Unbiased random circuit compiler for time-dependent Hamiltonian simulation

• URL: http://arxiv.org/abs/2212.09445v1
• Date: Mon, 19 Dec 2022 13:40:05 GMT
• Title: Unbiased random circuit compiler for time-dependent Hamiltonian simulation
• Authors: Xiao-Ming Zhang, Zixuan Huo, Kecheng Liu, Ying Li and Xiao Yuan
• Abstract summary: Time-dependent Hamiltonian simulation is a critical task in quantum computing. We develop an unbiased random compiler for TDHS. We perform numerical simulations for a spin model under the interaction picture and the adiabatic ground state preparation for molecular systems.
• Score: 8.694056486825318
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Time-dependent Hamiltonian simulation (TDHS) is a critical task in quantum computing. Existing algorithms are generally biased with a small algorithmic error $\varepsilon$, and the gate complexity scales as $O(\text{poly}(1/\varepsilon))$ for product formula-based methods and could be improved to be polylogarithmic with complicated circuit constructions. Here, we develop an unbiased random compiler for TDHS by combining Dyson expansion, an unbiased continuous sampling method for quantum evolution, and leading order rotations, and it is free from algorithmic errors. Our method has the single- and two-qubit gate complexity $O(\Lambda^2)$ with a constant sampling overhead, where $\Lambda$ is the time integration of the Hamiltonian strength. We perform numerical simulations for a spin model under the interaction picture and the adiabatic ground state preparation for molecular systems. In both examples, we observe notable improvements of our method over existing ones. Our work paves the way to efficient realizations of TDHS.

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