PEPS inspired quantum circuit ansatz
To make life easier, here is a simplified notebook version of MPS inspired qubit saving scheme for VQE. For a PEPS inpired ansatz solving the J1-J2 square lattice model, please checkout the following content.
To Install
Type ] in a Julia REPL to enter the pkg mode, then type
pkg> dev https://github.com/GiggleLiu/QuantumPEPS.jl.gitTo Run
First, enter the directory ~/.julia/dev/QuantumPEPS/ (the default development directory of Julia) in a terminal.
To run a toy example of J1-J2 model of size 4 x 4 with J2 = 0.5, type
julia> using QuantumPEPS
julia> Demo.j1j2peps(4, 4) # QPEPS
julia> Demo.j1j2mps(4, 4) # QMPSTo get some help on input arguments, type ? in the REPL to enter the help mode, and then type
help?> Demo.j1j2peps
j1j2peps(nx::Int=4, ny::Int=4; depth::Int=5, nvirtual::Int=1,
nbatch::Int=1024, maxiter::Int=200,
J2::Float64=0.5, lr::Float64=0.1,
periodic::Bool=false, use_cuda::Bool=false, write::Bool=false)
Faithful QPEPS traning for solving the J1-J2 hamiltonian ground state. Returns a triple of (optimizer, history, params).
Positional Arguments
======================
• nx and ny are the square lattice sizes.
Keyword Arguments
===================
• depth is the circuit depth, decides how many entangle layers between two measurements.
• nvirtual is the number of virtual qubits.
• nbatch is the batch size, or the number of shots.
• maxiter is the number of optimization iterations.
• J2 is the strength of the second nearest neighbor coupling.
• lr is the learning rate of the ADAM optimizer.
• periodic specifies the boundary condition of the lattice.
• use_cuda is true means uploading the code on GPU for faster computation.
• write is true will write training results to the data folder.Reference
@article{Liu_2019,
doi = {10.1103/physrevresearch.1.023025},
url = {https://doi.org/10.1103%2Fphysrevresearch.1.023025},
year = 2019,
month = {sep},
publisher = {American Physical Society ({APS})},
volume = {1},
number = {2},
author = {Jin-Guo Liu and Yi-Hong Zhang and Yuan Wan and Lei Wang},
title = {Variational quantum eigensolver with fewer qubits},
journal = {Physical Review Research}
}