Lindbladian Homotopy Analysis Method to Solve Nonlinear Partial Differential Equations

arXiv:2604.18924 · math.NA, cs.NA, quant-ph · Submitted 2026-04-21 · Read on arXiv

math.NA, cs.NA, quant-ph

Submitted: 2026-04-21

Updated: 2026-09-22

Comments: Keywords: quantum computing, homotopy analysis method, Lindblad master equation, nonlinear PDE

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Hilbert Space — 15× in this paper · explained in 2 episodes
• Unitary Dynamics — 7× in this paper · explained in 2 episodes
• Lindblad master equation — 6× in this paper · explained in 2 episodes
• Curse of Dimensionality — 4× in this paper · explained in 6 episodes
• Ancilla Qubits — 3× in this paper · explained in 1 episode
• Trace — 3× in this paper · explained in 2 episodes
• Magnetohydrodynamics (MHD) — 2× in this paper · explained in 3 episodes
• Post-Selection — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Ancillary Qubits — 1× in this paper · explained in 1 episode
• Lindblad Dynamics — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Query Complexity — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes

Sources

• Quantum algorithm for nonlinear differential equations
• Quantum algorithms for computing observables of nonlinear partial differential equations
• Quantum Homotopy Algorithm for Solving Nonlinear PDEs and Flow Problems
• A quantum algorithm to solve nonlinear differential equations
• Challenges for quantum computation of nonlinear dynamical systems using linear representations
• Hamiltonian Simulation Using Linear Combinations of Unitary Operations
• Quantum Simulation of Non-Unitary Dynamics via Amplitude-Phase Separation

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