Efficient quantum method speeds up Hermite transform calculations
Efficient Non-Uniform Quantum Hermite Transform through Adaptive Sampling
Distributed, Parallel, and Cluster ComputingEmerging Technologies
Summary
Some tasks in quantum computing involve changing how certain data is represented, like switching between wave modes and their positions. This paper shows a faster way to perform a specific transformation called the quantum Hermite transform using fewer quantum operations. The new method carefully chooses where to sample data to make the process more efficient without losing accuracy. This means quantum computers can handle certain calculations more quickly and with less overhead.
What this means in practice
- •For quantum algorithm developers: Implement faster quantum algorithms for systems involving harmonic oscillator modes by efficiently performing Hermite transforms with fewer quantum gates.
- •For quantum hardware engineers: Design quantum processors that optimize resource usage and gate count for transforms based on adaptive sampling techniques introduced by this work.
Authors
Nitay Mayo, Aryeh Lev Zabokritskiy
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 $O(N\operatorname{polylog}(N,1/\varepsilon))$ 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.