Efficient Non-Uniform Quantum Hermite Transform through Adaptive Sampling

arXiv:2609.20739 · quant-ph, cs.DC, cs.ET · Submitted 2026-09-17 · Read on arXiv

quant-ph, cs.DC, cs.ET

Submitted: 2026-09-17

Updated: 2026-10-05

Terminology

• Embeddings — 6× in this paper · explained in 2 episodes
• Accuracy — 3× in this paper · explained in 1 episode
• Adaptive Sampling — 3× in this paper · explained in 1 episode
• Trace — 2× in this paper · explained in 2 episodes
• Alignment — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Block Encoding — 1× in this paper · explained in 4 episodes
• Calibration — 1× in this paper · explained in 7 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Error Decomposition — 1× in this paper · explained in 3 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes

Sources

• Performance and structure of single-mode bosonic codes
• Quantum Amplitude Amplification and Estimation
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Efficient Quantum Hermite Transform
• Wavefunction preparation and resampling using a quantum computer
• Quantum Discrete Variable Representations
• Optimal ancilla-free Clifford+T approximation of z-rotations
• Stable Hermite transforms via the Golub-Welsch algorithm

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