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QI: Fachverband Quanteninformation

QI 1: Quantum Computing and Algorithms I

QI 1.3: Vortrag

Montag, 9. März 2026, 10:00–10:15, BEY/0137

Block encoding and QSVT for solving differential equations — •Abhishek Setty — Forschungszentrum Jülich, Germany — University of Cologne, Germany

We present a unified framework for efficient block encoding of arbitrary sparse matrices, addressing the key barriers to practical quantum algorithms: multi-controlled gate overhead, amplitude reordering, and hardware connectivity. Our method combines a combinatorial-optimization strategy for control-qubit assignment with coherent permutation operators, yielding explicit gate-level constructions with reduced depth. Building on this, we outline a quantum linear systems pathway for solving differential equations within the QSVT paradigm. We demonstrate this on a complex linear system and extend it to CFD problems, including the heat equation and Carleman-linearized Burgers equation. These results highlight both the potential and limitations of current methods, underscoring the need for efficient estimation of minimum singular value, depth-reduction techniques, and benchmarks against classical reachability. This pathway lays a foundation for advancing quantum linear system methods toward large-scale applications.

Keywords: Block Encoding; Quantum Singular Value Transformation; Quantum Linear Algebra; Differential Equations; Quantum Circuits