Out-of-time-ordered correlators and quantum walks
arXiv:1904.00439 · doi:10.1103/PhysRevE.99.062128
Abstract
Out-of time-ordered correlators (OTOC) have recently attracted significant attention from the physics of many-body systems, to quantum black-holes, with an exponential growth of the OTOC indicating quantum chaos. Here we consider OTOC in the context of coined discrete quantum walks, a very well studied model of quantization of classical random walks with applications to quantum algorithms. Three separate cases of operators, variously localized in the coin and walker spaces, are discussed in this context and it is found that the approximated behavior of the OTOCs is well described by simple algebraic functions in all these three cases with different time scale of growth. The quadratic increase of OTOC signals the absence of quantum chaos in these simplest forms of quantum walks.
arXiv comment19 pages, 3 figures
References in corpus (30)
- A bound on chaos
- Black holes and the butterfly effect
- Quantum random walks - an introductory overview
- Universal computation by quantum walk
- Spatial search by quantum walk
- The Spectrum in the Sachdev-Ye-Kitaev Model
- Localized shocks
- Universal quantum computation using the discrete time quantum walk
- The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
- Measuring the scrambling of quantum information
- Two-dimensional conformal field theory and the butterfly effect
- An example of the difference between quantum and classical random walks
- Out-of-time-order correlators in quantum mechanics
- Out-of-time-ordered correlators in many-body localized systems
- Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
- Out-of-time-ordered correlators in quantum Ising chain
- Out-of-time-order correlations in many-body localized and thermal phases
- Electric quantum walks with individual atoms
- Weak Quantum Chaos
- Optimizing the discrete time quantum walk using a SU(2) coin
- Quantum Walks in artificial electric and gravitational Fields
- Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos
- Exact out-of-time-ordered correlation functions for an interacting lattice fermion model
- Out-of-time-order correlators in finite open systems
- Out-of-time-ordered correlator in the quantum bakers map and truncated unitary matrices
- Out of Time Ordered Correlators and Entanglement Growth in the Random Field XX Spin Chain
- Operator Spreading in Quantum Maps
- Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice
- Creating cat states in one-dimensional quantum walks using delocalized initial states
- Quantum walk on a toral phase space
Cited by in corpus (9)
- Scrambling in strongly chaotic weakly coupled bipartite systems: Universality beyond the Ehrenfest time-scale
- Out-of-time-ordered correlators and the Loschmidt echo in the quantum kicked top: How low can we go?
- Quantum walks with quantum chaotic coins: Of the Loschmidt echo, classical limit and thermalization
- Exponential speedup in measuring out-of-time-ordered correlators with a single bit of quantum information
- Probing Dynamical Sensitivity of a Non-KAM System Through Out-of-Time-Order Correlators
- Late time dynamics in SUSY saddle-dominated scrambling through higher-point OTOC
- Out-of-Time Ordered Correlators in Kicked Coupled Tops: Information Scrambling in Mixed Phase Space and the Role of Conserved Quantities
- Loschmidt echo and scrambling of systematic errors in tomography -- a quantum signature of chaos
- Information acquisition, scrambling, and sensitivity to errors in quantum chaos