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Dr Ethan Epperly (UC Berkeley)5/18/26, 11:00 AMQuantum Numerical Linear AlgebraMinisymposium Talk
The fundamental building blocks of iterative linear algebra algorithms in ordinary digital computation are matrix–vector multiplications and inner products. In quantum computing, we lose easy access to both primitives. But we also gain replacements. Instead of matrix–vector products, we can apply the unitary time evolution operator $e^{-itA}$, and we have access to noisy—but statistically...
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Zeguan Wu (University of Pittsburgh)5/18/26, 11:25 AMQuantum Numerical Linear AlgebraMinisymposium Talk
Quantum computing relies heavily on the efficient manipulation of linear algebraic structures. This talk discusses the application of quantum linear algebra across two major domains: continuous optimization and differential equations. We demonstrate how quantum linear algebra can be utilized to solve these problems efficiently, discussing both the algorithmic construction and the theoretical...
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Mohammadhossein Mohammadisiahroudi (Department of Mathematics and Statistics, University of Maryland Baltimore County)5/18/26, 11:50 AMQuantum Numerical Linear AlgebraMinisymposium Talk
Quantum linear algebra has emerged as a promising framework for accelerating the solution of fundamental computational problems, including systems of linear equations—a core subroutine in many scientific and engineering tasks. These problems arise prominently in optimization algorithms. In this talk, we discuss the opportunities and challenges associated with integrating quantum linear algebra...
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Ryan LaRose5/18/26, 2:25 PMQuantum Numerical Linear AlgebraMinisymposium Talk
Quantum Krylov methods are strong candidates for computing ground states on NISQ and MegaQuop computers. While typically implemented with powers of the time evolution unitary $e^{-iH t}$ for a given Hamiltonian $H$, convergence can be markedly faster with powers of the Hamiltonian $H$ itself as in classical methods. We discuss these convergence rates and present several ways to implement...
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Liron Mor Yosef (Tel Aviv University)5/18/26, 2:50 PMQuantum Numerical Linear AlgebraMinisymposium Talk
The emergence of Quantum Numerical Linear Algebra (qNLA) offers a paradigm shift in solving large-scale linear systems and matrix functions. However, the practical utility of these algorithms, such as the seminal HHL, is fundamentally bottlenecked by the "input problem", namely the efficient representation of classical matrices as quantum circuits.
In this talk, we explore two distinct...
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Giacomo Antonioli5/19/26, 11:00 AMQuantum Numerical Linear AlgebraMinisymposium Talk
Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, providing an embedding of a given matrix into a suitable larger unitary matrix. Efficient techniques for QBE have primarily focused on sparse matrices, and less effort has been devoted to data-sparse matrices, such as rank-structured matrices.
In this talk, we examine a specific case of rank...
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Roel Van Beeumen (Lawrence Berkeley National Laboratory)5/19/26, 11:25 AMQuantum Numerical Linear AlgebraMinisymposium Talk
With the Quantum Singular Value Transformation (QSVT) emerging as a unifying framework for diverse quantum speedups, the efficient construction of block encodings—their fundamental input model—has become increasingly crucial. However, devising explicit block encoding circuits remains a significant challenge. A widely adopted strategy is the Linear Combination of Unitaries (LCU) method. While...
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Filippo Della Chiara (KU Leuven)5/19/26, 11:50 AMQuantum Numerical Linear AlgebraMinisymposium Talk
Quantum circuits naturally implement unitary operations on input quantum states. However, non-unitary operations can also be implemented through “block encodings”, where additional ancilla qubits are introduced and later measured. While block encoding has a number of well-established theoretical applications, its practical implementation has been prohibitively expensive for current quantum...
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