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7 results for “Tensor Network”
Code and Data for "Anticoncentration and state design of random tensor networks"
<p>We investigate quantum random tensor network states where the bond dimensions scale polynomially with the system size, N. Specifically, we examine the delocalization properties of random Matrix Product States (RMPS) in the computational basis by deriving an exact analytical expression for the Inverse Participation Ratio (IPR) of any degree, applicable to both open and closed boundary conditions. For bond dimensions χ∼γN, we determine the leading order of the associated overlaps probability distribution and demonstrate its convergence to the Porter-Thomas distribution, characteristic of Haar-random states, as γ increases. Additionally, we provide numerical evidence for the frame potential, measuring the 2-distance from the Haar ensemble, which confirms the convergence of random MPS to Haar-like behavior for χ≫\sqrt{N}. We extend this analysis to two-dimensional systems using random Projected Entangled Pair States (PEPS), where we similarly observe the convergence of IPRs to their Haar values for χ≫\sqrt{N}. These findings demonstrate that random tensor networks with bond dimensions scaling polynomially in the system size are fully Haar-anticoncentrated and approximate unitary designs, regardless of the spatial dimension.</p>
Dataset: Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model
<p>Dataset</p> <p>Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model</p> <p>Ryui Kaneko, Ippei Danshita</p>
Data associated to the paper "Reduced basis surrogates for quantum spin systems based on tensor networks"
<p>Within the reduced basis methods approach, an effective low-dimensional subspace of a quantum many-body Hilbert space is constructed in order to investigate, e.g., the ground-state phase diagram. The basis of this subspace is built from solutions of snapshots, i.e., ground states corresponding to particular and well-chosen parameter values. Here, we show how a greedy strategy to assemble the reduced basis and thus to select the parameter points can be implemented based on matrix-product-state calculations. Once the reduced basis has been obtained, observables required for the computation of phase diagrams can be computed with a computational complexity independent of the underlying Hilbert space for any parameter value. We illustrate the efficiency and accuracy of this approach for different one-dimensional quantum spin-1 models, including anisotropic as well as biquadratic exchange interactions, leading to rich quantum phase diagrams.</p>
Learning topological states from randomized measurements using variational tensor network tomography
<p>Dataset for paper <strong>Learning topological states from randomized measurements using variational tensor network tomography.</strong><br>The numerical code can be found at the repo: https://github.com/teng10/tn-shadow-qst</p>
Open-source release of tensor-network software
<p>This is a package<sup><a href="https://github.com/aspects-quantum/TFlucn_tedopa#user-content-fn-SBmodel-85d3b1b42ae4f41239f8975ec68008b2">1</a></sup> for calculating FLUCTUATIONS of heat transfer in the Spin-Boson model<sup><a href="https://github.com/aspects-quantum/TFlucn_tedopa#user-content-fn-PRX2020-85d3b1b42ae4f41239f8975ec68008b2">2</a></sup> using the <strong>Time Evolving Density matrices using Orthogonal Polynomial Algorithm (<em>TEDOPA</em>)</strong><sup><a href="https://github.com/aspects-quantum/TFlucn_tedopa#user-content-fn-Prior2010-85d3b1b42ae4f41239f8975ec68008b2">3</a></sup><sup><a href="https://github.com/aspects-quantum/TFlucn_tedopa#user-content-fn-Chin2010-85d3b1b42ae4f41239f8975ec68008b2">4</a></sup>.</p> <p>We employ the <strong>Thermofield-based chain-mapping approach for open quantum systems</strong><sup><a href="https://github.com/aspects-quantum/TFlucn_tedopa#user-content-fn-PRA2015-85d3b1b42ae4f41239f8975ec68008b2">5</a></sup> that enables us to use a vacuum initial matrix product state (pure) for the environment instead of a thermal state (mixed), thereby speeding up the computation greatly.</p> <p>In this package, we use the ITensor library<sup><a href="https://github.com/aspects-quantum/TFlucn_tedopa#user-content-fn-Itensor-85d3b1b42ae4f41239f8975ec68008b2">6</a></sup> in Julia for tensor network manipulations. </p> <p>This package uses <strong>julia = "1.8.2"</strong> version.</p>
Efficient parallelization of tensor network contractions for simulating quantum computation
<p> In this paper, we demonstrate a classical simulation framework for quantum computation by contracting tensor networks of sizes previously deemed out of reach. The main contribution of this work is a parallelization scheme called <em>index slicing</em> that breaks down an infeasibly large tensor network contraction task into smaller subtasks that can be executed fully in parallel, without interdependencies or intermediate communications. As a benchmarking example, we show that our algorithm can reduce the simulation of the Sycamore random circuit sampling task to less than 20 days, achieving an acceleration of over five orders of magnitude compared to the original proposal. We then showcase the capabilities of the simulation framework via investigations of near-term quantum algorithms and quantum error correction. Given the ubiquity of tensor networks in quantum information science, we believe that our simulation framework will be a valuable tool in the era of quantum information technology.</p>
Efficient parallelization of tensor network contractions for simulating quantum computation
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