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arXiv:2401.13156

Local Hamiltonian decomposition and classical simulation of parametrized quantum circuits

Bibhas Adhikari, Aryan Jha

Published Jan 24, 2024• 0 citations
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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.

DOI
10.48550/arxiv.2401.13156

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In this Letter, we present two analytic expressions that most generally simulate nnn-qubit controlled-UUU gates with standard one-qubit gates and CNOT gates using exponential and polynomial complexity respectively. Explicit circuits and general expressions of decomposition are derived. The exact numbers of basic operations in these two schemes are given using gate counting technique.
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