  We introduce an efficient and numerically stable technique to make use of a
BCS trial wave function in the computation of correlation functions of strongly
correlated quantum fermion systems. The technique is applicable to any
projection approach involving paths of independent-fermion propagators, for
example in mean-field or auxiliary-field quantum Monte Carlo (AFQMC)
calculations. Within AFQMC, in the absence of the sign problem, the methodology
allows the use of a BCS reference state which can greatly reduce the required
imaginary time of projection, and improves Monte Carlo sampling efficiency and
statistical accuracy for systems where pairing correlations are important. When
the sign problem is present, the approach provides a powerful generalization of
the constrained-path AFQMC technique which usually uses Slater determinant
trial wave functions. As a demonstration of the capability of the methodology,
we present benchmark results for the attractive Hubbard model, both
spin-balanced (no sign problem) and with a finite spin polarization (with sign
problem).
