Shock-Capturing Quantum Algorithm for the Linear Advection Operator

arXiv:2609.21153 · quant-ph · Submitted 2026-09-17 · Read on arXiv

quant-ph

Submitted: 2026-09-17

Updated: 2026-09-17

Comments: 24 pages, 8 figures, work presented at the 2025 APS Four Corners Meeting

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

Terminology

• Quantum Fourier Transform — 7× in this paper
• Ancilla Qubits — 4× in this paper · explained in 1 episode
• Quantum Circuits — 4× in this paper · explained in 2 episodes
• Block Encoding — 2× in this paper · explained in 4 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Ordinary Differential Equations (ODEs) — 1× in this paper · explained in 2 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes

Sources

• Second quantization of nonlinear Vlasov-Poisson system for quantum computation
• An approximate Fourier transform useful in quantum factoring
• Decomposition of Multi-controlled Special Unitary Single-Qubit Gates

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