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Structured matrix recovery from matrix‐vector products
Numerical Linear Algebra with Applications, 2023 AbstractCan one recover a matrix efficiently from only matrix‐vector products? If so, how many are needed? This article describes algorithms to recover matrices with known structures, such as tridiagonal, Toeplitz, Toeplitz‐like, and hierarchical low‐rank, from matrix‐vector products.
Diana Halikias, Alex Townsend
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Testing matrix product states [PDF]
, 2022 Devising schemes for testing the amount of entanglement in quantum systems has played a crucial role in quantum computing and information theory. Here, we study the problem of testing whether an unknown state $|\psi\rangle$ is a matrix product state (MPS) in the property testing model.
Mehdi Soleimanifar, John Wright 0004
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Simulating non-equilibrium dynamics and finite temperature physics: efficient representations for matrix product states [PDF]
, 2021 Experimental advances have made it possible to realize and control quantum many-body systems, allowing the experimental study of non-equilibrium phenomena.
Kohn, Lucas
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Commuting decomposition of Kn1,n2,...,nk through realization of the product A(G)A(GPk )
Special Matrices, 2018 In this paper, we introduce the notion of perfect matching property for a k-partition of vertex set of given graph. We consider nontrivial graphs G and GPk , the k-complement of graph G with respect to a kpartition of V(G), to prove that A(G)A(GPk ) is ...
Bhat K. Arathi, Sudhakara G.
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Machine Learning Matrix Product State Ansatz for strongly correlated systems
, 2022 Machine learning (ML) has been used to optimize the matrix product state (MPS) ansatz for wavefunction of strongly correlated systems. The ML optimization of MPS has been tested for Heisenberg Hamiltonian on one-dimensional and ladder lattices which ...
Debashree, Ghosh, Sumanta K., Ghosh
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AN ORDER-P TENSOR MULTIPLICATION WITH CIRCULANT STRUCTURE
Barekeng, 2023 Research on mathematical operations involving multidimensional arrays or tensors has increased along with the growing applications involving multidimensional data analysis. The -product of order- tensor is one of tensor multiplications.
Itsar Mangngiri +2 more
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Quantum Error Mitigation via Matrix Product Operators
PRX Quantum, 2022 In the era of noisy intermediate-scale quantum devices, the number of controllable hardware qubits is insufficient to implement quantum error correction.
Yuchen Guo, Shuo Yang
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Matrix product and sum rule for Macdonald polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We present a new, explicit sum formula for symmetric Macdonald polynomials Pλ and show that they can be written as a trace over a product of (infinite dimensional) matrices. These matrices satisfy the Zamolodchikov– Faddeev (ZF) algebra.
Luigi Cantini +2 more
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Lower Bounds for Matrix Product [PDF]
SIAM Journal on Computing, 2001 We prove lower bounds on the number of product gates in bilinear and quadratic circuits that compute the product of two $n \cross n$ matrices over finite fields. In particular we obtain the following results: 1. We show that the number of product gates in any bilinear (or quadratic) circuit that computes the product of two $n \cross n$ matrices over ...
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Optimising Matrix Product State Simulations of Shor's Algorithm [PDF]
Quantum, 2019 We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix ...
Aidan Dang +2 more
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