Quantum Krylov Learning

arXiv:2610.00537 · quant-ph, cond-mat.mes-hall, cond-mat.mtrl-sci, hep-th · Submitted 2026-09-30 · Read on arXiv

quant-ph, cond-mat.mes-hall, cond-mat.mtrl-sci, hep-th

Submitted: 2026-09-30

Updated: 2026-09-30

Comments: 46 pages, 7 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Hamiltonian Learning — 11× in this paper · explained in 2 episodes
• Trace — 11× in this paper · explained in 2 episodes
• Accuracy — 10× in this paper · explained in 1 episode
• Benchmark — 8× in this paper · explained in 2 episodes
• Quantum Krylov Learning — 8× in this paper
• Robustness — 7× in this paper · explained in 5 episodes
• Verification — 7× in this paper · explained in 2 episodes
• Sample Complexity — 6× in this paper · explained in 15 episodes
• Core — 5× in this paper · explained in 2 episodes
• Gibbs State — 4× in this paper · explained in 2 episodes
• Krylov Complexity — 4× in this paper · explained in 3 episodes
• Degeneracy — 3× in this paper · explained in 3 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Decoupling — 2× in this paper · explained in 2 episodes
• Calibration — 1× in this paper · explained in 7 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Gauge Freedom — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Lindblad Dynamics — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Self-consistency — 1× in this paper · explained in 2 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes
• System Identification — 1× in this paper · explained in 3 episodes
• Systematic Bias — 1× in this paper · explained in 3 episodes

Sources

• Coupling strength estimation for spin chains despite restricted access
• Indirect Hamiltonian Identification through a small gateway
• Optimal learning of quantum Hamiltonians from high-temperature Gibbs states
• Estimation of Coupling Constants of a Three-Spin Chain: Case Study of Hamiltonian Tomography with NMR
• Robustly learning the Hamiltonian dynamics of a superconducting quantum processor
• Quantum System Identification
• Hamiltonian identifiability assisted by single-probe measurement
• Quantum Probe Tomography
• Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware
• Generalized quantum subspace expansion
• Quantum Krylov subspace algorithms for ground and excited state energy estimation
• Real-Time Krylov Theory for Quantum Computing Algorithms
• Analysis of quantum Krylov algorithms with errors
• Exchange interaction of hole-spin qubits in double quantum dots in highly anisotropic semiconductors
• Two-qubit logic with anisotropic exchange in a fin field-effect transistor
• A Universal Operator Growth Hypothesis
• Quantum Dynamics in Krylov Space: Methods and Applications
• Extending Quantum Coherence in Diamond
• Engineering long spin coherence times of spin-orbit systems

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