14:30
15:30

Scientific computing problems in physics, chemistry, and engineering—such as the solution of large-scale linear systems, the simulation of dynamical equations, and spectral analysis—pose fundamental challenges for classical algorithms as system sizes grow. Quantum computing offers a promising avenue for addressing these challenges by exploiting quantum-mechanical resources to accelerate key computational primitives. This talk presents completed and ongoing thesis work on quantum algorithms for scientific computation. The first part focuses on Hamiltonian simulation viewed as a structured class of ordinary differential equations. We review product-formula methods, highlighting their strengths and limitations, and contrast them with asymptotically optimal approaches based on qubitization. Recent advances in multi-product formulas are then presented, showing how commutator scaling can be rigorously leveraged to achieve near-optimal dependence on both simulation time and target precision. The second part addresses quantum algorithms for Fourier analysis. In particular, we discuss a quantum algorithm for the non-uniform quantum Fourier transform, implemented using parametrized quantum circuits and quantum signal processing techniques. The talk concludes with brief remarks on ongoing work and directions for future research.

https://combalgo.labri.fr/pmwiki.php/Groupe/Info-Quantique

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