This thesis deals with the Bose gas at large scattering lengths using
quantum path-integral Monte Carlo simulations. At first, this type of simulation is presented through the example of the free Bose gas. The Bose gas is then studied in the regime where interactions become too strong for mean-field theories to be accurate, using a quantum Monte Carlo simulation that quantitatively reproduces both experimental results and theoretical predictions.
The second part of this thesis concerns the situation in which the interactions between bosons are resonant, called the unitary regime. In this situation, although two bosons cannot bind, three bosons may form a trimer state. This counter-intuitive effect, called the Efimov effect,
is described both through theoretical arguments and a dedicated three-body quantum path-integral Monte Carlo simulation. This simulation then serves as the building block of a simulation of the unitary Bose gas, that reproduces high-temperature theoretical results and predicts the existence of a low-temperature quantum liquid phase, of the same physical origin as the Efimov effect.