# Entanglement geometry separates circuit cutting, classical hardness, and trainability

arXiv: https://arxiv.org/abs/2607.17872 · HTML: https://mlsanity.com/paper/2607.17872/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 27 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Builds on (most cited first, 6 of 6)

- [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)
- [An Invitation to Distributed Quantum Neural Networks](https://mlsanity.com/paper/2211.07056/) (2022)
- [QNAS: A Neural Architecture Search Framework for Accurate and Efficient Quantum Neural Networks](https://mlsanity.com/paper/2604.07013/) (2026)
- [Adversarial Robustness in Distributed Quantum Machine Learning](https://mlsanity.com/paper/2508.11848/) (2025)
- [DistributedEstimator: Distributed Training of Quantum Neural Networks via Circuit Cutting](https://mlsanity.com/paper/2602.16233/) (2026)

## Abstract (arXiv)

Circuit cutting promises to scale quantum computations beyond current hardware, but variational quantum advantage also requires low cutting overhead, classical hardness, and trainability. We show that these properties are strongly constrained by entanglement geometry. Matrix product state (MPS) and tree tensor network (TTN) circuits with constant seam bond dimension can be cut with (O(1/varepsilon2)) sampling overhead, but remain efficiently classically simulable, ruling out asymptotic quantum advantage within these families. By independently controlling seam and intra-block entanglement, we construct a two-block circuit family that remains cheaply cuttable while requiring a super-polynomial global MPS bond dimension, as supported numerically up to (n=100). However, MPS hardness and trainability require incompatible depth regimes, (d=ω(log n)) and (d=O(log n)), respectively. Using magic rather than entanglement as the hardness resource avoids this conflict: shallow Clifford+(T) circuits remain cuttable and trainable while their stabiliser-simulation cost grows exponentially with the (T)-count.