Beyond boson sampling: higher spin sampling as a practical path to quantum supremacy

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, under standard complexity-theoretic assumptions, as a promising route toward quantum computational advantage. 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 introduce a higher-spin ( S ) sampling framework and show that it provides a practical path toward quantum computational advantage. We derive a quasi-linear scaling relation between the number of sites m and the number of spins n , namely m ~ n 1+ ϵ , where ϵ = 3/(2 S ) decreases with increasing spin quantum number. This suggests that, within a spin system, Fock-state boson sampling can be implemented in a quasi-linear mode regime ( m = Ω ( n 1+ ϵ )), significantly reducing experimental resource requirements.