  The quantum Schur transform maps the computational basis of a system of $n$
qudits onto a \textit{Schur basis}, which spans the minimal invariant subspaces
of the representations of the unitary and the symmetric groups acting on the
state space of $n$ $d$-level systems. We introduce a new algorithm for the task
of weak Schur sampling. Our algorithm efficiently determines both the Young
label which indexes the irreducible representations and the multiplicity label
of the symmetric group. There are two major advantages of our algorithm for
weak Schur sampling when compared to existing approaches which proceed via
quantum Schur transform algorithm or Generalized Phase Estimation algorithm.
First, our algorihtm is suitable for streaming applications and second it is
exponentially more efficient in its memory usage. We show that an instance of
our weak Schur sampling algorithm on $n$ qubits to accuracy $\epsilon$ requires
only $O(\log_2n)$ qubits of memory and $O(n^3\log_2(\frac{n}{\epsilon}))$ gates
from the Clifford+T set. Further, we show that our weak Schur sampling
algorithm on $n$ qudits decomposes into
$O\big(dn^{2d}\log_2^p\big(\frac{n^{2d}}{\epsilon}\big)\big)$ gates from an
arbitrary fault-tolerant qudit universal set, for $p\approx 4$, and requires a
memory of $O(\log_dn)$ qudits to implement.
