Conditioning-Free Non-Uniform Quantum Fourier and Chebyshev Transforms

arXiv:2609.40277 · quant-ph, cs.DS · Submitted 2026-09-30 · Read on arXiv

quant-ph, cs.DS

Submitted: 2026-09-30

Updated: 2026-10-06

Terminology

• Block Encoding — 29× in this paper · explained in 4 episodes
• Sparsity — 7× in this paper · explained in 4 episodes
• Chebyshev Polynomials — 5× in this paper · explained in 2 episodes
• Non-uniform Quantum Fourier Transform — 5× in this paper
• Accuracy — 3× in this paper · explained in 1 episode
• Quantum Circuits — 3× in this paper · explained in 2 episodes
• Frequency Dependence — 1× in this paper · explained in 2 episodes

Sources

• Non-Uniform Quantum Fourier Transform
• Quantum CORDIC -- Arcsine on a Budget
• Quantum Amplitude Amplification and Estimation
• Hamiltonian Simulation Using Linear Combinations of Unitary Operations
• Creating superpositions that correspond to efficiently integrable probability distributions
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Optimizing Quantum Circuits for Arithmetic
• Discrete Cosine Transforms on Quantum Computers
• Transformation of quantum states using uniformly controlled rotations
• Optimal ancilla-free Clifford+T approximation of z-rotations
• Quantum Chebyshev Transform: Mapping, Embedding, Learning and Sampling Distributions

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