“School of Physic”

Back to Papers Home
Back to Papers of School of Physic

Paper   IPM / Physic / 17720
School of Physics
  Title:   Phase-space negativity as a computational resource for quantum kernel methods
1.  U. Chabaud
2.  R. Ghobadi
3.  S. Beigi
4.  S. Rahimi-Keshari
  Status:   Preprint
  Year:  2024
  Supported by:  IPM
Quantum kernel methods are a proposal for achieving quantum computational advantage in machine learning. They are based on a hybrid classical-quantum computation where a function called the quantum kernel is estimated by a quantum device while the rest of the computation is performed classically. Quantum advantages may be achieved through this method only if the quantum kernel function cannot be estimated efficiently on a classical computer. In this paper, we provide sufficient conditions for the efficient classical estimation of quantum kernel functions for bosonic systems. Specifically, we show that if the negativity in the phase-space quasi-probability distributions of data-encoding quantum states associated with the quantum kernel scales at most polynomially with the size of the quantum circuit, then the kernel function can be estimated efficiently classically. We consider quantum optical examples involving linear-optical networks with and without adaptive non-Gaussian measurements and investigate the effects of loss on the efficiency of the classical simulation. Our results underpin the role of the negativity in phase-space quasi-probability distributions as an essential resource in quantum machine learning based on kernel methods.

Download TeX format
back to top
scroll left or right