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arXiv · 2210.09007

A non-Hermitian Ground State Searching Algorithm Enhanced by Variational Toolbox

Yu-Qin Chen·Shi-Xin Zhang·Chang-Yu Hsieh·Shengyu Zhang
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Abstract

Ground-state preparation for a given Hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization. We consider an approach to simulate dissipative non-Hermitian Hamiltonian quantum dynamics using Hamiltonian simulation techniques to efficiently recover the ground state of a target Hamiltonian. The proposed method facilitates the energy transfer by repeatedly projecting ancilla qubits to the desired state, rendering the effective non-Hermitian Hamiltonian evolution on the system qubits. To make the method more resource friendly in the noisy intermediate-scale quantum (NISQ) and early fault-tolerant era, we combine the non-Hermitian projection algorithm with multiple variational gadgets, including variational module enhancement and variational state recording, to reduce the required circuit depth and avoid the exponentially vanishing success probability for post-selections. We compare our method, the non-Hermitian-variational algorithm, with a pure variational method -- QAOA for solving the 3-SAT problem and preparing the ground state for the transverse-field Ising model. As demonstrated by numerical evidence, the non-Hermitian-variational algorithm outperforms QAOA in convergence speed with improved quantum resource efficiency.

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Yu-Qin Chen, Shi-Xin Zhang, Chang-Yu Hsieh, Shengyu Zhang. 2022-10-17. A non-Hermitian Ground State Searching Algorithm Enhanced by Variational Toolbox. https://arxiv.org/abs/2210.09007

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