Quantum relaxed row and column iteration methods based on block-encoding

[1]  Hua Xiang,et al.  An Extended Row and Column Method for Solving Linear Systems on a Quantum Computer , 2021, International Journal of Theoretical Physics.

[2]  Kui Du,et al.  A doubly stochastic block Gauss-Seidel algorithm for solving linear equations , 2019, Appl. Math. Comput..

[3]  Hua Xiang,et al.  Row and column iteration methods to solve linear systems on a quantum computer , 2019, Physical Review A.

[4]  Iordanis Kerenidis,et al.  A Quantum Interior Point Method for LPs and SDPs , 2018, ACM Transactions on Quantum Computing.

[5]  Rupak Biswas,et al.  Quantum Machine Learning , 2018 .

[6]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[7]  L. Wossnig,et al.  Quantum Linear System Algorithm for Dense Matrices. , 2017, Physical review letters.

[8]  S. Lloyd,et al.  Quantum gradient descent and Newton’s method for constrained polynomial optimization , 2016, New Journal of Physics.

[9]  Robert Gardner,et al.  Quantum generalisation of feedforward neural networks , 2016, npj Quantum Information.

[10]  S. Lloyd,et al.  Quantum machine learning , 2016, Nature.

[11]  P. Hansen,et al.  Convergence analysis for column-action methods in image reconstruction , 2016, Numerical Algorithms.

[12]  Andrew M. Childs,et al.  Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision , 2015, SIAM J. Comput..

[13]  Alán Aspuru-Guzik,et al.  A variational eigenvalue solver on a photonic quantum processor , 2013, Nature Communications.

[14]  A. Harrow,et al.  Quantum algorithm for linear systems of equations. , 2008, Physical review letters.

[15]  Adrian S. Lewis,et al.  Randomized Methods for Linear Constraints: Convergence Rates and Conditioning , 2008, Math. Oper. Res..

[16]  S. Lloyd,et al.  Quantum random access memory. , 2007, Physical review letters.

[17]  Lov K. Grover,et al.  Creating superpositions that correspond to efficiently integrable probability distributions , 2002, quant-ph/0208112.

[18]  Lov K. Grover Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[19]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[20]  A. Lent,et al.  Iterative algorithms for large partitioned linear systems, with applications to image reconstruction , 1981 .

[21]  G. Herman,et al.  Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography. , 1970, Journal of theoretical biology.

[22]  T. Whitney,et al.  Two Algorithms Related to the Method of Steepest Descent , 1967 .

[23]  W. Marsden I and J , 2012 .