Contour-integral and Fourier transform based multivariable quantum eigenvalue transformation for commuting matrices

arXiv:2609.32262 · quant-ph, cs.NA, math.NA · Submitted 2026-09-26 · Read on arXiv

quant-ph, cs.NA, math.NA

Submitted: 2026-09-26

Updated: 2026-10-03

Terminology

• Ancilla Qubits — 25× in this paper · explained in 1 episode
• Block Encoding — 21× in this paper · explained in 4 episodes
• Query Complexity — 8× in this paper · explained in 2 episodes
• Quantum Singular Value Transformation — 5× in this paper
• Chebyshev Polynomials — 2× in this paper · explained in 2 episodes
• Quantum Singular Value Transformation (QSVT) — 2× in this paper · explained in 4 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Entanglement — 1× in this paper · explained in 4 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 2 episodes

Sources

• Creating superpositions that correspond to efficiently integrable probability distributions
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Divided Differences and Multivariate Holomorphic Calculus
• Contour-integral based quantum eigenvalue transformation: analysis and applications
• On variants of multivariate quantum signal processing and their characterizations
• A Unified Poisson Summation Framework for Generalized Quantum Matrix Transformations

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