  The present paper intends to present an extension of the constrained-path
quantum Monte-Carlo approach allowing to reconstruct non-yrast states in order
to reach the complete spectroscopy of nuclei within the interacting shell
model. As in the yrast case studied in a previous work, the formalism involves
a variational symmetry-restored wave function assuming two central roles.
First, it guides the underlying Brownian motion to improve the efficiency of
the sampling. Second, it constrains the stochastic paths according to the
phaseless approximation to control sign or phase problems that usually plague
fermionic QMC simulations. Proof-of-principle results in the $sd$ valence space
are reported. They prove the ability of the scheme to offer remarkably accurate
binding energies for both even- and odd-mass nuclei irrespective of the
considered interaction.
