Quantum Complexity of Ancilla-Free Unitary Embeddings for Nonlinear Dynamics via Generalized State-Dependent Double-Bracket Flows

arXiv:2609.37802 · quant-ph · Submitted 2026-09-29 · Read on arXiv

quant-ph

Submitted: 2026-09-29

Updated: 2026-09-29

Terminology

• Query Complexity — 33× in this paper · explained in 2 episodes
• Accuracy — 31× in this paper · explained in 1 episode
• Trace — 29× in this paper · explained in 2 episodes
• Embeddings — 6× in this paper · explained in 2 episodes
• Ancilla Qubits — 4× in this paper · explained in 1 episode
• Unitary Dynamics — 4× in this paper · explained in 2 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes

Sources

• A quantum algorithm to solve nonlinear differential equations
• Quantum algorithm for nonlinear differential equations
• On the Schr\"odingerization method for linear non-unitary dynamics with optimal dependence on matrix queries
• Optimal quantum simulation of linear non-unitary dynamics
• Quantum algorithms for general nonlinear dynamics based on the Carleman embedding
• Quantum Algorithms for Nonlinear Differential Equations via Pivot-Shifted Carleman Linearization
• Geometric Optimization Methods for Adaptive Filtering
• On Lieb-Robinson Bounds for the Double Bracket Flow
• Double-bracket quantum algorithms for thermal state preparation
• Grover's algorithm is an approximation of imaginary-time evolution

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