Quantum Simulation of Non-Unitary Dynamics via Amplitude-Phase Separation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866916031566446592 |
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| author | Hu, Qitong Jin, Shi |
| author_facet | Hu, Qitong Jin, Shi |
| contents | Linear non-unitary dynamics arise in open quantum systems, non-Hermitian models, and numerical evolution problems, yet current quantum algorithms do not cleanly separate coherent and dissipative effects at the design level. We introduce Amplitude-Phase Separation (APS), a decomposition framework with two complementary forms: phase-driven APS isolates the unitary component and maps the remainder to a Hermitian problem, whereas amplitude-driven APS extracts the Hermitian component and treats the remaining interaction separately. For time-independent dynamics, the two routes capture complementary advantages within one framework: phase-driven APS yields additive rather than multiplicative tolerance dependence, while amplitude-driven APS yields square-root dissipative scaling in multiscale regimes. APS also provides a unified interpretation of representative methods, including LCHS (Linear Combination of Hamiltonian Simulation) and NDME (Non-Diagonal Density Matrix Encoding), and clarifies where coherent and dissipative bottlenecks enter non-unitary simulation. The benchmarks confirm the predicted crossover between phase-driven and amplitude-driven advantages in advection-diffusion and Bloch-relaxation models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09575 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Simulation of Non-Unitary Dynamics via Amplitude-Phase Separation Hu, Qitong Jin, Shi Quantum Physics Mathematical Physics Linear non-unitary dynamics arise in open quantum systems, non-Hermitian models, and numerical evolution problems, yet current quantum algorithms do not cleanly separate coherent and dissipative effects at the design level. We introduce Amplitude-Phase Separation (APS), a decomposition framework with two complementary forms: phase-driven APS isolates the unitary component and maps the remainder to a Hermitian problem, whereas amplitude-driven APS extracts the Hermitian component and treats the remaining interaction separately. For time-independent dynamics, the two routes capture complementary advantages within one framework: phase-driven APS yields additive rather than multiplicative tolerance dependence, while amplitude-driven APS yields square-root dissipative scaling in multiscale regimes. APS also provides a unified interpretation of representative methods, including LCHS (Linear Combination of Hamiltonian Simulation) and NDME (Non-Diagonal Density Matrix Encoding), and clarifies where coherent and dissipative bottlenecks enter non-unitary simulation. The benchmarks confirm the predicted crossover between phase-driven and amplitude-driven advantages in advection-diffusion and Bloch-relaxation models. |
| title | Quantum Simulation of Non-Unitary Dynamics via Amplitude-Phase Separation |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2602.09575 |