Related papers: Hypersensitivity to Perturbations in the Quantum B…
We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker's map could be investigated experimentally on a…
The quantum baker map possesses two symmetries: a canonical "spatial" symmetry, and a time-reversal symmetry. We show that, even when these features are taken into account, the asymptotic entangling power of the baker's map does not always…
We present here a canonical quantization for the baker's map. The method we use is quite different from that used in Balazs and Voros (ref. \QCITE{cite}{}{BV}) and Saraceno (ref. \QCITE{cite}{}{S}). We first construct a natural ``baker…
Quantum dynamics of the Harper model with self-duality exhibits localized, diffusive, and ballistic states depending on the potential strength $V$. By adding time-dependent harmonic perturbations composed of $M$ incommensurate frequencies,…
Hypersensitivity to perturbation is a criterion for chaos based on the question of how much information about a perturbing environment is needed to keep the entropy of a Hamiltonian system from increasing. In this paper we give a brief…
We demonstrate that the unitary dynamics of a multi-qubit system can display hypersensitivity to initial state perturbation. This contradicts the common belief that the classical approach based on the exponential divergence of initially…
We re-examine the problem of the "Loschmidt echo", which measures the sensitivity to perturbation of quantum chaotic dynamics. The overlap squared $M(t)$ of two wave packets evolving under slightly different Hamiltonians is shown to have…
We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
The complex dynamics of baker's map and its variants in an infinite-precision mathematical domain have been extensively analyzed in the past five decades. However, their real structure implemented in a finite-precision computer remains…
This study explores the effects of introducing a symmetry breaking disorder on the dynamics of a system invariant under particle permutation. The disorder forces quantum states, confined to the $N+1$ dimensional completely symmetric space…
We propose a quantum algorithm for simulation of the Anderson transition in disordered lattices and study numerically its sensitivity to static imperfections in a quantum computer. In the vicinity of the critical point the algorithm gives a…
Within an inherently classical perspective, there is always an unavoidable energy cost associated with the information deletion and this common lore is at the heart of the Landauer's conjecture that does not impose, per se, any relevant…
Is the dynamical evolution of physical systems objectively a manifestation of information processing by the universe? We find that an affirmative answer has important consequences for the measurement problem. In particular, we calculate the…
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some…
The kernel trick in supervised learning signifies transformations of an inner product by a feature map, which then restructures training data in a larger Hilbert space according to an endowed inner product. A quantum feature map corresponds…
Operators in ergodic spin-chains are found to grow according to hydrodynamical equations of motion. The study of such operator spreading has aided our understanding of many-body quantum chaos in spin-chains. Here we initiate the study of…
We investigate universal features of measurement-and-feedback control of quantum chaotic dynamics by examining the quantum Arnold cat map, a paradigmatic model of quantum chaos. Inspired by probabilistic control of classical chaos, our…
Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…
Classical chaotic dynamics is characterized by the exponential sensitivity to initial conditions. Quantum mechanics, however, does not show this feature. We consider instead the sensitivity of quantum evolution to perturbations in the…