Optimization and Noise Analysis of the Quantum Algorithm for Solving
One-Dimensional Poisson Equation
- URL: http://arxiv.org/abs/2108.12203v1
- Date: Fri, 27 Aug 2021 09:44:41 GMT
- Title: Optimization and Noise Analysis of the Quantum Algorithm for Solving
One-Dimensional Poisson Equation
- Authors: Guolong Cui, Zhimin Wang, Shengbin Wang, Shangshang Shi, Ruimin Shang,
Wendong Li, Zhiqiang Wei, Yongjian Gu
- Abstract summary: We propose an efficient quantum algorithm for solving one-dimensional Poisson equation.
We further develop this algorithm to make it closer to the real application on the noisy intermediate-scale quantum (NISQ) devices.
We analyze the effect of common noise existing in the real quantum devices on our algorithm using the IBM Qiskit toolkit.
- Score: 17.65730040410185
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Solving differential equations is one of the most promising applications of
quantum computing. Recently we proposed an efficient quantum algorithm for
solving one-dimensional Poisson equation avoiding the need to perform quantum
arithmetic or Hamiltonian simulation. In this letter, we further develop this
algorithm to make it closer to the real application on the noisy
intermediate-scale quantum (NISQ) devices. To this end, we first develop a new
way of performing the sine transformation, and based on it the algorithm is
optimized by reducing the depth of the circuit from n2 to n. Then, we analyze
the effect of common noise existing in the real quantum devices on our
algorithm using the IBM Qiskit toolkit. We find that the phase damping noise
has little effect on our algorithm, while the bit flip noise has the greatest
impact. In addition, threshold errors of the quantum gates are obtained to make
the fidelity of the circuit output being greater than 90%. The results of noise
analysis will provide a good guidance for the subsequent work of error
mitigation and error correction for our algorithm. The noise-analysis method
developed in this work can be used for other algorithms to be executed on the
NISQ devices.
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