Nonstabilizerness of the entangling layer in quantum circuit Born machines
Abstract
The entangling layer of a quantum circuit Born machine can supply both entanglement and nonstabilizerness. In this work we show that the entangling layer can be a Clifford circuit, which supplies no nonstabilizerness. We use an architecture in which a fixed, non-trainable entangler is reused in every layer and only single-qubit rotations are optimized. There, a Clifford entangler reaches the same Kullback--Leibler divergence as a near-Haar one at sufficient circuit depth, and entanglers spanning zero to Haar-typical nonstabilizerness reach the same loss, up to a small offset for a free-fermion matchgate entangler. A doping control that raises the entangler's nonstabilizerness while leaving the entangling power of every gate unchanged leaves the loss flat. With a Clifford entangler the nonstabilizerness of the trained state comes entirely from the rotations, which take the trained circuit outside the stabilizer formalism. We also show that, among all pure states whose Born distribution is a given target, the one whose amplitudes are the positive square roots of the probabilities has the smallest stabilizer Rényi entropy, so this minimum can be computed without training.
Related
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- Trainability of IQP Quantum Circuit Born Machines Under Gaussian Initialization
- Characterizing Large Scale Quantum Systems with Error Per Circuit Layer
- Deployment of Large IQP Circuit Born Machines on Qubit-Limited Hardware Using Noise Injection
- Entangling Atomic Quantum Memories Using High-Order Modulated Coherent States
BibTeX
@misc{plodzien2026nonstabilizerness,
title = {{Nonstabilizerness of the entangling layer in quantum circuit Born machines}},
author = {Marcin Płodzień},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32025},
eprint = {2609.32025},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32025},
}
RIS
TY - UNPB
TI - Nonstabilizerness of the entangling layer in quantum circuit Born machines
AU - Marcin Płodzień
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.32025
UR - https://arxiv.org/abs/2609.32025
AB - The entangling layer of a quantum circuit Born machine can supply both entanglement and nonstabilizerness. In this work we show that the entangling layer can be a Clifford circuit, which supplies no nonstabilizerness. We use an architecture in which a fixed, non-trainable entangler is reused in every layer and only single-qubit rotations are optimized. There, a Clifford entangler reaches the same Kullback--Leibler divergence as a near-Haar one at sufficient circuit depth, and entanglers spanning zero to Haar-typical nonstabilizerness reach the same loss, up to a small offset for a free-fermion matchgate entangler. A doping control that raises the entangler's nonstabilizerness while leaving the entangling power of every gate unchanged leaves the loss flat. With a Clifford entangler the nonstabilizerness of the trained state comes entirely from the rotations, which take the trained circuit outside the stabilizer formalism. We also show that, among all pure states whose Born distribution is a given target, the one whose amplitudes are the positive square roots of the probabilities has the smallest stabilizer Rényi entropy, so this minimum can be computed without training.
ER -