Stacking the Deck: Tunable Trainability in Stacked LCUs

Quick overview

Variational quantum circuits (VQCs) face a fundamental trade-off: ansätze expressive enough to resist classical simulation tend to suffer from barren plateaus, while those that provably avoid barren plateaus are often classically simulable. This paper proposes Stacked Linear Combination of Unitaries (S-LCU), a variational ansatz that uses the number of layers l as a single dial to tune the balance between barren plateaus and classical simulability. The authors prove a lower bound of Ω(1/(n k^{3l})) on the loss-landscape variance for the Free Fermion S-LCU, with a classical simulation cost of O(k^{2l} n^3) and quantum gate complexity of only O(lkn^2). This work offers a systematic method for constructing ansätze with a controlled complexity-trainability trade-off.

• Proposes the S-LCU variational ansatz, using a single dial (layer count l) to tune the trade-off between barren plateaus and classical simulability.
• Proves a loss-landscape variance lower bound of Ω(1/(n k^{3l})) for the Free Fermion S-LCU, avoiding complete barren plateaus.
• Classical simulation cost is O(k^{2l} n^3) while quantum gate complexity is only O(lkn^2), highlighting a quantum advantage regime.
• Provides a systematic method for practitioners to choose layer count based on hardware and application needs for optimal complexity-trainability balance.