Stacking the Deck: Tunable Trainability in Stacked LCUs

• URL: http://arxiv.org/abs/2607.24686v1
• Date: Mon, 27 Jul 2026 17:25:14 GMT
• Title: Stacking the Deck: Tunable Trainability in Stacked LCUs
• Abstract summary: Variational quantum circuits have been central to many proposed near-term applications of quantum computing.<n>We propose a stacked linear combination of unitaries (S-LCU) as a variational ansatz which provides a tunable trade-off between barren plateaus and classical simulability.
• Score: 5.3795542973467905
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Variational quantum circuits have been central to many proposed near-term applications of quantum computing, but a growing body of evidence suggests that trainability and quantum advantage are fundamentally at odds: ansätze expressive enough to resist efficient classical simulation tend to exhibit barren plateaus, while structures that provably rule out barren plateaus typically render them classically simulable. We propose a stacked linear combination of unitaries (S-LCU) as a variational ansatz which provides a tunable trade-off between barren plateaus and classical simulability. Using a diagrammatic analysis, we bound the loss-landscape variance of the Free Fermion S-LCU, whose elements are fermionic Gaussian unitaries. We prove a variance lower bound of $Ω(1/(n k^{3l}))$, with a simulation cost of $O(k^{2l} n^3)$ using the best known classical algorithm, compared to a quantum gate complexity of only $O(lkn^2)$. The number of layers $l$ serves as a single dial that trades computational complexity against the rate of cost concentration. This offers practitioners a systematic method for constructing ansätze with a complexity-trainability trade-off that best suits their application and hardware.

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