Local Hamiltonian decomposition and classical simulation of parametrized quantum circuits

• URL: http://arxiv.org/abs/2401.13156v2
• Date: Wed, 31 Jan 2024 18:20:04 GMT
• Title: Local Hamiltonian decomposition and classical simulation of parametrized quantum circuits
• Authors: Bibhas Adhikari, Aryan Jha
• Abstract summary: We develop a classical algorithm of complexity $O(K, 2n)$ to simulate parametrized quantum circuits (PQCs) of $n$ qubits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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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