Related papers: Quantum chaos in the spectrum of operators used in…
The construction of large, coherent quantum systems necessary for quantum computation remains an entreating but elusive goal, due to the ubiquitous nature of decoherence. Recent progress in quantum error correction schemes have given new…
A set of zero-range scatterers along its axis lifts the integrability of a harmonic waveguide. Effective solution of the Schr\"odinger equation for this model is possible due to the separable nature of the scatterers and millions of…
We review the main ideas and results in the stationary problems of quantum chaos in generic (mixed) systems, whose classical dynamics has regular (invariant tori) and chaotic regions coexisting in the phase space. First we discuss the…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…
We analyze quantum computers which perform Shor's factoring algorithm, paying attention to asymptotic properties as the number L of qubits is increased. Using numerical simulations and a general theory of the stabilities of many-body…
Decoherence in quantum systems which are classically chaotic is studied. It is well-known that a classically chaotic system when quantized loses many prominent chaotic traits. We show that interaction of the quantum system with an…
Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed.…
Using the random matrix description of open quantum chaotic systems we calculate in closed form the universal autocorrelation function and the probability distribution of the total photodissociation cross section in the regime of quantum…
The appearance of chaotic quantum dynamics significantly depends on the symmetry properties of the system, and in cold atomic systems many of these can be experimentally controlled. In this work, we systematically study the emergence of…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
Quantum weak chaos is studied in a perturbed degenerate system --- a charged particle interacting with a monochromatic wave in a transverse magnetic field. The evolution operator for an arbitrary number of periods of the external field is…
Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm.…
We study the influence of errors and decoherence on both the performance of Shor's factoring algorithm and Grover's search algorithm, and on the amount of interference in these algorithms using a recently proposed interference measure. We…
Quantum chaos is a quantum many-body phenomenon that is associated with a number of intricate properties, such as level repulsion in energy spectra or distinct scalings of out-of-time ordered correlation functions. In this work, we…
We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball…
We study scarring phenomena in open quantum systems. We show numerical evidence that individual resonance eigenstates of an open quantum system present localization around unstable short periodic orbits in a similar way as their closed…
We consider stability of a general quantum algorithm with respect to a fixed but unknown residual interaction between qubits, and show a surprising fact, namely that the average fidelity of quantum computation increases by decreasing…
Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the…
Operator scrambling is a crucial ingredient of quantum chaos. Specifically, in the quantum chaotic system, a simple operator can become increasingly complicated under unitary time evolution. This can be diagnosed by various measures such as…
We study numerically the imperfection effects in the quantum computing of the kicked rotator model in the regime of quantum chaos. It is shown that there are two types of physical characteristics: for one of them the quantum computation…