Sign-embedding quantum algorithms deliver explicit block-encodings for Sylvester equations and related matrix problems with query complexity linear in inverse-conditioning parameters and logarithmic in error tolerance.
Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost
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abstract
We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving non-unitary processes, such as the quantum singular value transformation (QSVT). The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.
fields
quant-ph 2years
2026 2representative citing papers
A regularized function inserted into Carleman linearization, derived from a Möbius conformal map, removes the long-time divergence for logistic, KPP-Fisher, and phase-field models and supports an LCU quantum implementation.
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Sign Embedding Quantum Algorithms for Matrix Equations and Matrix Functions
Sign-embedding quantum algorithms deliver explicit block-encodings for Sylvester equations and related matrix problems with query complexity linear in inverse-conditioning parameters and logarithmic in error tolerance.
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Fixing Divergence in Carleman Linearization via Analytical Continuation
A regularized function inserted into Carleman linearization, derived from a Möbius conformal map, removes the long-time divergence for logistic, KPP-Fisher, and phase-field models and supports an LCU quantum implementation.