• DOI:10.1103/PhysRevA.101.012328
• Corpus ID: 199543515

Hardware-efficient quantum algorithm for the simulation of open-system dynamics and the thermalisation on quantum computer

@article{Su2019HardwareefficientQA,
  title={Hardware-efficient quantum algorithm for the simulation of open-system dynamics and the thermalisation on quantum computer},
  author={Hong-Yi Su and Ying Li},
  journal={arXiv: Quantum Physics},
  year={2019}
}

• H. Su, Ying Li
• Published 10 August 2019
• Physics, Computer Science
• arXiv: Quantum Physics

The quantum open system simulation is an important category of quantum simulation. By simulating the thermalisation process of the zero temperature, we can solve the ground-state problem of quantum systems. To realise the open-system evolution on the quantum computer, we need to encode the environment using qubits. However, usually the environment is much larger than the system, i.e. plenty of qubits are required if the environment is directly encoded. In this paper, we propose a way to simulate open-system dynamics by reproducing reservoir correlation functions using a minimised Hilbert space. In this way, we only need a small number of qubits to represent the environment. To simulate the $n$-th-order expansion of the time-convolutionless master equation by reproducing up to $n$-th-order correlation functions, the number of qubits representing the environment is $\sim \frac{n}{2}\log_2(N_\omega N_\beta)$. Here, $N_\omega$ is the number of frequencies in the discretised environment spectrum, and $N_\beta$ is the number of terms in the system-environment coupling. By reproducing second-order correlation functions, i.e. taking $n = 2$, we can simulate the Markovian quantum master equation. In our algorithm, the environment on the quantum computer could be even smaller than the system.