89 research outputs found
Lower Bounds for Ground States of Condensed Matter Systems
Standard variational methods tend to obtain upper bounds on the ground state
energy of quantum many-body systems. Here we study a complementary method that
determines lower bounds on the ground state energy in a systematic fashion,
scales polynomially in the system size and gives direct access to correlation
functions. This is achieved by relaxing the positivity constraint on the
density matrix and replacing it by positivity constraints on moment matrices,
thus yielding a semi-definite programme. Further, the number of free parameters
in the optimization problem can be reduced dramatically under the assumption of
translational invariance. A novel numerical approach, principally a combination
of a projected gradient algorithm with Dykstra's algorithm, for solving the
optimization problem in a memory-efficient manner is presented and a proof of
convergence for this iterative method is given. Numerical experiments that
determine lower bounds on the ground state energies for the Ising and
Heisenberg Hamiltonians confirm that the approach can be applied to large
systems, especially under the assumption of translational invariance.Comment: 16 pages, 4 figures, replaced with published versio
Efficient and feasible state tomography of quantum many-body systems
We present a novel method to perform quantum state tomography for
many-particle systems which are particularly suitable for estimating states in
lattice systems such as of ultra-cold atoms in optical lattices. We show that
the need for measuring a tomographically complete set of observables can be
overcome by letting the state evolve under some suitably chosen random circuits
followed by the measurement of a single observable. We generalize known results
about the approximation of unitary 2-designs, i.e., certain classes of random
unitary matrices, by random quantum circuits and connect our findings to the
theory of quantum compressed sensing. We show that for ultra-cold atoms in
optical lattices established techniques like optical super-lattices, laser
speckles, and time-of-flight measurements are sufficient to perform fully
certified, assumption-free tomography. Combining our approach with tensor
network methods - in particular the theory of matrix-product states - we
identify situations where the effort of reconstruction is even constant in the
number of lattice sites, allowing in principle to perform tomography on
large-scale systems readily available in present experiments.Comment: 10 pages, 3 figures, minor corrections, discussion added, emphasizing
that no single-site addressing is needed at any stage of the scheme when
implemented in optical lattice system
Quantum Discord and entropic measures of quantum correlations: Optimization and behavior in finite spin chains
We discuss a generalization of the conditional entropy and one-way
information deficit in quantum systems, based on general entropic forms. The
formalism allows to consider simple entropic forms for which a closed
evaluation of the associated optimization problem in qudit-qubit systems is
shown to become feasible, allowing to approximate that of the quantum discord.
As application, we examine quantum correlations of spin pairs in the exact
ground state of finite spin chains in a magnetic field through the quantum
discord and information deficit. While these quantities show a similar
behavior, their optimizing measurements exhibit significant differences, which
can be understood and predicted through the previous approximations. The
remarkable behavior of these quantities in the vicinity of transverse and
non-transverse factorizing fields is also discussed.Comment: 10 pages, 3 figure
Using online databases to produce comprehensive accounts of the vascular plants from the Brazilian protected areas: The Parque Nacional do Itatiaia as a case study.
Brazil is one of the most biodiverse countries in the world, with about 37,000 species of land plants. Part of this biodiversity is within protected areas. The development of online databases in the last years greatly improved the available biodiversity data. However, the existing databases do not provide information about the protected areas in which individual plant species occur. The lack of such information is a crucial gap for conservation actions. This study aimed to show how the information captured from online databases, cleaned by a protocol and verified by taxonomists allowed us to obtain a comprehensive list of the vascular plant species from the "Parque Nacional do Itatiaia", the first national park founded in Brazil. All existing records in the online database JABOT (15,100 vouchers) were downloaded, resulting in 11,783 vouchers identified at the species level. Overall, we documented 2,316 species belonging to 176 families and 837 genera of vascular plants in the "Parque Nacional do Itatiaia". Considering the whole vascular flora, 2,238 species are native and 78 are non-native
Efficient tomography of a quantum many-body system
Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory [1]. Its application to systems with more than a few constituents (e.g. particles) soon becomes impractical as the e ff ort required grows exponentially with the number of constituents. Developing more e ffi cient techniques is particularly pressing as precisely-controllable quantum systems that are well beyond the reach of QST are emerging in laboratories. Motivated by this, there is a considerable ongoing e ff ort to develop new state characterisation tools for quantum many-body systems [2–11]. Here we demonstrate Matrix Product State (MPS) tomography [2], which is theoretically proven to allow the states of a broad class of quantum systems to be accurately estimated with an e ff ort that increases e ffi ciently with constituent number. We use the technique to reconstruct the dynamical state of a trapped-ion quantum simulator comprising up to 14 entangled and individually-controlled spins (qubits): a size far beyond the practical limits of QST. Our results reveal the dynamical growth of entanglement and description complexity as correlations spread out during a quench: a necessary condition for future beyond-classical performance. MPS tomography should therefore find widespread use to study large quantum many-body systems and to benchmark and verify quantum simulators and computers
Quantum Magnetism of Spin-Ladder Compounds with Trapped-Ion Crystals
The quest for experimental platforms that allow for the exploration, and even
control, of the interplay of low dimensionality and frustration is a
fundamental challenge in several fields of quantum many-body physics, such as
quantum magnetism. Here, we propose the use of cold crystals of trapped ions to
study a variety of frustrated quantum spin ladders. By optimizing the trap
geometry, we show how to tailor the low dimensionality of the models by
changing the number of legs of the ladders. Combined with a method for
selectively hiding of ions provided by laser addressing, it becomes possible to
synthesize stripes of both triangular and Kagome lattices. Besides, the degree
of frustration of the phonon-mediated spin interactions can be controlled by
shaping the trap frequencies. We support our theoretical considerations by
initial experiments with planar ion crystals, where a high and tunable
anisotropy of the radial trap frequencies is demonstrated. We take into account
an extensive list of possible error sources under typical experimental
conditions, and describe explicit regimes that guarantee the validity of our
scheme
Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics
We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox "absolute" quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a long-standing debate on the subject
Permutationally invariant state reconstruction
Feasible tomography schemes for large particle numbers must possess, besides
an appropriate data acquisition protocol, also an efficient way to reconstruct
the density operator from the observed finite data set. Since state
reconstruction typically requires the solution of a non-linear large-scale
optimization problem, this is a major challenge in the design of scalable
tomography schemes. Here we present an efficient state reconstruction scheme
for permutationally invariant quantum state tomography. It works for all common
state-of-the-art reconstruction principles, including, in particular, maximum
likelihood and least squares methods, which are the preferred choices in
today's experiments. This high efficiency is achieved by greatly reducing the
dimensionality of the problem employing a particular representation of
permutationally invariant states known from spin coupling combined with convex
optimization, which has clear advantages regarding speed, control and accuracy
in comparison to commonly employed numerical routines. First prototype
implementations easily allow reconstruction of a state of 20 qubits in a few
minutes on a standard computer.Comment: 25 pages, 4 figues, 2 table
Reproductive system of Eriocnema fulva Naudin (Melastomataceae), an endemic species of Minas Gerais state, SE Brazil
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