A unifying framework for quantum algorithms for time-dependent non-unitary dynamics

arXiv:2608.07133 · quant-ph · Submitted 2026-08-07 · Read on arXiv

quant-ph

Submitted: 2026-08-07

Updated: 2026-09-21

Terminology

• Unitary Dynamics — 26× in this paper · explained in 2 episodes
• Query Complexity — 6× in this paper · explained in 2 episodes
• Ancilla Qubits — 2× in this paper · explained in 1 episode
• Embeddings — 2× in this paper · explained in 2 episodes
• Homogenization — 2× in this paper · explained in 2 episodes
• Quantum Circuits — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Block Encoding — 1× in this paper · explained in 4 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Initial Data — 1× in this paper · explained in 2 episodes
• Quantum Linear System Algorithm — 1× in this paper
• Regularization — 1× in this paper · explained in 3 episodes

Sources

• Hamiltonian Simulation in the Interaction Picture
• Quantum simulation of partial differential equations via Schrodingerisation
• Structure-preserving quantum algorithms for linear and nonlinear Hamiltonian systems
• Optimal quantum simulation of linear non-unitary dynamics
• Transmutation based Quantum Simulation for Non-unitary Dynamics
• From Linear Differential Equations to Unitaries: A Moment-Matching Dilation Framework with Near-Optimal Quantum Algorithms
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Lecture Notes on Quantum Algorithms for Scientific Computation

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