Related papers: Quantum Chaos and Quantum Algorithms
As a model of decohering environment, we show that quantum chaotic system behave equivalently as many-body system. An approximate formula for the time evolution of the reduced density matrix of a system interacting with a quantum chaotic…
The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic…
The standard setting of quantum computation for continuous problems uses deterministic queries and the only source of randomness for quantum algorithms is through measurement. This setting is related to the worst case setting on a classical…
We speak of chaos in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
Decoherence in quantum systems which are classically chaotic is studied. The Arnold cat map and the quantum kicked rotor are chosen as examples of linear and nonlinear chaotic systems. The Feynman-Vernon influence functional formalism is…
We investigate the transition to quantum chaos, induced by static imperfections, for an operating quantum computer that simulates efficiently a dynamical quantum system, the sawtooth map. For the different dynamical regimes of the map, we…
The manner in which unpredictable chaotic dynamics manifests itself in quantum mechanics is a key question in the field of quantum chaos. Indeed, very distinct quantum features can appear due to underlying classical nonlinear dynamics. Here…
We introduce an analytical solution to the one of the most familiar problems from the elementary quantum mechanics textbooks. The following discussion provides simple illustrations to a number of general concepts of quantum chaology, along…
According to general relativity, the generic early-universe dynamics is chaotic. Various quantum-gravity effects have been suggested that may change this behavior in different ways. Here, it is shown how key mathematical properties of the…
We study a two-spin quantum Turing architecture, in which discrete local rotations \alpha_m of the Turing head spin alternate with quantum controlled NOT-operations. Substitution sequences are known to underlie aperiodic structures. We show…
In this work, the term ``quantum chaos'' refers to spectral correlations similar to those found in the random matrix theory. Quantum chaos can be diagnosed through the analysis of level statistics using e.g.~the spectral form factor, which…
It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more…
A flagship application of quantum computers is the simulation of other quantum systems, including quantum field theories. In this article, we show how quantum computers can be employed to naturally calculate Feynman diagrams and their…
A Quantum Computer is a new type of computer which can solve problems such as factoring and database search very efficiently. The usefulness of a quantum computer is limited by the effect of two different types of errors, decoherence and…
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. We demonstrate numerically that…
A simple experiment using radioactive decay is proposed to test the possibility of a determinsistic, but chaotic, origin of quantum mechanical randomness.
The presence of chaos and quantum chaos is shown in two different nuclear systems. We analyze the chaotic behaviour of the classical SU(2) Yang--Mills--Higgs system, and then we study quantum chaos in the nuclear shell model calculating the…
Besides the superior efficiency compared to their classical counterparts, quantum algorithms known so far are basically task-dependent, and scarcely any common features are shared between them. In this work, however, we show that the…
Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that…