Error bounds for constrained dynamics in gapped quantum systems: Rigorous results and generalizations
arXiv:2001.03421 · doi:10.1103/PhysRevA.101.052122
Abstract
In arXiv:2001.03419 we introduce a universal error bound for constrained unitary dynamics within a well-gapped energy band of an isolated quantum system. Here, we provide the full details on the derivation of the bound. In addition, we generalize the result to isolated quantum many-body systems by employing the local Schrieffer-Wolff transformation, obtaining an error bound that grows polynomially in time. We also generalize the result to Markovian open quantum systems and quantitatively explain the quantum Zeno effect.
arXiv comment19 pages, 9 figures. Accompanying letter arXiv:2001.03419. Here, we prove the exact (rather than asymptotic) bound and rigorously derive the many-body bound without numerical demonstration. Generalization to open systems is also discussed
References in corpus (43)
- Cold bosonic atoms in optical lattices
- Probing many-body dynamics on a 51-atom quantum simulator
- QuTiP 2: A Python framework for the dynamics of open quantum systems
- Decoherence Free Subspaces for Quantum Computation
- Fermi-liquid instabilities at magnetic quantum phase transitions
- Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
- Quantum many-body scars
- Quantum trajectories and open many-body quantum systems
- Light-cone-like spreading of correlations in a quantum many-body system
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Dynamics of Loschmidt echoes and fidelity decay
- Schrieffer-Wolff transformation for quantum many-body systems
- Quantum Zeno subspaces
- Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace
- Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
- Quantum Phase Transition and Universal Dynamics in the Rabi model
- High-temperature superfluidity of fermionic atoms in optical lattices
- Lieb-Robinson Bounds and the Exponential Clustering Theorem
- Emergent SU(2) dynamics and perfect quantum many-body scars
- Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach
- Spread of correlations in long-range interacting quantum systems
- Effective operator formalism for open quantum systems
- Adiabatic Elimination in a Lambda System
- Constrained dynamics via the Zeno effect in quantum simulation: Implementing non-Abelian lattice gauge theories with cold atoms
- Experimental realization of quantum zeno dynamics
- Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields
- Stability of Frustration-Free Hamiltonians
- Breakdown of quasilocality in long-range quantum lattice models
- Enhancing optomechanical coupling via the Josephson effect
- Minimal Self-Contained Quantum Refrigeration Machine Based on Four Quantum Dots
- Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
- Time-Resolved Observation of Spin-Charge Deconfinement in Fermionic Hubbard Chains
- Persistence of locality in systems with power-law interactions
- Finite speed of quantum scrambling with long range interactions
- Vibrational Sidebands and Kondo-effect in Molecular Transistors
- Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems
- Reliability of lattice gauge theories
- Generalized Schrieffer-Wolff Formalism for Dissipative Systems
- Adiabatic Theorem for Quantum Spin Systems
- Zeno Hall Effect
- Magnetism, coherent many-particle dynamics, and relaxation with ultracold bosons in optical superlattices
- Universal Error Bound for Constrained Quantum Dynamics
- A cavity-mediated quantum CPHASE gate between NV spin qubits in diamond
Cited by in corpus (15)
- Non-Hermitian Physics
- Gauge protection in non-Abelian lattice gauge theories
- Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field
- Speed Limits for Macroscopic Transitions
- Bounds in Nonequilibrium Quantum Dynamics
- Stabilizing lattice gauge theories through simplified local pseudo generators
- One bound to rule them all: from Adiabatic to Zeno
- How does geometry affect quantum gases?
- Topological lower bound on quantum chaos by entanglement growth
- Universal Error Bound for Constrained Quantum Dynamics
- Eternal Adiabaticity
- Reliability of lattice gauge theories in the thermodynamic limit
- Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems
- Quantum gases on a torus
- Kinetically constrained models constructed from dissipative quantum dynamics