Krylov-Lie Algebras for Variational Quantum Algorithms: Geometric, Depth-Aware Insights into Expressivity and Trainability

arXiv:2607.02626 · quant-ph, math-ph, math.MP · Submitted 2026-07-02 · Read on arXiv

quant-ph, math-ph, math.MP

Submitted: 2026-07-02

Updated: 2026-09-24

Terminology

Loss Function — 12× in this paper · explained in 2 episodes
Hilbert Space — 8× in this paper · explained in 2 episodes
Quantum Circuits — 5× in this paper · explained in 2 episodes
Trace — 4× in this paper · explained in 2 episodes
Quantum Approximate Optimization Algorithm — 2× in this paper
Redundancy — 2× in this paper · explained in 2 episodes
Accuracy — 1× in this paper · explained in 1 episode
Algorithmic Redundancy — 1× in this paper · explained in 1 episode
Approximate Unitary t-design — 1× in this paper · explained in 1 episode
Benchmark — 1× in this paper · explained in 2 episodes
Combinatorial Optimization — 1× in this paper · explained in 2 episodes
Consistency — 1× in this paper · explained in 3 episodes
Degeneracy — 1× in this paper · explained in 3 episodes
Entanglement — 1× in this paper · explained in 4 episodes
Fidelity — 1× in this paper · explained in 2 episodes
Gauge Freedom — 1× in this paper · explained in 2 episodes
Generalization — 1× in this paper · explained in 13 episodes
Inverse Problem — 1× in this paper · explained in 2 episodes
Objective Function — 1× in this paper · explained in 2 episodes
Sparsity — 1× in this paper · explained in 4 episodes
Unitary Dynamics — 1× in this paper · explained in 2 episodes
Verification — 1× in this paper · explained in 2 episodes

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