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.
Globalizing the carleman linear embedding method for nonlinear dynamics,
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The reduced basis algorithm exactly reproduces the nonlinear dynamics of polynomial ODEs and PDEs over m timesteps using a linear quantum operator on a reduced monomial basis, with qubit scaling logarithmic in grid size for PDEs.
Pivot-shifted Carleman linearization with Lyapunov transform enables logarithmic truncation and removes initial-condition lower bounds for quantum simulation of a broader class of nonlinear ODEs.
Quantum Koopman Algorithms define an observable-space quantum framework for simulating linear quantum and nonlinear classical dynamics with polylog gate costs in some cases.
Duplicate-aware shift-and-lift Carleman linearization with moving centers reduces monomial duplication overhead and improves local validity along trajectories compared to standard Jacobian linearization on bilinear and logistic benchmarks.
citing papers explorer
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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.
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Reduced basis algorithm for solving nonlinear differential equations on quantum computers
The reduced basis algorithm exactly reproduces the nonlinear dynamics of polynomial ODEs and PDEs over m timesteps using a linear quantum operator on a reduced monomial basis, with qubit scaling logarithmic in grid size for PDEs.
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Quantum Algorithms for Nonlinear Differential Equations via Pivot-Shifted Carleman Linearization
Pivot-shifted Carleman linearization with Lyapunov transform enables logarithmic truncation and removes initial-condition lower bounds for quantum simulation of a broader class of nonlinear ODEs.
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Quantum Koopman Algorithms
Quantum Koopman Algorithms define an observable-space quantum framework for simulating linear quantum and nonlinear classical dynamics with polylog gate costs in some cases.
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Duplicate-Aware Shift-and-Lift Carleman Linearization:Structure, Complexity, and Comparative Evaluation
Duplicate-aware shift-and-lift Carleman linearization with moving centers reduces monomial duplication overhead and improves local validity along trajectories compared to standard Jacobian linearization on bilinear and logistic benchmarks.