Sign Embedding Quantum Algorithms for Matrix Equations and Matrix Functions

arXiv:2604.25333 · quant-ph, cs.NA, math.NA · Submitted 2026-04-28 · Read on arXiv

quant-ph, cs.NA, math.NA

Submitted: 2026-04-28

Updated: 2026-09-21

Comments: 81 pages, 3 figures, 6 tables

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

Terminology

• Query Complexity — 25× in this paper · explained in 2 episodes
• Embeddings — 8× in this paper · explained in 2 episodes
• Quantum Singular Value Transformation — 4× in this paper
• Unitary Dynamics — 3× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Quantum Singular Value Transformation (QSVT) — 2× in this paper · explained in 4 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Linear Combination of Unitaries — 1× in this paper

Sources

• Quantum algorithm for linear matrix equations
• Quantum linear systems algorithms: a primer
• A Unified Poisson Summation Framework for Generalized Quantum Matrix Transformations
• The Akhiezer iteration and inverse-free solvers for Sylvester matrix equations
• Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost
• Quantum Estimation of Non-Hermitian Pseudospectra
• AI Mathematician: Towards Fully Automated Frontier Mathematical Research

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