Properties of Krylov state complexity in qubit dynamics
arXiv:2407.21776 · doi:10.1103/PhysRevD.111.076014
Abstract
We analyze the properties of Krylov state complexity in qubit dynamics, considering a single qubit and a qubit pair. A geometrical picture of the Krylov complexity is discussed for the single-qubit case, whereas it becomes non-trivial for the two-qubit case. Considering the particular case of interacting Rydberg two-level atoms, we show that the Krylov basis obtained using an effective Hamiltonian minimizes the time-averaged spread complexity compared to that which is obtained from the original Hamiltonian. We further generalize the latter property to an arbitrary Hamiltonian in which the entire Hilbert space comprises of two subspaces provided a weak coupling between them.
15 pages, 10 figures
References in corpus (56)
- Quantum information with Rydberg atoms
- Probing many-body dynamics on a 51-atom quantum simulator
- Many-Body Physics with Individually-Controlled Rydberg Atoms
- Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
- Observation of Rydberg blockade between two atoms
- Complexity Equals Action
- Observation of collective excitation of two individual atoms in the Rydberg blockade regime
- Complexity and Shock Wave Geometries
- Entanglement of two individual neutral atoms using Rydberg blockade
- Complexity, action, and black holes
- Schrieffer-Wolff transformation for quantum many-body systems
- Quantum Computation as Geometry
- A Universal Operator Growth Hypothesis
- Evidence for coherent collective Rydberg excitation in the strong blockade regime
- Holographic Complexity
- Quantum chaos and the complexity of spread of states
- Observation of coherent many-body Rabi oscillations
- On The Evolution Of Operator Complexity Beyond Scrambling
- Hamiltonian complexity
- Quantum Complexity and Negative Curvature
- Optimal control, geometry, and quantum computing
- Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
- Models of quantum complexity growth
- Universal chaotic dynamics from Krylov space
- Black holes, complexity and quantum chaos
- Quantum Complexity of Time Evolution with Chaotic Hamiltonians
- Quantum complexity and topological phases of matter
- Probing quantum scars and weak ergodicity-breaking through quantum complexity
- On Krylov complexity in open systems: an approach via bi-Lanczos algorithm
- Krylov complexity and chaos in quantum mechanics
- Complexity Growth in Integrable and Chaotic Models
- Spread Complexity and Topological Transitions in the Kitaev Chain
- Krylov complexity of density matrix operators
- Rydberg superatoms: An artificial quantum system for quantum information processing and quantum optics
- Spectral and Krylov Complexity in Billiard Systems
- A universal approach to Krylov State and Operator complexities
- Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model
- Spread complexity in saddle-dominated scrambling
- Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos
- Spread complexity as classical dilaton solutions
- Quantum state complexity meets many-body scars
- A relation between Krylov and Nielsen complexity
- Krylov construction and complexity for driven quantum systems
- Krylov fractality and complexity in generic random matrix ensembles
- Spread complexity for measurement-induced non-unitary dynamics and Zeno effect
- Krylov Complexity and Dynamical Phase Transition in the quenched LMG model
- Dynamics of Rydberg excitations and quantum correlations in an atomic array coupled to a photonic crystal waveguide
- Thermalization in Krylov Basis
- Holographic fluctuations and the principle of minimal complexity
- Spread complexity and quantum chaos for periodically driven spin chains
- Observation of interaction induced blockade and local spin freezing in a NMR quantum simulator
- Black Holes and Marchenko-Pastur Distribution
- Spread complexity and dynamical transition in multimode Bose-Einstein condensates
- Dynamics and Quantum correlations in Two independently driven Rydberg atoms with distinct laser fields
- Quantum Spread Complexity in Neutrino Oscillations
- Complexity Measure Diagnostics of Ergodic to Many-Body Localization Transition