The infamous numerical sign problem poses a fundamental obstacle to long-time stochastic Wigner simulations in high dimensional phase space. Although the existing particle annihilation via uniform mesh (PAUM) significantly alleviates the sign problem when dimensionality D $le$ 4, the setting of regular grids gives rise to another challenge in data storage when D $ge$ 6 due to the curse of dimensionality. In this paper, we propose to use a recently developed adaptive particle annihilation, termed sequential-clustering particle annihilation via discrepancy estimation (SPADE), to overcome the numerical sign problem. SPADE consists of adaptive clustering of particles via controlling their number-theoretic discrepancies and independent random matching in each group, and may learn the minimal amount of particles that can accurately capture the oscillating nature of the Wigner function. Combining SPADE with a recently proposed variance reduction technique via the stationary phase approximation, we make the first attempt to simulate the transitions of hydrogen energy levels in 6-D phase space, where the feasibility of PAUM with sample sizes about $10^9$-$10^{10}$ has also been explored as a comparison.
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