Amplitude-Phase Separation toward Optimal and Fast-Forwardable Simulation of Non-Unitary Dynamics

• URL: http://arxiv.org/abs/2602.09575v1
• Date: Tue, 10 Feb 2026 09:23:55 GMT
• Title: Amplitude-Phase Separation toward Optimal and Fast-Forwardable Simulation of Non-Unitary Dynamics
• Authors: Qitong Hu, Shi Jin,
• Abstract summary: Amplitude-Phase Separation (APS) methods formulates any non-unitary evolution into separate simulation of a unitary operator and a Hermitian operator.<n>APS provides an effective and generic pathway for developing efficient quantum algorithms for general non-unitary dynamics.
• Score: 39.740772144144366
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum simulation of the linear non-unitary dynamics is crucial in scientific computing. In this work, we establish a generic framework, referred to as the Amplitude-Phase Separation (APS) methods, which formulates any non-unitary evolution into separate simulation of a unitary operator and a Hermitian operator, thus allow one to take best advantage of, and to even improve existing algorithms, developed for unitary or Hermitian evolution respectively. We utilize two techniques: the first achieves a provably optimal query complexity via a shifted Dyson series; the second breaks the conventional linear dependency, achieving fast-forwarding by exhibiting a square-root dependence on the norm of the dissipative part. Furthermore, one can derive existing methods such as the LCHS (Linear Combination of Hamiltonian Simulation) and the NDME (Non-Diagonal Density Matrix Encoding) methods from APS. The APS provides an effective and generic pathway for developing efficient quantum algorithms for general non-unitary dynamics to achieve either optimal query complexity or fast-forwarding property, outperforming the existing algorithms for the same problems.

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