Quantum advantage with membosonsampling

Quantum computer,harnessing quantum superposition to boost a parallel computational power,promises to outperform its classical counterparts and offer an exponentially increased scaling.The term“quantum advantage”was proposed to mark the key point when peo-ple can solve a classically intractable problem by artificially control-ling a quantum system in an unprecedented scale,even without er-ror correction or known practical applications.Boson sampling,a problem about quantum evolutions of multi-photons on multimode photonic networks,as well as its variants,has been considered as a promising candidate to reach this milestone.However,the current photonic platforms suffer from the scaling problems,both in pho-ton numbers and circuit modes.Here,we propose a new variant of the problem,membosonsampling,exploiting the scaling of the prob-lem can be in principle extended to a large scale.We experimentally verify the scheme on a self-looped photonic chip inspired by mem-ristor,and obtain multi-photon registrations up to 56-fold in 750,000 modes with a Hilbert space up to 10254.The results exhibit an inte-grated and cost-efficient shortcut stepping into the“quantum advan-tage”regimeina photonic systemfarbeyondpreviousscenarios,and provide a scalable and controllable platform for quantum information processing.