QRSI spans degenerate quantum eigenspaces almost surely by conjugating the Hamiltonian with random unitaries on g parallel branches and using subspace estimation, while exactly preserving the spectral gap.
Under Haar measure, the equivariance ˆw(SR) =Sˆw(R) combined with left-invariance (SR∼Haar) givesSˆw d = ˆw for allS∈U(g), so ˆwis uniform onS 2g−1
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Quantum Randomized Subspace Iteration
QRSI spans degenerate quantum eigenspaces almost surely by conjugating the Hamiltonian with random unitaries on g parallel branches and using subspace estimation, while exactly preserving the spectral gap.