In this work we proof that boson sampling with $N$ particles in $M$ modes is equivalent to short-time evolution with $N$ excitations in an XY model of $2N$ spins. This mapping is efficient whenever the boson bunching probability is small, and errors can be efficiently postselected. This mapping opens the door to boson sampling with quantum simulators or general purpose quantum computers, and highlights the complexity of time-evolution with critical spin models, even for very short times.
