Equivalence of maximal and generic reachability for non-universal Variational Quantum Circuits

arXiv:2609.27053 · quant-ph · Submitted 2026-09-22 · Read on arXiv

quant-ph

Submitted: 2026-09-22

Updated: 2026-09-22

Terminology

• Quantum Circuits — 7× in this paper · explained in 2 episodes
• Dynamical Lie Algebra — 5× in this paper
• Fisher Information — 2× in this paper · explained in 3 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Additivity — 1× in this paper · explained in 1 episode
• Degeneracy — 1× in this paper · explained in 3 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Redundancy — 1× in this paper · explained in 2 episodes

Sources

• Training variational quantum algorithms is NP-hard
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Barren Plateaus in Variational Quantum Computing
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Reachability Deficits in Quantum Approximate Optimization
• Capacity and quantum geometry of parametrized quantum circuits
• Ground-state reachability for variational quantum eigensolvers: a Rydberg-atom case study
• Reachability Constraints in Variational Quantum Circuits: Optimization within Polynomial Group Module
• Lie-algebraic classical simulations for quantum computing
• Symmetry Principles in Quantum Systems Theory
• Subspace Controllability and Clebsch-Gordan Decomposition of Symmetric Quantum Networks
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• Exploiting symmetry in variational quantum machine learning
• Building spatial symmetries into parameterized quantum circuits for faster training
• PennyLane: Automatic differentiation of hybrid quantum-classical computations
• Trainability and Expressivity of Hamming-Weight Preserving Quantum Circuits for Machine Learning
• On the gauge orbit space stratification (a review)
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• On the dynamical Lie algebras of quantum approximate optimization algorithms
• Full classification of Pauli Lie algebras

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