We consider the quantum implementations of two classical iterative solvers for a system of linear equations, including the row (Kaczmarz) method which utilizes a row of the coefficient matrix in each iteration step, and the column (coordinate descent) method which uses a column instead. These two methods are widely applied in big data science due to their simple iteration schemes. We propose fast quantum algorithms for these two approaches by constructing efficient unitary operators in each iteration step based on the block-encoding technique. The construction is based on the unitaries to prepare the quantum states of rows or columns of the coefficient matrix. If the quantum states are efficiently prepared, for example, by qRAM, then the qu...
An n-qubit quantum circuit performs a unitary operation on an exponentially large, 2n-dimensional, H...
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algori...
The field of quantum computing has gained much attention in recent years due to further advances in ...
Many quantum algorithms for numerical linear algebra assume black-box access to a block-encoding of ...
In this thesis, I make a comparison of two quantum algorithms for solving systems of linear equation...
Most quantum algorithms offering speedups over classical algorithms are based on the three technique...
We apply the framework of block-encodings, introduced by Low and Chuang (under the name standard-for...
Quantum algorithms for solving the Quantum Linear System (QLS) problem are among the most investigat...
We introduce a new quantum optimization algorithm for dense linear programming problems, which can b...
Quantum control plays a key role in quantum technology, in particular for steer-ing quantum systems....
Optimization problems in disciplines such as machine learning are commonly solved with iterative met...
Quantum algorithms for solving the Quantum Linear System (QLS) problem are among the most investigat...
Quantum computation is a subject born out of the combination between physics and computer science. I...
We give two new quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-...
We study quantum algorithms that learn properties of a matrix using queries that return its action o...
An n-qubit quantum circuit performs a unitary operation on an exponentially large, 2n-dimensional, H...
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algori...
The field of quantum computing has gained much attention in recent years due to further advances in ...
Many quantum algorithms for numerical linear algebra assume black-box access to a block-encoding of ...
In this thesis, I make a comparison of two quantum algorithms for solving systems of linear equation...
Most quantum algorithms offering speedups over classical algorithms are based on the three technique...
We apply the framework of block-encodings, introduced by Low and Chuang (under the name standard-for...
Quantum algorithms for solving the Quantum Linear System (QLS) problem are among the most investigat...
We introduce a new quantum optimization algorithm for dense linear programming problems, which can b...
Quantum control plays a key role in quantum technology, in particular for steer-ing quantum systems....
Optimization problems in disciplines such as machine learning are commonly solved with iterative met...
Quantum algorithms for solving the Quantum Linear System (QLS) problem are among the most investigat...
Quantum computation is a subject born out of the combination between physics and computer science. I...
We give two new quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-...
We study quantum algorithms that learn properties of a matrix using queries that return its action o...
An n-qubit quantum circuit performs a unitary operation on an exponentially large, 2n-dimensional, H...
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algori...
The field of quantum computing has gained much attention in recent years due to further advances in ...