Implementing discrete Hamiltonian ensemble simulation of qubit pure dephasing on near-term quantum computers

Chien Yu Chen^1*

¹Department of Engineering Sciences, National Cheng Kung University, Tainan City, Taiwan

* Presenter:Chien Yu Chen, email:N96104365@gs.ncku.edu.tw

It's not easy to study real quantum systems, so we found the ways to simulate the real quantum systems. After discretizing the real quantum system with continuous spectrum to obtain a set of probability distributions, the next most important step is to reconstruct the quantum circuit of the quantum system. we need the qiskit toolbox to decompose the quantum circuit, which is the so-called amplitude encoding in the quantum machine learning. And put the circuit into a quantum computer to simulate, and finally compare the difference between the real quantum system and the simulated quantum system. When the number of qubits increases, the entire system will become larger, and the computing time and resources will increase accordingly. From the experimental results, it can be known that when the qubit number is too small, the probability data is not enough, which will make the simulated quantum system almost inconsistent with the real quantum system. However, if the number of qubits in the environment is sufficient, the frequency will not be completely distributed on the spectrum, and the fitting will be more distorted, so the size of the spacing should also be controlled. That is to say, when the spacing becomes smaller, the number of the peaks also needs to be increased, so that the fitting effect will be better, but the disadvantage is that it consumes more computing resources. Since it is not easy for a classical computer to simulate a quantum computer, and as long as it is equal spacing, there will be deep valleys in a fixed period, so it is not yet possible to simulate a fully consistent quantum system.

Keywords: quantum, IBMQ