Toward Efficient End-to-End Quantum Elliptic PDE Solvers: a Multilevel Correction Algorithm for Direct Observable Estimation

arXiv:2606.01270 · quant-ph · Submitted 2026-05-31 · Read on arXiv

quant-ph

Submitted: 2026-05-31

Updated: 2026-09-22

Terminology

• Block Encoding — 34× in this paper · explained in 4 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Heisenberg Scaling — 4× in this paper · explained in 4 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Unitary Dynamics — 2× in this paper · explained in 2 episodes
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Consistency — 1× in this paper · explained in 3 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes

Sources

• A Quantum Spectral Framework for Solving PDEs
• A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners
• Circuit-Efficient Randomized Quantum Simulation of Non-Unitary Dynamics with Observable-Driven and Symmetry-Aware Designs
• Schr\"odingerization for quantum linear systems problems with near-optimal dependence on matrix queries

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