Quantum algorithm approximates k-th spectral gap Δ_k and midpoint μ_k of Hermitian matrix to εΔ_k error with O(N²/(ε² Δ_k²) polylog) QRAM complexity, claiming speedup for large gaps, plus Ω(N²) black-box lower bound.
The fast johnson–lindenstrauss transform and ap- proximate nearest neighbors.SIAM Journal on computing, 39(1):302–322, 2009
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Spectral Gaps with Quantum Counting Queries and Oblivious State Preparation
Quantum algorithm approximates k-th spectral gap Δ_k and midpoint μ_k of Hermitian matrix to εΔ_k error with O(N²/(ε² Δ_k²) polylog) QRAM complexity, claiming speedup for large gaps, plus Ω(N²) black-box lower bound.