residue theorem to matrix-valued functions and directly decomposes a non-Hermitian function into a linear combination of Hermitian ones, which can be implemented efficiently using techniques such as quantum singular value transformation (QSVT). For non-Hermitian dynamics, CBMD achieves optimal query complexity. With an additional eigenvalue-shifting technique, the improved complexity depends on the spectral range of the system instead of its spectral norm. For more general dynamics that can be approximated by non-Hermitian polynomials, where algorithms like QSVT face significant difficulties, CBMD remains applicable and avoids the assumptions of diagonalizability as well as the dependence on condition numbers that limit other approaches.

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