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.
Quantum speedup for graph sparsification, cut approximation, and laplacian solving.SIAM Journal on Computing, 51(6):1703–1742, 2022
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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.