An end-to-end quantum algorithm for nonlinear fluid dynamics with bounded quantum advantage

arXiv:2512.03758 · quant-ph, physics.flu-dyn · Submitted 2025-12-03 · Read on arXiv

quant-ph, physics.flu-dyn

Submitted: 2025-12-03

Updated: 2026-09-25

Comments: 57 pages, 9 figures. Published version

Journal ref: PRX Quantum 7, 033060 (2026)

DOI: 10.1103/xysy-q3fp

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

Terminology

• Boltzmann Equation — 30× in this paper · explained in 2 episodes
• Query Complexity — 19× in this paper · explained in 2 episodes
• Ancillary Qubits — 7× in this paper · explained in 1 episode
• Accuracy — 4× in this paper · explained in 1 episode
• Core — 3× in this paper · explained in 2 episodes
• Quantum Circuits — 3× in this paper · explained in 2 episodes
• Scaling Improvement — 2× in this paper · explained in 2 episodes
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 2 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes

Sources

• Randomized adiabatic quantum linear solver algorithm with optimal complexity scaling and detailed running costs
• Quantum Linear System Solvers: A Survey of Algorithms and Applications
• Toward end-to-end quantum simulation of rapidly distorted turbulence
• Explicit Error Bounds for Carleman Linearization
• Quantum algorithms for general nonlinear dynamics based on the Carleman embedding
• Potential quantum advantage for simulation of fluid dynamics
• Detailed assessment of calculating drag force with quantum computers: Explicit time-evolution precludes exponential advantage for nonlinear differential equations
• Practical Application of the Quantum Carleman Lattice Boltzmann Method in Industrial CFD Simulations
• Fast-forwarding quantum algorithms for linear dissipative differential equations
• Quantum sampling algorithms for quantum state preparation and matrix block-encoding
• Optimal ancilla-free Clifford+T approximation of z-rotations
• Synthesis of unitaries with Clifford+T circuits

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