All you need is spin: SU(2) equivariant variational quantum circuits based on spin-networks

This repository contains code to reproduce the experiments reported in the paper East, Alonso-Linaje and Park: "All you need is spin: SU(2) equivariant variational quantum circuits based on spin-networks".

Usage

In the python_src directory, there are two scripts to simulate the variational algorithm with SU(2) equivariant gates on two different problems. For example, the following will simulate the algorithm with two-qubit vertex gates (given by --gate argument) for 20 qubits (--num_qubits), $J_2=0.44$ (--j2), and four blocks of gates (--num_blocks; $p$ in the paper). The default learning rate 5e-3 is used.

python3 ./python_src/heisenberg_1d.py --num-qubits 20 --gate 2 --num-blocks 4 --j2 0.44

Similarly, one can simulate the model on the Kagome lattice with $n=18$ qubits.

python3 ./python_src/kagome_lattice.py --num-qubits 20 --gate 3 --num-blocks 5 --no-share-param

The final parameter, --no-share-param, controls whether we want to share parameters among gates. We have used --no-share-param for all data presented in the paper.

Warnings

Currently, the feature we used for the simulations is not fully integrated with the latest release of PennLane-Lightning. It is instead implemented in merge_mat_sparse_adj branch of PennyLane-Lightning. Thus users need to compile this branch from source. The recommended way is using a Python virtual environment populated with the packages in requirements.txt. After cloning the repository, you may run

$ python3 -m venv env
$ source ./env/bin/activate
$ pip install -r ./requirements.txt

You need a compiler with proper C++20 support. See the PennyLane-Lightning repository for further instructions.