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Exploiting Constant Trace Property in Large-scale Polynomial Optimization [PDF]
ACM Transactions on Mathematical Software, 2022 We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant trace property (CTP). As a result, such moment relaxations
Ngoc Hoang Anh +3 more
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Lebesgue functions and Lebesgue constants in polynomial interpolation [PDF]
Journal of Inequalities and Applications, 2016 The Lebesgue constant is a valuable numerical instrument for linear interpolation because it provides a measure of how close the interpolant of a function is to the best polynomial approximant of the function.
Bayram Ali Ibrahimoglu
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Constant Terms of Near-Dyson Polynomials [PDF]
The Electronic Journal of Combinatorics, 2018 We formulate and prove a formula for the constant term for a certain class of Laurent polynomials, which include the Dyson conjecture and its generalizations by Bressoud and Goulden. Our method is explicit Combinatorial Nullstellensatz.
Alexey Gordeev
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Polynomial solutions to constant coefficient differential equations [PDF]
Transactions of the American Mathematical Society, 1992 Let D 1 , … , D r ∈ C [ ∂ / ∂ x 1 , … , ∂ / ∂
Paul Smith, S. P. Smith
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Homogeneous Polynomial Solutions to Constant Coefficient PDE's
Advances in Mathematics, 1996 Given any field \(K\) and a polynomial \(p\in K[X]= K[X_1,\dots,X_n]\), the differential operator \(p(D)\) on \(K[X]\) is defined by substituting \(\partial/\partial x_i\) for the variable \(X_i\). For the case that \(K\) is algebraically closed for characteristic 0, and \(p\) is homogeneous, the set of homogeneous solutions of the PDE \(p(D)=0\) is ...
B. Reznick
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On Correctness of Cauchy problem for a Polynomial Difference Operator with Constant Coefficients
Известия Иркутского государственного университета: Серия "Математика", 2018 The theory of linear difference equations is applied in various areas of ma\-the\-matics and in the one-dimensional case is quite established. For $n>1$, the situation is much more difficult and even for the constant coefficients a general description of
M. S. Apanovich, E.K. Leinartas
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Learning Quantum Hamiltonians at Any Temperature in Polynomial Time [PDF]
Symposium on the Theory of Computing, 2023 We study the problem of learning a local quantum Hamiltonian H given copies of its Gibbs state ρ = e−β H/(e−β H) at a known inverse temperature β>0. Anshu, Arunachalam, Kuwahara, and Soleimanifar gave an algorithm to learn a Hamiltonian on n qubits to ...
Ainesh Bakshi +3 more
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Convergence for score-based generative modeling with polynomial complexity [PDF]
Neural Information Processing Systems, 2022 Score-based generative modeling (SGM) is a highly successful approach for learning a probability distribution from data and generating further samples. We prove the first polynomial convergence guarantees for the core mechanic behind SGM: drawing samples
Holden Lee, Jianfeng Lu, Yixin Tan
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Multivariate trace estimation in constant quantum depth [PDF]
Quantum, 2022 There is a folkloric belief that a depth-Θ(m) quantum circuit is needed to estimate the trace of the product of m density matrices (i.e., a multivariate trace), a subroutine crucial to applications in condensed matter and quantum information science.
Yihui Quek, M. Wilde, Eneet Kaur
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Unconditional advantage of noisy qudit quantum circuits over biased threshold circuits in constant depth [PDF]
Nature CommunicationsThe rapid evolution of quantum devices fuels concerted efforts to experimentally establish quantum advantage over classical computing. Many demonstrations of quantum advantage, however, rely on computational assumptions and face verification challenges ...
Michael de Oliveira +3 more
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