Efficient Quantum Hermite Transform

What is it about?

A new quantum algorithmic primitive inspired by the quantum Fourier transform, which lies at the heart of almost all exponential quantum speedups. As an important subroutine, we give a nearly optimal way to simulate the quantum harmonic oscillator (QHO), a fundamental model in quantum mechanics.

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Photo by Logan Voss on Unsplash

Photo by Logan Voss on Unsplash

Why is it important?

Physical simulation is still the most promising application of quantum computers, as proposed by Feynman more than four decades ago. We give an important tool which has already shown to have applications in quantum simulation, and also give a nearly optimal simulation algorithm for the single most studied model in quantum mechanics, the QHO. More generally, QHT enables the simulation of systems which are efficient in the Fock basis on a digital quantum computer.