Quantum imaginary time evolution on 1D infinite-size lattice

Hao-Ti Hung^1*, Tung-Tsao¹, Ying-Jer Kao¹

¹Department of Physics, National Taiwan University, Taipei City, Taiwan

* Presenter:Hao-Ti Hung, email:hunghaoti852@gmail.com

In the presentation, I will show how to convert the uniform matrix product state (uMPS, which is a kind of tensor-network state to describe a 1D infinite-size lattice system) into a quantum circuit. I will also demonstrate the process of developing an algorithm for the time-dependent variational principle (TDVP) based on a quantum circuit. We will use this algorithm to perform quantum imaginary time evolution (QITE) and then optimize the results using the QLanczos method to obtain the ground state energy of the system. Additionally, we will use the algorithm to simulate the transverse-field Ising model on both simulators and quantum real devices, then comparing the simulation results obtained from the classical tensor network TDVP algorithm with those from the quantum circuit.

Keywords: quantum circuit, quantum imaginary time evolution, matrix product state