Quantum Generative Training Using Rényi Divergences

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Method claims efficient gradient-based training of quantum generative models by minimizing the max Rényi divergence (α=2) so the gradient is differentiable without matrix logarithms, using linear combination of unitaries and a hybrid Swapomar test to estimate traces and a block-encoding of ρ⁻¹. Efficiency requires well-conditioned ρ (or pseudo-inverse/noise for pure states) and matches polynomial query scaling in the condition number; numerics on 3-qubit thermal states show exponentially shrinking loss and rising fidelity, but low-temperature cases remain hard (NP implications).

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1. 0:00Intro
2. 1:13What is machine learning? The aim of machine learning is to create algorithms that teach concepts to computers by example
3. 4:47Deep learning networks
4. 8:38Barren Plateau Due to entanglement
5. 12:43Quantum Generative Training
6. 14:13Generative Classical Training
7. 15:37What is a good distance measure?
8. 17:25Optimizing Models
9. 22:21Digression: Are there entanglement induced barren plateaus?
10. 23:29Expression for the gradient
11. 25:47Swapamard Test
12. 30:22Complexity of thermal states (LCU)
13. 31:41Ok but how does this work in practice?
14. 33:40Conclusions