Thermal rectification is the phenomenon by which the flux of heat depends on the direction of the flow. It has attracted much interest in recent years due to the possibility of devising thermal diodes. In this paper, we consider the rectification phenomenon in the quantum XXZ chain subject to an inhomogeneous field. The chain is driven out of equilibrium by the contact at its boundaries with two different reservoirs, leading to a constant flow of magnetization from one bath to the other. The nonunitary dynamics of this system, which is modeled by a Lindblad master equation, is treated exactly for small sizes and numerically for larger ones. The functional dependence of the rectification coefficient on the model parameters (anisotropy, field amplitude, and out of equilibrium driving strength) is investigated in full detail. Close to the XX point and at small inhomogeneity and low driving, we have found an explicit expression for the rectification coefficient that is valid at all system sizes. In particular, it shows that the phenomenon of rectification persists even in the thermodynamic limit. Finally, we prove that in the case of the XX chain, there is no rectification.

We study a model of frustration of decoherence in an open quantum system. Contrary to other dissipative Ohmic impurity models, such as the Kondo model or the dissipative two-level system, the impurity model discussed here never presents overdamped dynamics even for strong coupling to the environment. We show that this unusual effect has its origins in the quantum-mechanical nature of the coupling between the quantum impurity and the environment. We study the problem using analytic and numerical renormalization group methods and obtain expressions for the frequency and temperature dependence of the impurity susceptibility in different regimes.

We discuss the problem of a spin 1/2 impurity immersed in a spin S magnetically ordered background. We show that the problem maps onto a generalization of the dissipative two level system with two independent heat baths, associated with the Goldstone modes of the magnet, that couple to different components of the impurity spin operator. Using analytical perturbative renormalization group methods and accurate numerical renormalization group we show that contrary to other dissipative models there is quantum frustration of decoherence and quasiscaling even in the strong coupling regime. We make predictions for the behavior of the impurity magnetic susceptibility. Our results may also have relevance to quantum computation.

We study the fidelity of the surface code in the presence of correlated errors induced by the coupling of physical qubits to a bosonic environment. By mapping the time evolution of the system after one quantum error correction cycle onto a statistical spin model, we show that the existence of an error threshold is related to the appearance of an order-disorder phase transition in the statistical model in the thermodynamic limit. This allows us to relate the error threshold to bath parameters and to the spatial range of the correlated errors.Comment: 5 pages, 2 figure

, in press Phys. Rev. Lett. 97, 040501 (2006)) We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. The general theory is then applied to the spin-boson model. Our results demonstrate that effects of long-range correlations can be systematically reduced by small changes in the error correction codes.PACS numbers: 03.67. Lx,03.67.Pp,03.65.Yz, Quantum computers bear the promise to solve certain problems exponentially faster than their classical counterparts [1]. Although small computers have been successfully tested [2], the development of large computers has been hindered by decoherence. The most promising method to tame decoherence is quantum error correction (QEC) [1,2,3,4]. In QEC, it is usually assumed that correlations in the environment either are non-existent or decay exponentially in time and space. In contrast, recent work argues that correlated environments can lead to quadratically worse error-levels [5,6,7,8]. Though the assumption of uncorrelated noise is often reasonable, it is not fulfilled in several physical systems proposed for realizing quantum computers, notably solid state systems using superconductors [9] or quantum dots [10]. Hence, it is far from clear how much protection from decoherence QEC gives in these important cases [5,7].In this paper, we consider the long time dynamics of a quantum computer immersed in a correlated quantum environment and protected by QEC. First, we describe the parameters which quantify the level of protection from QEC and give explicit expressions for them. Second, we calculate these quantities in a concrete example: the spin-boson model [11]. This model is directly applicable to solid state quantum computers [9,10] but formally outside the scope of QEC [7].Our work shows that some protection against longrange correlations can be built into QEC codes. The new element here is that the periodic measurements in the QEC method separate the environmental modes into high and low frequencies. This natural "new" scale can then be used to engineer quantum codes to better cope with the long-range correlations.To follow the long time behavior of the computer, we remove non-essential elements and assume: (1) Quantum gates are perfect and operate much more quickly than the characteristic response of the environment. (2) States of the computer can be prepared with no errors. (3) Thermal fluctuations are suppressed. Finally, for clarity in the spin-boson example, we consider ohmic coupling between the environment and the qubits. Extensions to sub-ohmic and super-ohmic coupling are straightforward.Decoherence, QEC, and correlations-The wave functions of the computer and the environment are unavoidably entangled during their time evolution. When a measurement is performed, this entanglement is translated into the ...

The surface code is a promising alternative for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attractive features. We develop an exact formulation for the fidelity of the surface code that allows us to probe much further on this promise of strong protection. This formulation goes beyond the stochastic single-qubit error model approximation and can take into account both correlated errors and inhomogeneities in the coupling between physical qubits and the environment. For the case of a bit-flipping environment, we map the complete evolution after one quantum error correction cycle onto the problem of computing correlation functions of a two-dimensional Ising model with boundary fields. Exact results for the fidelity threshold of the surface code are then obtained for several relevant types of noise. Analytical predictions for a representative case are confirmed by Monte Carlo simulations.

Tailoring the properties of magnetic vortices through the preparation of structured multilayers is discussed. The dependence of the vortex core radius r on the effective anisotropy is derived within a simple model, which agrees with our simulations. As the perpendicular anisotropy increases, r also increases until a perpendicular magnetization appears in the disk rim. Co/Pt multilayer disks were studied; x-ray microscopy confirms qualitatively the predicted behavior. This is a favorable system for implementing vortex-based spin-transfer nano-oscillator devices, with enhanced rf power resulting both from the increase in the core size and synchronization afforded by the coupling of the Co layers.

We study the resilience of the surface code to decoherence caused by the presence of a bosonic bath. This approach allows us to go beyond the standard stochastic error model commonly used to quantify decoherence and error threshold probabilities in this system. The full quantum mechanical system-bath dynamics is computed exactly over one quantum error correction cycle. Since all physical qubits interact with the bath, space-time correlations between errors are taken into account. We compute the fidelity of the surface code as a function of the quantum error correction time. The calculation allows us to map the problem onto an Ising-like statistical spin model with two-body interactions and a fictitious temperature which is related to the inverse bath coupling constant. The model departs from the usual Ising model in the sense that interactions can be long ranged and can involve complex exchange couplings; in addition, the number of allowed configurations is restricted by the syndrome extraction. Using analytical estimates and numerical calculations, we argue that, in the limit of an infinite number of physical qubits, the spin model sustain a phase transition which can be associated to the existence of an error threshold in the surface code. An estimate of the transition point is given for the case of nearest-neighbor interactions.Comment: 15 pages, 5 figure