Universal Effectiveness of High-Depth Circuits in Variational Eigenproblems

This repository provides the source codes to reproduce the results of arXiv:2010.00157, which explores the effectiveness of high-depth, noiseless, parameteric quantum circuits by challenging their capability to simulate the ground states of quantum many-body Hamiltonians. Please refer our paper to find the details of experimental results and discussions.

Prerequisites

The code mainly depends on jax and qutip. We lists the environments that our experiment performed on.

• python 3.7
• CUDA 10.1
• Python Packages:
  • jax==0.1.75
  • jaxlib==0.1.52
  • qutip==4.5.2
  • wandb==0.9.6

The required python packages are listed in requirements.txt and you can install the packages with the following command.

  $ pip install -r requirements.txt

Basically the experimental results are managed through wandb package. Please refer the installation guide for setting up the wandb.

How to Run

There are three main experiments to evaluate the circuit's capability.

• expressibility.py: Random states.
• ising_model.py: Ground state of Ising model.
• SYK4_model.py: Ground state of Sachdev-Ye-Kitaev (SYK) model.

Also, there are the barren plateau phenomena experiments for Ising and SYK models.

• ising_bp.py: Ground state of Ising model.
• SYK4_bp.py: Ground state of Sachdev-Ye-Kitaev (SYK) model.

To run the experiments, simply run the script below.

  $ python expressibility.py --n-qubits 8 --n-layers 56 --lr 0.05 --train-steps 1000 --seed 1
  $ python ising_model.py --n-qubits 8 --n-layers 56 --g 2 --h 0 --lr 0.01 --train-steps 1000 --seed 1
  $ python SYK_hamiltonian.py --n-qubits 8 --n-layers 56 --lr 0.1 --train-steps 3000 --seed 1 --seed-SYK 1
  $ python ising_bp.py --n-qubits 8 --max-n-layers 300 --g 2 --h 0 --sample-size 1000 --seed 1
  $ python SYK_bp.py --n-qubits 8 --max-n-layers 300 --sample-size 100 --seed 1 --seed-SYK 1

Here, it is necessary to provide the seed value for the reproducibility. You can find two different seeds from the options. --seed-SYK is for determining the SYK model and --seed is for all the other random values. After running, you can find the resulting files under the experiment directory ./results/{datetime}_{exp_name}.