# Stacking the Deck: Tunable Trainability in Stacked LCUs

arXiv: https://arxiv.org/abs/2607.24686 · HTML: https://mlsanity.com/paper/2607.24686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 47 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Builds on (most cited first, 9 of 9)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (2020)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [Challenges and Opportunities in Quantum Optimization](https://mlsanity.com/paper/2312.02279/) (2023)
- [The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation](https://mlsanity.com/paper/1804.01973/) (2018)
- [On the Sample Complexity of Quantum Boltzmann Machine Learning](https://mlsanity.com/paper/2306.14969/) (2023)
- [Training-efficient density quantum machine learning](https://mlsanity.com/paper/2405.20237/) (2024)

## Abstract (arXiv)

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: ans"atze 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 Omega(1/(n k3l)), with a simulation cost of O(k2l n3) using the best known classical algorithm, compared to a quantum gate complexity of only O(lkn2). 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 ans"atze with a complexity-trainability trade-off that best suits their application and hardware.