Trainability and Expressivity of Hamming-Weight Preserving Quantum
Circuits for Machine Learning
- URL: http://arxiv.org/abs/2309.15547v1
- Date: Wed, 27 Sep 2023 10:11:07 GMT
- Title: Trainability and Expressivity of Hamming-Weight Preserving Quantum
Circuits for Machine Learning
- Authors: L\'eo Monbroussou, Jonas Landman, Alex B. Grilo, Romain Kukla, and
Elham Kashefi
- Abstract summary: We analyze the trainability and controllability of specific Hamming weight preserving quantum circuits.
These circuits use gates that preserve subspaces of the Hilbert space, spanned by basis states with fixed Hamming weight $k$.
They are good candidates for mimicking neural networks, by both loading classical data and performing trainable layers.
- Score: 2.3420045370973828
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum machine learning has become a promising area for real world
applications of quantum computers, but near-term methods and their scalability
are still important research topics. In this context, we analyze the
trainability and controllability of specific Hamming weight preserving quantum
circuits. These circuits use gates that preserve subspaces of the Hilbert
space, spanned by basis states with fixed Hamming weight $k$. They are good
candidates for mimicking neural networks, by both loading classical data and
performing trainable layers. In this work, we first design and prove the
feasibility of new heuristic data loaders, performing quantum amplitude
encoding of $\binom{n}{k}$-dimensional vectors by training a n-qubit quantum
circuit. Then, we analyze more generally the trainability of Hamming weight
preserving circuits, and show that the variance of their gradients is bounded
according to the size of the preserved subspace. This proves the conditions of
existence of Barren Plateaus for these circuits, and highlights a setting where
a recent conjecture on the link between controllability and trainability of
variational quantum circuits does not apply.
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