Fig. 4: Evolution of the energy towards the ground state of two and three noninteracting fermions in a 1D harmonic potential.

a Performed by variational Monte Carlo with a relative error for two fermions 0.004% and three fermions 10.34% respectively. b Using the stochastic representation introduced here with a relative error for two fermions 0.002% and for three fermions 0.004%. The initial guess (τ = 0) for the trial wavefunction is chosen to be the noninteracting fermionic solution with the potential in Eq. (6) and offsets u = (−1.0, 1.0) for two fermions and u = (0.8, 0.0, − 0.8) for three fermions. Source data are provided as a Source Data file.