66 research outputs found
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 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
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
Block Spin Density Matrix of the Inhomogeneous AKLT Model
We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain
model. Spins at each lattice site could be different. Under certain conditions,
the ground state of this AKLT model is unique and is described by the
Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous
block of bulk spins in this ground state. The density matrix is independent of
spins outside the block. It is diagonalized and shown to be a projector onto a
subspace. We prove that for large block the density matrix behaves as the
identity in the subspace. The von Neumann entropy coincides with Renyi entropy
and is equal to the saturated value.Comment: 20 page
The Interspersed Spin Boson Lattice Model
We describe a family of lattice models that support a new class of quantum
magnetism characterized by correlated spin and bosonic ordering [Phys. Rev.
Lett. 112, 180405 (2014)]. We explore the full phase diagram of the model using
Matrix-Product-State methods. Guided by these numerical results, we describe a
modified variational ansatz to improve our analytic description of the
groundstate at low boson frequencies. Additionally, we introduce an
experimental protocol capable of inferring the low-energy excitations of the
system by means of Fano scattering spectroscopy. Finally, we discuss the
implementation and characterization of this model with current circuit-QED
technology.Comment: Submitted to EPJ ST issue on "Novel Quantum Phases and Mesoscopic
Physics in Quantum Gases
Entanglement Entropy dynamics in Heisenberg chains
By means of the time-dependent density matrix renormalization group algorithm
we study the zero-temperature dynamics of the Von Neumann entropy of a block of
spins in a Heisenberg chain after a sudden quench in the anisotropy parameter.
In the absence of any disorder the block entropy increases linearly with time
and then saturates. We analyze the velocity of propagation of the entanglement
as a function of the initial and final anisotropies and compare, wherever
possible, our results with those obtained by means of Conformal Field Theory.
In the disordered case we find a slower (logarithmic) evolution which may
signals the onset of entanglement localization.Comment: 15 pages, 9 figure
Entanglement and Density Matrix of a Block of Spins in AKLT Model
We study a 1-dimensional AKLT spin chain, consisting of spins in the bulk
and at both ends. The unique ground state of this AKLT model is described
by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a
contiguous block of bulk spins in this ground state. It is shown that the
density matrix is a projector onto a subspace of dimension . This
subspace is described by non-zero eigenvalues and corresponding eigenvectors of
the density matrix. We prove that for large block the von Neumann entropy
coincides with Renyi entropy and is equal to .Comment: Revised version, typos corrected, references added, 31 page
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