Tangent-space methods for truncating uniform MPS

An essential primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a smaller bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for contracting projected entangled pair states. We formulate a tangent-space based variational algorithm to achieve this goal for uniform (infinite) matrix product states. The algorithm exhibits a favourable scaling of the computational cost, and we demonstrate its usefulness by several examples involving the multiplication of a matrix product state with a matrix product operator.

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Matrix Product State–Based Quantum Classifier

Neural Computation ◽

10.1162/neco_a_01202 ◽

2019 ◽

Vol 31 (7) ◽

pp. 1499-1517 ◽

Cited By ~ 2

Author(s):

Amandeep Singh Bhatia ◽

Mandeep Kaur Saggi ◽

Ajay Kumar ◽

Sushma Jain

Keyword(s):

Performance Metrics ◽

Quantum Computer ◽

Binary Classification ◽

Learning Ability ◽

Matrix Product ◽

Product State ◽

Data Set ◽

Matrix Product State ◽

Tensor Network ◽

Network States

Interest in quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled correlated systems. Matrix product state (MPS) is a well-designed class of tensor network states that plays an important role in processing quantum information. In this letter, we show that MPS, as a one-dimensional array of tensors, can be used to classify classical and quantum data. We have performed binary classification of the classical machine learning data set Iris encoded in a quantum state. We have also investigated its performance by considering different parameters on the ibmqx4 quantum computer and proved that MPS circuits can be used to attain better accuracy. Furthermore the learning ability of an MPS quantum classifier is tested to classify evapotranspiration (ET[Formula: see text]) for the Patiala meteorological station located in northern Punjab (India), using three years of a historical data set (Agri). We have used different performance metrics of classification to measure its capability. Finally, the results are plotted and the degree of correspondence among values of each sample is shown.

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Scaling and efficient classical simulation of the quantum Fourier transform

Quantum Information and Computation ◽

10.26421/qic17.1-2-1 ◽

2017 ◽

Vol 17 (1&2) ◽

pp. 1-14

Author(s):

Kieran J. Woolfe ◽

Charles D. Hill ◽

Lloyd C. L. Hollenberg

Keyword(s):

Fourier Transform ◽

Matrix Product ◽

Product State ◽

Quantum Fourier Transform ◽

Numerical Evidence ◽

Matrix Product State ◽

Product Operator ◽

Classical Simulation ◽

Schmidt Rank

We provide numerical evidence that the quantum Fourier transform can be efficiently represented in a matrix product operator with a size growing relatively slowly with the number of qubits. Additionally, we numerically show that the tensors in the operator converge to a common tensor as the number of qubits in the transform increases. Together these results imply that the application of the quantum Fourier transform to a matrix product state with n qubits of maximum Schmidt rank χ can be simulated in O(n (log(n))2 χ 2 ) time. We perform such simulations and quantify the error involved in representing the transform as a matrix product operator and simulating the quantum Fourier transform of periodic states.

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