The race for quantum supremacy: pushing the classical limit for photonic hardware

The strong efforts towards the realization of scalable quantum computing aremotivatedby thepromiseof super-polynomial speed-up in several computational tasks. A first fundamental step in this route is to provide concrete evidence of ‘quantum supremacy’. Such a regime is obtained when a quantumdevice is capable of solving a specific problem faster than the best classical hardware. A serious attempt to provide a first demonstration of quantum speed-up with affordable resources is represented by boson sampling [1,2], a non-universal quantum-computational protocol exploiting indistinguishable single photons and linear optical devices. In this context, strong theoretical evidence has been reported that the interference pattern generated by a boson sampler is hard to simulate with classical resources, this pattern being related to the calculation of a hard-to-compute quantity known as a matrix permanent. Formal achievement of the regime of quantum supremacywill answer two very relevant questions: Are we able to benefit from the power of quantum mechanics or does there exist a fundamental reason why this achievement is forbidden? Once this regime has been achieved, are we able to certify the correct functioning of the quantum boson samplers or do we face an undecidability problem? Starting from these intriguing and promising theoretical results, an experimental race kicked off with the aim of reaching the quantum supremacy regime withboson samplingby employing aphotonic platform [3]. A large amount of effort has been devoted to pushing the Classical Quantum