A QSVT-Based Quantum Jacobi Algorithm for Linear Systems with Application to the Poisson Equation

arXiv:2609.24266 · quant-ph · Submitted 2026-09-21 · Read on arXiv

quant-ph

Submitted: 2026-09-21

Updated: 2026-09-21

Terminology

• Block Encoding — 46× in this paper · explained in 4 episodes
• Ancilla Qubits — 14× in this paper · explained in 1 episode
• Quantum Circuits — 9× in this paper · explained in 2 episodes
• Quantum Singular Value Transformation — 7× in this paper
• Quantum Singular Value Transformation (QSVT) — 4× in this paper · explained in 4 episodes
• Benchmark — 3× in this paper · explained in 2 episodes
• Quantum Eigenvalue Transformation — 3× in this paper
• Ancillary Qubits — 2× in this paper · explained in 1 episode
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Quantum Physics — 2× in this paper · explained in 10 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Latent Space — 1× in this paper · explained in 7 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Quantum Eigen-Value Transformation — 1× in this paper
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes

Sources

• Physics-Informed Quantum Machine Learning: Solving nonlinear differential equations in latent spaces without costly grid evaluations
• Quantum Linear System Solvers: A Survey of Algorithms and Applications
• Variable time amplitude amplification and a faster quantum algorithm for solving systems of linear equations
• A shortcut to an optimal quantum linear system solver
• Evaluation of block encoding for sparse matrix inversion using QSVT
• Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian
• Explicit Block Encodings of Discrete Laplacians with Mixed Boundary Conditions
• Finding Angles for Quantum Signal Processing with Machine Precision
• Lecture Notes on Quantum Algorithms for Scientific Computation
• PennyLane: Automatic differentiation of hybrid quantum-classical computations
• A Hybrid Quantum-Classical CFD Methodology with Benchmark HHL Solutions
• Practical block encodings of matrix polynomials that can also be trivially controlled
• Quantum Eigenvalue Transformations for Arbitrary Matrices

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