Bounds on universal quantum computation with perturbed 2d cluster states

Motivated by the possibility of universal quantum computation under noise perturbations, we compute the phase diagram of the 2d cluster state Hamiltonian in the presence of Ising terms and magnetic fields. Unlike in previous analysis of perturbed 2d cluster states, we find strong evidence of a very well defined cluster phase, separated from a polarized phase by a line of 1st and 2nd order transitions compatible with the 3d Ising universality class and a tricritical end point. The phase boundary sets an upper bound for the amount of perturbation in the system so that its ground state is still useful for measurement-based quantum computation purposes. Moreover, we also compute the local fidelity with the unperturbed 2d cluster state. Besides a classical approximation, we determine the phase diagram by combining series expansions and variational infinite Projected entangled-Pair States (iPEPS) methods. Our work constitutes the first analysis of the non-trivial effect of few-body perturbations in the 2d cluster state, which is of relevance for experimental proposals.Comment: 7 pages, 4 figures, revised version, to appear in PR

Fate of the cluster state on the square lattice in a magnetic field

The cluster state represents a highly entangled state which is one central object for measurement-based quantum computing. Here we study the robustness of the cluster state on the two-dimensional square lattice at zero temperature in the presence of external magnetic fields by means of different types of high-order series expansions and variational techniques using infinite Projected Entangled Pair States (iPEPS). The phase diagram displays a first-order phase transition line ending in two critical end points. Furthermore, it contains a characteristic self-dual line in parameter space allowing many precise statements. The self-duality is shown to exist on any lattice topology.Comment: 12 pages, 9 figure

Critical current modulation induced by an electric field in superconducting tungsten-carbon nanowires

The critical current of a superconducting nanostructure can be suppressed by applying an electric field in its vicinity. This phenomenon is investigated throughout the fabrication and electrical characterization of superconducting tungsten-carbon (W-C) nanostructures grown by Ga+ focused ion beam induced deposition (FIBID). In a 45 nm-wide, 2.7 mu m-long W-C nanowire, an increasing side-gate voltage is found to progressively reduce the critical current of the device, down to a full suppression of the superconducting state below its critical temperature. This modulation is accounted for by the squeezing of the superconducting current by the electric field within a theoretical model based on the Ginzburg-Landau theory, in agreement with experimental data. Compared to electron beam lithography or sputtering, the single-step FIBID approach provides with enhanced patterning flexibility and yields nanodevices with figures of merit comparable to those retrieved in other superconducting materials, including Ti, Nb, and Al. Exhibiting a higher critical temperature than most of other superconductors, in which this phenomenon has been observed, as well as a reduced critical value of the gate voltage required to fully suppress superconductivity, W-C deposits are strong candidates for the fabrication of nanodevices based on the electric field-induced superconductivity modulation

Entanglement, subsystem particle numbers and topology in free fermion systems

We study the relationship between bipartite entanglement, subsystem particle number and topology in a half-filled free fermion system. It is proposed that the spin-projected particle numbers can distinguish the quantum spin Hall state from other states, and can be used to establish a new topological index for the system. Furthermore, we apply the new topological invariant to a disordered system and show that a topological phase transition occurs when the disorder strength is increased beyond a critical value. It is also shown that the subsystem particle number fluctuation displays behavior very similar to that of the entanglement entropy. This provides a lower-bound estimation for the entanglement entropy, which can be utilized to obtain an estimate of the entanglement entropy experimentally.Comment: 14 pages, 6 figure

Non-perturbative k-body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins

An algebraic method has been developed which allows one to engineer several energy levels including the low-energy subspace of interacting spin systems. By introducing ancillary qubits, this approach allows k-body interactions to be captured exactly using 2-body Hamiltonians. Our method works when all terms in the Hamiltonian share the same basis and has no dependence on perturbation theory or the associated large spectral gap. Our methods allow problem instance solutions to be embedded into the ground energy state of Ising spin systems. Adiabatic evolution might then be used to place a computational system into it's ground state.Comment: Published versio

Numerical study of the one-dimensional quantum compass model

The ground state magnetic phase diagram of the one-dimensional quantum compass model (QCM) is studied using the numerical Lanczos method. A detailed numerical analysis of the low energy excitation spectrum is presented. The energy gap and the spin-spin correlation functions are calculated for finite chains. Two kind of the magnetic long-range orders, the Neel and a type of the stripe-antiferromagnet, in the ground state phase diagram are identified. Based on the numerical analysis, the first and second order quantum phase transitions in the ground state phase diagram are identified.Comment: 6 pages, 8 figures. arXiv admin note: text overlap with arXiv:1105.211

Electron density extrapolation above F2 peak by the linear Vary-Chap model supporting new Global Navigation Satellite Systems-LEO occultation missions

The new radio-occultation (RO) instrument on board the future EUMETSAT Polar System-Second Generation (EPS-SG) satellites, flying at a height of 820 km, is primarily focusing on neutral atmospheric profiling. It will also provide an opportunity for RO ionospheric sounding, but only below impact heights of 500 km, in order to guarantee a full data gathering of the neutral part. This will leave a gap of 320 km, which impedes the application of the direct inversion techniques to retrieve the electron density profile. To overcome this challenge, we have looked for new ways (accurate and simple) of extrapolating the electron density (also applicable to other low-Earth orbiting, LEO, missions like CHAMP): a new Vary-Chap Extrapolation Technique (VCET). VCET is based on the scale height behavior, linearly dependent on the altitude above hmF2. This allows extrapolating the electron density profile for impact heights above its peak height (this is the case for EPS-SG), up to the satellite orbital height. VCET has been assessed with more than 3700 complete electron density profiles obtained in four representative scenarios of the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) in the United States and the Formosa Satellite Mission 3 (FORMOSAT-3) in Taiwan, in solar maximum and minimum conditions, and geomagnetically disturbed conditions, by applying an updated Improved Abel Transform Inversion technique to dual-frequency GPS measurements. It is shown that VCET performs much better than other classical Chapman models, with 60% of occultations showing relative extrapolation errors below 20%, in contrast with conventional Chapman model extrapolation approaches with 10% or less of the profiles with relative error below 20%.Peer ReviewedPostprint (published version

Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition

In a previous paper we examined a geometric measure of entanglement based on the minimum distance between the entangled target state of interest and the space of unnormalized product states. Here we present a detailed study of this entanglement measure for target states with a large degree of symmetry. We obtain analytic solutions for the extrema of the distance function and solve for the Hessian to show that, up to the action of trivial symmetries, the solutions correspond to local minima of the distance function. In addition, we show that the conditions that determine the extremal solutions for general target states can be obtained directly by parametrizing the product states via their Schmidt decomposition.Comment: 16 pages, references added and discussion expande

Entanglement and alpha entropies for a massive Dirac field in two dimensions

We present some exact results about universal quantities derived from the local density matrix, for a free massive Dirac field in two dimensions. We first find the trace of powers of the density matrix in a novel fashion, which involves the correlators of suitable operators in the sine-Gordon model. These, in turn, can be written exactly in terms of the solutions of non-linear differential equations of the Painlev\'e V type. Equipped with the previous results, we find the leading terms for the entanglement entropy, both for short and long distances, and showing that in the intermediate regime it can be expanded in a series of multiple integrals. The previous results have been checked by direct numerical calculations on the lattice, finding perfect agreement. Finally, we comment on a possible generalization of the entanglement entropy c-theorem to the alpha-entropies.Comment: Clarification in section 2, one reference added. 15 pages, 3 figure