Beyond Boson Sampling: Higher Spin Sampling as a Practical Path to Quantum Supremacy

TL;DR

This paper proposes higher spin sampling as a practical approach to achieve quantum supremacy, showing that it can reduce resource requirements compared to traditional boson sampling methods.

Contribution

It introduces spin sampling for arbitrary spin-$S$ states and establishes a quasi-linear scaling relation, offering a feasible experimental path to quantum advantage.

Findings

Quasi-linear scaling relation between sites and spins: m ~ n^{1+ε}.

Higher spin systems can perform boson sampling with fewer resources.

Potential for experimentally feasible quantum supremacy demonstrations.

Abstract

Since the dawn of quantum computation science, a range of quantum algorithms have been proposed, yet few have experimentally demonstrated a definitive quantum advantage. Shor's algorithm, while renowned, has not been realized at a scale to outperform classical methods. In contrast, Fock-state boson sampling has been theoretically established as a means of achieving quantum supremacy. However, most existing experimental realizations of boson sampling to date have been based on Gaussian boson sampling, in which the input states consist of squeezed states of light. In this work, we first introduce spin sampling for arbitrary spin-$S$ states as a practical path to quantum supremacy. We identified a quasi-linear scaling relation between the number of sites $m$ and the number of spins $n$ as $m\sim n^{1+\epsilon}$, where $\epsilon=3/(2S)$ is inversely proportional to the spin quantum number. This suggests that, within a spin system, an equivalent Fock-state boson sampling task in the linear mode region, characterized by $m\sim \Omega(n^{1+\epsilon})$, is experimentally feasible with reduced resource requirements.