  The infamous numerical sign problem poses a fundamental obstacle to
particle-based stochastic Wigner simulations in high dimensional phase space.
Although the existing particle annihilation via uniform mesh significantly
alleviates the sign problem when dimensionality D $\le$ 4, the mesh size grows
dramatically when D $\ge$ 6 due to the curse of dimensionality and consequently
makes the annihilation very inefficient. In this paper, we propose an adaptive
particle annihilation algorithm, termed Sequential-clustering Particle
Annihilation via Discrepancy Estimation (SPADE), to overcome the sign problem.
SPADE follows a divide-and-conquer strategy: Adaptive clustering of particles
via controlling their number-theoretic discrepancies and independent random
matching in each group, and it may learn the minimal amount of particles that
can accurately capture the non-classicality of the Wigner function. Combining
SPADE with the variance reduction technique based on the stationary phase
approximation, we attempt to simulate the proton-electron couplings in 6-D and
12-D phase space. A thorough performance benchmark of SPADE is provided with
the reference solutions in 6-D phase space produced by a
characteristic-spectral-mixed scheme under a $73^3 \times 80^3$ uniform grid,
which fully explores the limit of grid-based deterministic Wigner solvers.
