From Symmetric Toeplitz Hamiltonians to Quantum Circuits

Rayan Trabelsi

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arXiv · 2508.10167

From Symmetric Toeplitz Hamiltonians to Quantum Circuits

Rayan Trabelsi

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Abstract

This work introduces a quantum circuit synthesis framework for simulating the unitary time evolution under a subclass of symmetric Toeplitz Hamiltonians by decomposing them into specific diagonal matrices $M_k$. These matrices are then classified, to achieve significant simplification, into, $M_k$ when $k$ is a power of two, and congruence classes with constant coefficients. Finally, we construct the explicit quantum circuit for the one-dimensional discrete Poisson equation. This research was conducted under the supervision of Benoit Valiron during a Master's internship.

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Rayan Trabelsi. 2025-08-13. From Symmetric Toeplitz Hamiltonians to Quantum Circuits. https://arxiv.org/abs/2508.10167

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