Does bound entanglement naturally appear in quantum many-body systems? We address this question by showing the existence of bound-entangled thermal states for harmonic oscillator systems consisting of an arbitrary number of particles. By explicit calculations of the negativity for different partitions, we find a range of temperatures for which no entanglement can be distilled by means of local operations, despite the system being globally entangled. We offer an interpretation of this result in terms of entanglement-area laws, typical of these systems. Finally, we discuss generalizations of this result to other systems, including spin chains.
We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then, performing a controlled truncation of the resulting tensor. We benchmark this approximation procedure in two dimensions against an exact contraction. We then apply the same idea to a three dimensional system. The underlying rational for emphasizing the exact coarse graining renormalization group step prior to truncation is related to monogamy of entanglement.PACS numbers: 03.67. Mn, 05.10.Cc, 05.50.+q Computing analytically the properties of a quantum model is, in general, not possible. It is then necessary to resort to classical simulations that rely on approximation techniques. From a quantum information perspective, the presence of a small amount of entanglement in the system has been identified as the key ingredient that allows for efficient classical simulations. This has been exploited in one dimension (1D) in a series of algorithms based on a description of the system as a tensor network. Following this approach, condensed matter systems can be simulated using Matrix Product States (MPS, [1,2]) as the testbed for the variational procedure of the density-matrix renormalization group (DMRG,[3]) to study ground states of local 1D Hamiltonians. Beyond the 1D setting, the computation of physical magnitudes using tensor networks is limited by the numerical effort necessary to perform the contraction of the tensor network, i.e. to sum all its indices. The efficiency for performing this task is limited by the area law scaling of the entanglement entropy in the system [4][5][6][7]. To overcome this problem, several strategies aim at finding the best possible approximation to the contraction of tensor networks after identifying the relevant degrees of freedom of the system [8][9][10].Let us briefly recall the key elements of the tensor network representation. Given a quantum state of N particles |ψ = c i1,...,iN |i 1 . . . i N its coefficients can be represented as a contraction of local tensors c i1,...,iN = tr(A 1,i1 . . . A N,iN ), where each local tensor A j carries a physical index i j and ancillary indices (which are not written) that get contracted according to a prescribed geometry. The rank of these ancillary indices, that we shall call χ, controls the amount of entanglement which is captured by the tensor representation. If the tensors are simple matrices on a line, the tensor network is called MPS [1,2]. Other possible geometries are regular squared grids in any dimensions that correspond to PEPS [11], and tree-like structures that go under the name of TTN [12] and MERA [13].In this letter we propose a new strategy to contract tensor networks in general geometries, that we shall illustrate in detail for PEPS in 2D and 3D. The method is based on following as strictly as possible the renormalization group (RG) philosophy. First, an exact contraction of a set of local tenso...
We address the presence of bound entanglement in strongly-interacting spin systems at thermal equilibrium. In particular, we consider thermal graph states composed of an arbitrary number of particles. We show that for a certain range of temperatures no entanglement can be extracted by means of local operations and classical communication, even though the system is still entangled. This is found by harnessing the independence of the entanglement in some bipartitions of such states with the system's size. Specific examples for one-and two-dimensional systems are given. Our results thus prove the existence of thermal bound entanglement in an arbitrary large spin system with finite-range local interactions.
A single-qubit circuit can approximate any bounded complex function stored in the degrees of freedom defining its quantum gates. The single-qubit approximant presented in this work is operated through a series of gates that take as their parameterization the independent variable of the target function and an additional set of adjustable parameters. The independent variable is re-uploaded in every gate while the parameters are optimized for each target function. The output state of this quantum circuit becomes more accurate as the number of re-uploadings of the independent variable increases, i. e., as more layers of gates parameterized with the independent variable are applied. In this work, we provide two different proofs of this claim related to both Fourier series and the Universal Approximation Theorem for Neural Networks, and we benchmark both methods against their classical counterparts. We further implement a single-qubit approximant in a real superconducting qubit device, demonstrating how the ability to describe a set of functions improves with the depth of the quantum circuit. This work shows the robustness of the re-uploading technique on Quantum Machine Learning.
We present Qibo, a new open-source software for fast evaluation of quantum circuits and adiabatic evolution which takes full advantage of hardware accelerators. The growing interest in quantum computing and the recent developments of quantum hardware devices motivates the development of new advanced computational tools focused on performance and usage simplicity. In this work we introduce a new quantum simulation framework that enables developers to delegate all complicated aspects of hardware or platform implementation to the library so they can focus on the problem and quantum algorithms at hand. This software is designed from scratch with simulation performance, code simplicity and user friendly interface as target goals. It takes advantage of hardware acceleration such as multi-threading CPU, single GPU and multi-GPU devices.
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