L2O-$g^\dagger$: Learning to Optimize Parameterized Quantum Circuits with Fubini–Study Metric Tensor

Introduction

This is the official repository of the paper "L2O-$g^\dagger$: Learning to Optimize Parameterized Quantum Circuits with Fubini–Study Metric Tensor".

Before the advent of fault-tolerant quantum computers, variational quantum algorithms (VQAs) play a crucial role in noisy intermediate-scale quantum (NISQ) machines. Conventionally, the optimization of VQAs predominantly relies on manually designed optimizers. However, learning to optimize (L2O) demonstrates impressive performance by training small neural networks to replace handcrafted optimizers. In our work, we propose L2O-$g^\dagger$, a quantum-aware learned optimizer that leverages the Fubini-Study metric tensor ($g^\dagger$) and long short-term memory networks. We theoretically derive the update equation inspired by the lookahead optimizer and incorporate the quantum geometry of the optimization landscape in the learned optimizer to balance fast convergence and generalization. Empirically, we conduct comprehensive experiments across a range of VQA problems. Our results demonstrate that L2O-$g^\dagger$ not only outperforms the current SOTA hand-designed optimizer without any hyperparameter tuning but also shows strong out-of-distribution generalization compared to previous L2O optimizers. We achieve this by training L2O-$g^\dagger$ on just a single generic PQC instance. Our novel quantum-aware learned optimizer, L2O-$g^\dagger$, presents an advancement in addressing the challenges of VQAs, making it a valuable tool in the NISQ era.

Installation

1. Create a new conda environment with Python 3.10:

   conda create --name [name] python=3.10

2. Activate the newly created environment:

   conda activate [name]

3. Install the required packages using pip:

   pip install -r requirements.txt

WandB

To configure WandB, follow these steps:

1. Obtain your WandB API key from your WandB account.

2. Add the WandB API key to the file utils/wandb_api_key.txt:

   [Your WandB API Key]
   

3. When running use --record optition.

Options

• --train: Default is False. Use --train to train the optimizer.
• --verbose: Default is False. Use --verbose for verbose output.
• --data: Default is 'VQE-H2'. Use --data to specify the task.
• --load_model: Default is 'None'. Use --load_model to specify the model name.
• --checkpoints: Default is './checkpoints/'. Use --checkpoints to specify the location to store the model.
• --seed: Default is 0. Use --seed to set the random seed.

HPO Arguments

• --preproc: Default is True. Use --preproc to enable preprocessing.
• --preproc_factor: Default is 10. Use --preproc_factor to set the preprocessing factor.
• --hidden_sz: Default is 30. Use --hidden_sz to set the hidden size.
• --lamb_a: Default is 0.01. Use --lamb_a to set lambda a.
• --lamb_b: Default is 0.01. Use --lamb_b to set lambda b.
• --lr: Default is 0.001. Use --lr to set the optimizer learning rate.
• --ep: Default is 20. Use --ep to set the number of epochs for the trained optimizer.
• --period: Default is 5. Use --period to set the number of periods for each epoch.
• --itr: Default is 200. Use --itr to set the number of optimizer iterations.
• --repeat: Default is 10. Use --repeat to set the number of experiment repetitions.
• --n_tests: Default is 100. Use --n_tests to set the number of tests.

GPU Arguments

• --use_gpu: Default is False. Use --use_gpu to enable GPU usage.
• --gpu: Default is 0. Use --gpu to specify the GPU id.

WandB Arguments

• --record: Default is False. Use --record to enable WandB recording.
• --project: Default is 'l2o-g'. Use --project to specify the project name.

VQE Problem Arguments

• --H2_bond: Default is 0.7. Use --H2_bond to set the bond length for the VQE-H2 problem.
• --molname: Default is 'H2'. Use --molname to specify the molecule name.
• --bond_length: Default is 0.7. Use --bond_length to set the bond length for the VQE-UCSSD problem.
• --charge: Default is 0. Use --charge to set the charge of the molecule.
• --rale_layers: Default is 1. Use --rale_layers to set the number of layers in RALE.

Rand_VC Problem Arguments

• --VC_qubits: Default is 4. Use --VC_qubits to set the number of qubits in the random VC problem.
• --VC_layers: Default is 1. Use --VC_layers to set the number of layers in the random VC problem.
• --VC_seed: Default is 0. Use --VC_seed to set the seed for the random VC problem.
• --VC_rand_ham: Default is False. Use --VC_rand_ham to enable random Hamiltonian.

Reupload Circuit Arguments

• --RP_func_type: Default is 'circle'. Use --RP_func_type to specify the classifier function type.

• --RP_qubits: Default is 1. Use --RP_qubits to set the number of qubits in the random VC problem.

• --RP_layers: Default is 3. Use --RP_layers to set the number of layers in the random VC problem.

• --RP_ndata: Default is 5000. Use --RP_ndata to set the total number of data points.

• --RP_seed: Default is 0. Use --RP_seed to set the seed for the random VC problem.

• --batch_size: Default is 32. Use --batch_size to set the batch size.

QAOA MaxCut Arguments

• --QAOA_n_nodes: Default is 3. Use --QAOA_n_nodes to set the number of nodes in QAOA MaxCut.
• --QAOA_p_layers: Default is 1. Use --QAOA_p_layers to set the number of layers in QAOA MaxCut.
• --QAOA_edge_prob: Default is 0.5. Use --QAOA_edge_prob to set the QAOA edge probability.
• --QAOA_seed: Default is 0. Use --QAOA_seed to set the QAOA seed.

Test Option

• --save_path: Default is 'results/'. Use --save_path to specify the save path.
• --save_traj: Default is False. Use --save_traj to save the parameter trajectory.

Ablation Option

• --abl_cl: Default is False. Use --abl_cl to enable ablation on CL.
• --abl_g: Default is False. Use --abl_g to enable ablation on g.

Usage

To train the a new model use --train option. An example is:

python main.py --train --data QAOA_MaxCut --verbose --QAOA_n_nodes 6 --QAOA_p_layers 4 --QAOA_edge_prob 0.7

If you want to use the trained model to optimize a new problem, here is an example:

python main.py --load_model [model_name] --data VQE-UCCSD --verbose --repeat 5 --molname BeH2 --bond_length 0.9 --itr 200

Results / Checkpoints

When saving results, the output folder follows this format:

results/mod_[train_name]-[train_hash]set[problem_name]-[problem_hash]

• [train_name]: This is the name of the problem l2o-g is train on. For example, QAOA_MaxCut.
• [train_hash]: This is the hash of the problem configuration. For example, 0b785a1f.
• [problem_name]: This is the name of the problem being tested. For example, QAOA_MaxCut.
• [problem_hash]: This is the hash of the problem configuration. For example, 0b785a1f.

When saving model checkpoints, the folder follows this format:

checkpoints/[train_name]-[train_hash]

• QAOA_MaxCut: This is the name of the problem being trained.
• d8ef508e: This is the hash of the poeblem configuration.

Implement New VQAs Problem

We want to make the implementation of new VQAs problem as easy as possible. Follow these steps:

1. Add problem argument(s) in main.py. For example:

   parser.add_argument('--new_arg', type=float, default=1.0, help='some description')

2. Add a new option for the problem in utils/tool.py. For example:

   elif args.data == 'new_problem':
       print('Running Problem new_problem')
       problem = new_problem()
       dimension = 
       cost_func = problem.get_loss_function()
       metric_fn = problem.get_metric_fn()
       return dimension, cost_func, metric_fn

3. Add the new problem implementation in the problems/new_problem.py. And import into utils/tool.py.

News

• [2024.07.23] 🚀 Our paper is now available on arXiv.

🔖 Citation

📚 If you find our work or this code to be useful in your own research, please kindly cite our paper :-)

@article{huang2024l2o,
  title={L2O-$ g\^{}$\{$$\backslash$dagger$\}$ $: Learning to Optimize Parameterized Quantum Circuits with Fubini-Study Metric Tensor},
  author={Huang, Yu-Chao and Goan, Hsi-Sheng},
  journal={arXiv preprint arXiv:2407.14761},
  year={2024}
}

🖌️ Authors

Yu-Chao Huang, Hsi-Sheng Goan.