  The nonstabilizerness, or magic, is an essential quantum resource to perform
universal quantum computation. Robustness of magic (RoM) in particular
characterizes the degree of usefulness of a given quantum state for
non-Clifford operation. While the mathematical formalism of RoM can be given in
a concise manner, it is extremely challenging to determine the RoM in practice,
since it involves superexponentially many pure stabilizer states. In this work,
we present efficient novel algorithms to compute the RoM. The crucial technique
is a subroutine that achieves the remarkable features in calculation of
overlaps between pure stabilizer states: (i) the time complexity per each
stabilizer is reduced exponentially, (ii) the space complexity is reduced
superexponentially. Based on this subroutine, we present algorithms to compute
the RoM for arbitrary states up to $n=7$ qubits on a laptop, while brute-force
methods require a memory size of 86 TiB. As a byproduct, the proposed
subroutine allows us to simulate the stabilizer fidelity up to $n=8$ qubits,
for which naive methods require memory size of 86 PiB so that any
state-of-the-art classical computer cannot execute the computation. We further
propose novel algorithms that utilize the preknowledge on the structure of
target quantum state such as the permutation symmetry of disentanglement, and
numerically demonstrate our state-of-the-art results for copies of magic states
and partially disentangled quantum states. The series of algorithms constitute
a comprehensive ``handbook'' to scale up the computation of the RoM, and we
envision that the proposed technique applies to the computation of other
quantum resource measures as well.
