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