Fidelity of the surface code in the presence of a bosonic bath

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

Universal Properties in Low Dimensional Fermionic Systems and Bosonization

We analyze the universal transport behavior in 1D and 2D fermionic systems by following the unified framework provided by bosonization. The role played by the adiabatic transition between interacting and noninteracting regions is emphasized.Comment: 2 pages, RevTex, contribution for the Proceedings of the XVIII Autumn School `Topology of Strongly Correlated Systems', Lisbon, Portugal, October, 200

Surface code fidelity at finite temperatures

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.Comment: 13 pages, 6 figure

Fast counting with tensor networks

We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of satisfying assignments of that formula, and use graph theoretical methods to determine favorable orders of contraction. We employ our heuristics for the solution of #P-hard counting boolean satisfiability (#SAT) problems, namely monotone #1-in-3SAT and #Cubic-Vertex-Cover, and find that they outperform state-of-the-art solvers by a significant margin.Comment: v2: added results for monotone #1-in-3SAT; published versio

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.Comment: 5 pages, 2 figure

Adiabatic Charge Pumping through Quantum Dots in the Coulomb Blockade Regime

We investigate the influence of the Coulomb interaction on the adiabatic pumping current through quantum dots. Using nonequilibrium Green's functions techniques, we derive a general expression for the current based on the instantaneous Green's function of the dot. We apply this formula to study the dependence of the charge pumped per cycle on the time-dependent pumping potentials. The possibility of charge quantization in the presence of a finite Coulomb repulsion energy is investigated in the light of recent experiments.Comment: 11 pages, 10 figure

A tight-binding model for MoS2_2 monolayers

We propose an accurate tight-binding parametrization for the band structure of MoS$_2$ monolayers near the main energy gap. We introduce a generic and straightforward derivation for the band energies equations that could be employed for other monolayer dichalcogenides. A parametrization that includes spin-orbit coupling is also provided. The proposed set of model parameters reproduce both the correct orbital compositions and location of valence and conductance band in comparison with ab initio calculations. The model gives a suitable starting point for realistic large-scale atomistic electronic transport calculations.Comment: 35 pages, 8 figure