Local Hamiltonian decomposition and classical simulation of parametrized quantum circuits

Bibhas Adhikari; Aryan Jha

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arXiv · 2401.13156

Local Hamiltonian decomposition and classical simulation of parametrized quantum circuits

Bibhas Adhikari·Aryan Jha

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Abstract

In this paper we develop a classical algorithm of complexity $O(K \, 2^n)$ to simulate parametrized quantum circuits (PQCs) of $n$ qubits, where $K$ is the total number of one-qubit and two-qubit control gates. The algorithm is developed by finding $2$-sparse unitary matrices of order $2^n$ explicitly corresponding to any single-qubit and two-qubit control gates in an $n$-qubit system. Finally, we determine analytical expression of Hamiltonians for any such gate and consequently a local Hamiltonian decomposition of any PQC is obtained. All results are validated with numerical simulations.

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Bibhas Adhikari, Aryan Jha. 2024-01-24. Local Hamiltonian decomposition and classical simulation of parametrized quantum circuits. https://arxiv.org/abs/2401.13156

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