Spin models and boson sampling

  title={Spin models and boson sampling},
  author={Borja Peropadre and Al{\'a}n Aspuru‐Guzik and Juan Jos{\'e} Garc{\'i}a-Ripoll},
  journal={arXiv: Quantum Physics},
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. 

Figures from this paper

Nonadaptive fault-tolerant verification of quantum supremacy with noise
A trap-based verification scheme for quantum supremacy that only requires the verifier to prepare single-qubit states is presented, and it is shown that classically sampling upto additive errors is likely hard in both these schemes.
Universal bound on sampling bosons in linear optics and its computational implications
The fundamental limit in the transition amplitudes of bosons is presented, applicable to all physical linear optical networks, and implies that computational decision problems encoded in linear optics, prepared and detected in the Fock basis, can be solved efficiently by classical computers within additive errors.
Boson sampling with Gaussian measurements
We develop an alternative boson sampling model operating on single-photon states followed by linear interferometry and Gaussian measurements. The hardness proof for simulating such
Quantum Emulation of Molecular Force Fields: A Blueprint for a Superconducting Architecture
This work proposes a flexible architecture of microwave resonators with tuneable couplings to perform quantum simulations of molecular chemistry problems, and discusses several aspects of these emulations, such as dynamical ranges of the physical parameters, quenching times necessary for diabaticity and the possibility of implementing anharmonic corrections to the force fields by exploiting certain nonlinear features of superconducting devices.