Density matrix reconstruction using non-negative matrix product states

• URL: http://arxiv.org/abs/2204.12383v2
• Date: Thu, 12 May 2022 17:09:25 GMT
• Title: Density matrix reconstruction using non-negative matrix product states
• Authors: Donghong Han and Chu Guo and Xiaoting Wang
• Abstract summary: Quantum state tomography is a key technique for quantum information processing, but is challenging due to the exponential growth of its complexity with the system size. We propose an algorithm which iteratively finds the best non-negative matrix product state approximation based on a set of measurement outcomes whose size does not necessarily grow exponentially. As applications, our algorithm is numerically demonstrated to reconstruct the ground state of the XXZ spin chain under depolarizing noise.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum state tomography is a key technique for quantum information processing, but is challenging due to the exponential growth of its complexity with the system size. In this work, we propose an algorithm which iteratively finds the best non-negative matrix product state approximation based on a set of measurement outcomes whose size does not necessarily grow exponentially. Compared to the tomography method based on neural network states, our scheme utilizes a so-called tensor train representation that allows straightforward recovery of the unknown density matrix in the matrix product state form. As applications, the effectiveness of our algorithm is numerically demonstrated to reconstruct the ground state of the XXZ spin chain under depolarizing noise.

Related papers

• Deep Unrolling for Nonconvex Robust Principal Component Analysis [75.32013242448151]
  We design algorithms for Robust Component Analysis (A) It consists in decomposing a matrix into the sum of a low Principaled matrix and a sparse Principaled matrix.
  arXiv  Detail & Related papers  (2023-07-12T03:48:26Z)
• Optimal Algorithms for the Inhomogeneous Spiked Wigner Model [89.1371983413931]
  We derive an approximate message-passing algorithm (AMP) for the inhomogeneous problem. We identify in particular the existence of a statistical-to-computational gap where known algorithms require a signal-to-noise ratio bigger than the information-theoretic threshold to perform better than random.
  arXiv  Detail & Related papers  (2023-02-13T19:57:17Z)
• Quantum state tomography with tensor train cross approximation [84.59270977313619]
  We show that full quantum state tomography can be performed for such a state with a minimal number of measurement settings. Our method requires exponentially fewer state copies than the best known tomography method for unstructured states and local measurements.
  arXiv  Detail & Related papers  (2022-07-13T17:56:28Z)
• Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography [58.60249163402822]
  Unknown-view tomography (UVT) reconstructs a 3D density map from its 2D projections at unknown, random orientations. The proposed OMR is more robust and performs significantly better than the previous state-of-the-art OMR approach.
  arXiv  Detail & Related papers  (2022-07-06T21:40:59Z)
• Quantum algorithms for matrix operations and linear systems of equations [65.62256987706128]
  We propose quantum algorithms for matrix operations using the "Sender-Receiver" model. These quantum protocols can be used as subroutines in other quantum schemes.
  arXiv  Detail & Related papers  (2022-02-10T08:12:20Z)
• Entanglement estimation in tensor network states via sampling [0.688204255655161]
  We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. We test our method on the one-dimensional critical XX chain and the two-dimensional toric code in a checkerboard geometry.
  arXiv  Detail & Related papers  (2022-02-08T19:00:03Z)
• Contour Integral-based Quantum Algorithm for Estimating Matrix Eigenvalue Density [5.962184741057505]
  We propose a quantum algorithm for computing the eigenvalue density in a given interval. The eigenvalue count in a given interval is derived as the probability of observing a bit pattern in a fraction of the qubits of the output state.
  arXiv  Detail & Related papers  (2021-12-10T08:58:44Z)
• Learning a Compressive Sensing Matrix with Structural Constraints via Maximum Mean Discrepancy Optimization [17.104994036477308]
  We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. Recent success of such metrics in neural network related topics motivate a solution of the problem based on machine learning.
  arXiv  Detail & Related papers  (2021-10-14T08:35:54Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Quantum inspired K-means algorithm using matrix product states [4.846953392700506]
  Matrix product state has become the algorithm of choice when studying one-dimensional interacting quantum many-body systems. We propose a quantum inspired K-means clustering algorithm which first maps the classical data into quantum states represented as matrix product states. We show that this algorithm could reach higher prediction accuracies and that it is less likely to be trapped in local minima compared to the classical K-means algorithm.
  arXiv  Detail & Related papers  (2020-06-11T03:00:48Z)
• Tangent-space methods for truncating uniform MPS [0.0]
  A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. We formulate a tangent-space based variational algorithm to achieve this for uniform (infinite) matrix product states.
  arXiv  Detail & Related papers  (2020-01-31T14:54:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.