A hardware-efficient binary-tree ansatz has a closed-form diagonal Fubini–Study metric, enabling metric-aware VQE and time evolution without auxiliary circuits, with linear-in-k pruning for sparse sectors.
Trainability and Expressivity of Hamming-Weight Preserving Quantum Circuits for Machine Learning
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Quantum machine learning (QML) 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 variational quantum circuits (VQCs). These circuits use qubit gates that preserve subspaces of the Hilbert space, spanned by basis states with fixed Hamming weight $k$. 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 an $n$-qubit quantum circuit. These data loaders are obtained using controllability arguments, by checking the Quantum Fisher Information Matrix (QFIM)'s rank. Second, we provide a theoretical justification for the fact that the rank of the QFIM of any VQC state is almost-everywhere constant, which is of separate interest. Lastly, we analyze the trainability of Hamming weight preserving circuits, and show that the variance of the $l_2$ cost function gradient is bounded according to the dimension $\binom{n}{k}$ of the subspace. This proves conditions of existence/lack 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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Analytical expression for dynamical Lie algebra of QAOA-MaxCut on complete graphs with proof that loss variance scales linearly in qubit number.
A dual-valued phase shifter in linear optics creates variational cost landscapes with fewer local minima and outperforms prior linear-optical variational algorithms by mitigating barren plateaus.
QCNNs are classically simulable via Pauli shadows on low-bodyness subspaces of locally-easy datasets, with explicit simulation demonstrated up to 1024 qubits for phases of matter classification.
Numerical study of five symmetry-preserving HVAs for Z2 gauge theory finds overparametrization eliminates local minima and loss decay rate scales linearly with number of parameters.
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A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling
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The Dynamical Lie Algebra of QAOA-MaxCut on the Complete Graph
Analytical expression for dynamical Lie algebra of QAOA-MaxCut on complete graphs with proof that loss variance scales linearly in qubit number.
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Mitigating the barren plateau problem in linear optics
A dual-valued phase shifter in linear optics creates variational cost landscapes with fewer local minima and outperforms prior linear-optical variational algorithms by mitigating barren plateaus.
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Quantum Convolutional Neural Networks are Effectively Classically Simulable
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Symmetries and overparametrization properties of Hamiltonian variational ansatzes for the $(1+1)$d $\mathbb{Z}_2$ lattice gauge theory
Numerical study of five symmetry-preserving HVAs for Z2 gauge theory finds overparametrization eliminates local minima and loss decay rate scales linearly with number of parameters.