Breaking the Curse of Dimensionality in Quantum PDE Solvers via Gevrey Regularity

arXiv:2608.07893 · quant-ph, cs.NA, math.NA · Submitted 2026-08-08 · Read on arXiv

quant-ph, cs.NA, math.NA

Submitted: 2026-08-08

Updated: 2026-09-25

Terminology

• Block Encoding — 26× in this paper · explained in 4 episodes
• Accuracy — 10× in this paper · explained in 1 episode
• Curse of Dimensionality — 6× in this paper · explained in 6 episodes
• Quantization — 6× in this paper · explained in 12 episodes
• Query Complexity — 5× in this paper · explained in 2 episodes
• Ancilla Qubits — 3× in this paper · explained in 1 episode
• Boltzmann Equation — 2× in this paper · explained in 2 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Core — 2× in this paper · explained in 2 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Self-consistency — 2× in this paper · explained in 2 episodes
• Ab Initio — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Adiabatic Evolution — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Metastability — 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
• Spectral Gap — 1× in this paper · explained in 5 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• The Need for Structure in Quantum Speedups
• Quantum Implications of Huang's Sensitivity Theorem
• A new quantum ripple-carry addition circuit
• A note on the quantum query complexity of permutation symmetric functions
• A shortcut to an optimal quantum linear system solver
• A comprehensive framework to simulate real-time chemical dynamics on a fault-tolerant quantum computer
• Cut-off Jastrow Factors and Spectral Barron Regularity of Coulombic Electronic Wave Functions
• Fast Solution of the Linearized Poisson-Boltzmann Equation with nonaffine Parametrized Boundary Conditions Using the Reduced Basis Method
• Operator-Level Quantum Acceleration of Non-Logconcave Sampling
• A quantum algorithm to solve nonlinear differential equations
• Efficient Simulation of Pre-Born-Oppenheimer Dynamics on a Quantum Computer
• Asymptotically Optimal Quantum Circuits for Comparators and Incrementers

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