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.
High-order quantum algorithm for solving linear differential equations.Journal of Physics A: Mathe- matical and Theoretical, 47(10):105301, 2014
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Hybrid algorithm classically diagonalizes Hamiltonian tensor factors to construct block-encodings for quantum simulation via QSVD, with extensions for commuting time-dependent cases.
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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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Hybrid Quantum-Classical Algorithm for Hamiltonian Simulation
Hybrid algorithm classically diagonalizes Hamiltonian tensor factors to construct block-encodings for quantum simulation via QSVD, with extensions for commuting time-dependent cases.