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About this paper
Nikhil Khatri, Stefan Zohren, Gabriel Matos
Researchers from the University of Oxford and Quantinuum developed the stacked linear combination of unitaries (S-LCU) variational ansatz to address the expressivity-trainability dilemma in Variational Quantum Algorithms. Their analysis demonstrates that for Free Fermion S-LCUs, the loss landscape variance decays polynomially with system size and LCU terms for a fixed number of layers, while the number of layers offers a tunable polynomial separation between classical simulation cost and quantum gate complexity.
Key insights
- The number of layers ('l') in the S-LCU serves as a 'tunable dial' to systematically control the trade-off between classical simulation cost and the ansatz's trainability.
- For a fixed number of layers 'l', the FF-S-LCU exhibits a polynomial decay of loss-landscape variance with respect to system size and the number of LCU terms, thereby avoiding exponential barren plateaus.
- The S-LCU can achieve a significant and tunable polynomial separation between its direct classical simulation cost (exponential in 'l') and its quantum gate count (linear in 'l').
Summary by alphaXiv.
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