Quantum algorithms prepare states for normalized correlated Gaussians and their exponentials with gate complexities scaling as Õ(‖Σ‖_F/λ_max ⋅ κ^1.5), achieving subcubic scaling in N for fractional processes and enabling quantum advantage in rough Bergomi variance modeling.
Grand unification of quantum algorithms
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A polylog-sized quantum computer achieves exponential advantage over classical machines in classification and dimension reduction of massive classical data using quantum oracle sketching combined with classical shadows.
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Quantum analog-encoding for correlated Gaussian vectors and their exponentiation with application to rough volatility
Quantum algorithms prepare states for normalized correlated Gaussians and their exponentials with gate complexities scaling as Õ(‖Σ‖_F/λ_max ⋅ κ^1.5), achieving subcubic scaling in N for fractional processes and enabling quantum advantage in rough Bergomi variance modeling.
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Exponential quantum advantage in processing massive classical data
A polylog-sized quantum computer achieves exponential advantage over classical machines in classification and dimension reduction of massive classical data using quantum oracle sketching combined with classical shadows.