18,698 research outputs found
Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians
A key feature of ground states of gapped local 1D Hamiltonians is their
relatively low entanglement --- they are well approximated by matrix product
states (MPS) with bond dimension scaling polynomially in the length of the
chain, while general states require a bond dimension scaling exponentially. We
show that the bond dimension of these MPS approximations can be improved to a
constant, independent of the chain length, if we relax our notion of
approximation to be more local: for all length- segments of the chain, the
reduced density matrices of our approximations are -close to those of
the exact state. If the state is a ground state of a gapped local Hamiltonian,
the bond dimension of the approximation scales like ,
and at the expense of worse but still scaling of
the bond dimension, we give an alternate construction with the additional
features that it can be generated by a constant-depth quantum circuit with
nearest-neighbor gates, and that it applies generally for any state with
exponentially decaying correlations. For a completely general state, we give an
approximation with bond dimension , which is exponentially
worse, but still independent of . Then, we consider the prospect of
designing an algorithm to find a local approximation for ground states of
gapped local 1D Hamiltonians. When the Hamiltonian is translationally
invariant, we show that the ability to find -accurate local
approximations to the ground state in time implies the ability to
estimate the ground state energy to precision in time.Comment: 24 pages, 3 figures. v2: Theorem 1 extended to include construction
for general states; Lemma 7 & Theorem 2 slightly improved; figures added;
lemmas rearranged for clarity; typos fixed. v3: Reformatted & additional
references inserte
The q-gradient method for global optimization
The q-gradient is an extension of the classical gradient vector based on the
concept of Jackson's derivative. Here we introduce a preliminary version of the
q-gradient method for unconstrained global optimization. The main idea behind
our approach is the use of the negative of the q-gradient of the objective
function as the search direction. In this sense, the method here proposed is a
generalization of the well-known steepest descent method. The use of Jackson's
derivative has shown to be an effective mechanism for escaping from local
minima. The q-gradient method is complemented with strategies to generate the
parameter q and to compute the step length in a way that the search process
gradually shifts from global in the beginning to almost local search in the
end. For testing this new approach, we considered six commonly used test
functions and compared our results with three Genetic Algorithms (GAs)
considered effective in optimizing multidimensional unimodal and multimodal
functions. For the multimodal test functions, the q-gradient method
outperformed the GAs, reaching the minimum with a better accuracy and with less
function evaluations.Comment: 12 pages, 1 figur
Witnessed Entanglement
We present a new measure of entanglement for mixed states. It can be
approximately computable for every state and can be used to quantify all
different types of multipartite entanglement. We show that it satisfies the
usual properties of a good entanglement quantifier and derive relations between
it and other entanglement measures.Comment: Revised version. 7 pages and one figur
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Centrolene savagei
Number of Pages: 11Geological SciencesIntegrative Biolog
Phantom cosmologies and fermions
Form invariance transformations can be used for constructing phantom
cosmologies starting with conventional cosmological models. In this work we
reconsider the scalar field case and extend the discussion to fermionic fields,
where the "phantomization" process exhibits a new class of possible accelerated
regimes. As an application we analyze the cosmological constant group for a
fermionic seed fluid.Comment: 5 pages, version which was accepted for publication in CQ
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