Equivalent qubit dynamics under classical and quantum noise

We study the dynamics of quantum systems under classical and quantum noise, focusing on decoherence in qubit systems. Classical noise is described by a random process leading to a stochastic temporal evolution of a closed quantum system, whereas quantum noise originates from the coupling of the microscopic quantum system to its macroscopic environment. We derive deterministic master equations describing the average evolution of the quantum system under classical continuous-time Markovian noise and two sets of master equations under quantum noise. Strikingly, these three equations of motion are shown to be equivalent in the case of classical random telegraph noise and proper quantum environments. Hence fully quantum-mechanical models within the Born approximation can be mapped to a quantum system under classical noise. Furthermore, we apply the derived equations together with pulse optimization techniques to achieve high-fidelity one-qubit operations under random telegraph noise, and hence fight decoherence in these systems of great practical interest.Comment: 5 pages, 2 figures; converted to PRA format, added Fig. 2, corrected typo

The Linear Boltzmann Equation as the Low Density Limit of a Random Schrodinger Equation

We study the evolution of a quantum particle interacting with a random potential in the low density limit (Boltzmann-Grad). The phase space density of the quantum evolution defined through the Husimi function converges weakly to a linear Boltzmann equation with collision kernel given by the full quantum scattering cross section.Comment: 74 pages, 4 figures, (Final version -- typos corrected

Universal spectra of random Lindblad operators

To understand typical dynamics of an open quantum system in continuous time, we introduce an ensemble of random Lindblad operators, which generate Markovian completely positive evolution in the space of density matrices. Spectral properties of these operators, including the shape of the spectrum in the complex plane, are evaluated by using methods of free probabilities and explained with non-Hermitian random matrix models. We also demonstrate universality of the spectral features. The notion of ensemble of random generators of Markovian qauntum evolution constitutes a step towards categorization of dissipative quantum chaos.Comment: 6 pages, 4 figures + supplemental materia

Quantum walks can unitarily match random walks on finite graphs

Quantum and random walks were proven to be equivalent on finite graphs by demonstrating how to construct a time-dependent random walk sharing the exact same evolution of vertex probability of any given discrete-time coined quantum walk. Such equivalence stipulated a deep connection between the processes that is far stronger than simply considering quantum walks as quantum analogues of random walks. This article expands on the connection between quantum and random walks by demonstrating a procedure that constructs a time-dependent quantum walk matching the evolution of vertex probability of any given random walk in a unitary way. It is a trivial fact that a quantum walk measured at all time steps of its evolution degrades to a random walk. More interestingly, the method presented describes a quantum walk that matches a random walk without measurement operations, such that the unitary evolution of the quantum walk captures the probability evolution of the random walk. The construction procedure is general, covering both homogeneous and non-homogeneous random walks. For the homogeneous random walk case, the properties of unitary evolution imply that the quantum walk described is time-dependent since homogeneous quantum walks do not converge for arbitrary initial conditionsComment: 9 pages, 1 figur

Entanglement Generation of Nearly-Random Operators

We study the entanglement generation of operators whose statistical properties approach those of random matrices but are restricted in some way. These include interpolating ensemble matrices, where the interval of the independent random parameters are restricted, pseudo-random operators, where there are far fewer random parameters than required for random matrices, and quantum chaotic evolution. Restricting randomness in different ways allows us to probe connections between entanglement and randomness. We comment on which properties affect entanglement generation and discuss ways of efficiently producing random states on a quantum computer.Comment: 5 pages, 3 figures, partially supersedes quant-ph/040505

Measurement master equation

We derive a master equation describing the evolution of a quantum system subjected to a sequence of observations. These measurements occur randomly at a given rate and can be of a very general form. As an example, we analyse the effects of these measurements on the evolution of a two-level atom driven by an electromagnetic field. For the associated quantum trajectories we find Rabi oscillations, Zeno-effect type behaviour and random telegraph evolution spawned by mini quantum jumps as we change the rates and strengths of measurement.Comment: 14 pages and 8 figures, Optics Communications in pres