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Quantum Algorithms
Efficient Non-Uniform Quantum Hermite Transform through Adaptive Sampling
arXiv
Authors: Nitay Mayo, Aryeh Lev Zabokritskiy
Year
2026
Paper ID
78424
Status
Preprint
Abstract Read
~2 min
Abstract Words
83
Citations
N/A
Abstract
On the span of the first N oscillator modes, Gauss--Hermite quadrature gives an exact change of basis between mode coefficients and N weighted position space samples. We implement this transform with O\(Noperatorname{polylog}(N,1/varepsilon\)) logical gates and polylogarithmic quantum width. The operator-error bound varepsilon holds on arbitrary superpositions and includes all auxiliary registers. The construction uses signed averages on adaptive windows to convert uniform-grid samples into weighted Hermite-root samples. Their varying widths control the amplification cost, giving the near-linear bound.
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- It adds a 2026 reference point for readers tracking recent quantum research.
- On the span of the first N oscillator modes, Gauss--Hermite quadrature gives an exact change of basis between mode coefficients and N weighted position space samples.
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