E. Novais

Quantum Magnetic Impurities in Magnetically Ordered Systems

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.

Surface Code Threshold in the Presence of Correlated Errors

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.

Nuclear spin qubits in a pseudospin quantum chain

We analyze a quantum-computer design based on nuclear spin qubits in a quasi-one-dimensional chain of non-Kramers doublet atoms. We explore the use of spatial symmetry breaking to obtain control over the local dynamics of a qubit. We also study the decoherence mechanisms at the single qubit level and the interactions mediated by the magnetic media. The design can be realized in

Coulomb gas approach to the anisotropic one-dimensional Kondo lattice model at arbitrary filling

{\mathrm{PrBr}}_{3\ensuremath{-}x}{\mathrm{F}}_{x}

Fidelity threshold of the surface code beyond single-qubit error models

with nuclear magnetic resonance techniques.

Phase diagram of the anisotropic Kondo chain.

We establish a mapping of a general spin-fermion system in one dimension into a classical generalized Coulomb gas. This mapping allows a renormalization-group treatment of the anisotropic Kondo chain both at and away fromhalf-filling. We find that the phase diagram contains regions of paramagnetism, partial, and full ferromagnetic order. We also use the method to analyze the phases of the Ising-Kondo chain.

Surface code fidelity at finite temperatures

The surface code is one the most promising alternatives for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attrative 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.

Fixed Points of the Dissipative Hofstadter Model

We establish the phase diagram of the one-dimensional anisotropic Kondo lattice model at T = 0 using a generalized two-dimensional classical Coulomb gas description. We analyze the problem by means of a renormalization group treatment. We find that the phase diagram contains regions of paramagnetism, partial and full ferromagnetic order.

Rescuing a Quantum Phase Transition with Quantum Noise

We study the dependence of the fidelity of the surface code in the presence of a single finite-temperature massless bosonic environment after a quantum error correction cycle. The three standard types of environment are considered: super-Ohmic, Ohmic, and sub-Ohmic. Our results show that, for regimes relevant to current experiments, quantum error correction works well even in the presence of environment-induced, long-range inter-qubit interactions. A threshold always exists at finite temperatures, although its temperature dependence is very sensitive to the type of environment. For the super-Ohmic case, the critical coupling constant separating high- from low-fidelity decreases with increasing temperature. For both Ohmic and super-Ohmic cases, the dependence of the critical coupling on temperature is weak. In all cases, the critical coupling is determined by microscopic parameters of the environment. For the sub-Ohmic case, it also depends strongly on the duration of the QEC cycle.

Long-time efficacy of the surface code in the presence of a super-Ohmic environment

The phase diagram of a dissipative particle in a periodic potential and a magnetic field is studied in the weak barrier limit and in the tight binding regime. For the case of half flux per plaquette, and for a wide range of values of the dissipation, the physics of the model is determined by a nontrivial fixed point. A combination of exact and variational results is used to characterize this fixed point. Finally, it is also argued that there is an intermediate energy scale that separates the weak coupling physics from the tight binding solution.