Binary Control Pulse Optimization for Quantum Systems

This repository contains the source code used in the computational experiments of the paper: Binary Control Pulse Optimization for Quantum Systems.

In our paper, we first apply GRAPE algorithm to solve the continuous relaxation of binary quantum control problems with SOS1 property. Then we apply two rounding techniques, sum-up rounding (SUR) and combinatorial integral approximation (CIA) to obtain the binary controls. Furthermore, we apply our improvement heuristic to improve the solutions.

Citation

If you use our code in your research, please cite our paper:

Binary Control Pulse Optimization for Quantum Systems
Xinyu Fei, Lucas T. Brady, Jeffrey Larson, Sven Leyffer, Siqian Shen
Quantum, 2023

@article{fei2023binary,
  title={Binary control pulse optimization for quantum systems},
  author={Fei, Xinyu and Brady, Lucas T and Larson, Jeffrey and Leyffer, Sven and Shen, Siqian},
  journal={Quantum},
  volume={7},
  pages={892},
  year={2023},
  publisher={Verein zur F{\"o}rderung des Open Access Publizierens in den Quantenwissenschaften}
}

Test Instances

There are three test instances in the paper:

• Energy minimization problem
• CNOT gate estimation problem
• Circuit compilation problem

For each instance, we solve the following optimization problems:

• Continuous relaxation
• Model with TV regularizer
• Rounding techniques
• Improvement heuristic

The instances are provided in the folder /example/.

Installation

Requirements

• Python >= 3.8
• qiskit >= 0.29.0, scipy >= 1.6.2
• pycombina >= 0.3.2 (only for rounding)
• Developed version of Qutip (https://github.com/qutip/qutip).

To install pycombina, please refer to https://pycombina.readthedocs.io/en/latest/.

To install the developed version of Qutip, first clone the repository locally:

git clone https://github.com/xinyufei/Quantum-Control-qutip.git

Then, install Qutip by

python setup.py develop

Usage

Stored results

All the control results are stored in the folder example/control/. All the output control figures are stored in example/figure/. The output files are stored in example/output/. One can change the paths in files to change the positions.

Before starting your own experiments, we suggest deleting the above three folders to clear all the existing results.

Continuous relaxation

First, change to the example file folder:

cd example/Continuous/

To run an energy minimization problem with 4 qubits, randomly generated graph for Hamiltonian controllers, evolution time as 2, time steps as 40, constant initial control values 0.5, run:

python energy.py --n=4 --num_edges=2 --rgraph=1 --seed=1 \
    --evo_time=2 --n_ts=40 --initial_type=CONSTANT --offset=0.5

To run a CNOT estimation problem with evolution time 10, time steps 200, constant initial control values 0.5, run:

python CNOT.py --evo_time=10 --n_ts=200 --initial_type=CONSTANT --offset=0.5

To run a circuit compilation problem on molecule LiH with evolution time 20, time steps 200, automatically generating target circuit, constant initial control values 0.5, and without SOS1 property, run

python Molecule.py --gen_target=1 --name=MoleculeVQE \
    --molecule=LiH --qubit_num=4 --evo_time=20 --n_ts=100 \
    --initial_type=CONSTANT --offset=0.5

In circuit compilation problem, to penalize the SOS1 property, one can set the penalty parameter. For example, with the above setting adding penalty, run:

python Molecule.py --gen_target=1 --name=MoleculeVQE \
    --molecule=LiH --qubit_num=4 --evo_time=20 --n_ts=100 \
    --initial_type=CONSTANT --offset=0.5 --sum_penalty=0.1

The output control files are stored in example/control/Continuous/. The output control figures are stored in example/figure/Continuous/. The output files are stored in example/output/Continuous/.

TV regularizer

First, change to the example file folder:

cd example/ADMM/

To run ADMM for solving the model with TV regularizer on energy minimization problem, run:

python energy.py --n=4 --rgraph=1 --seed=1 --num_edges=2 --evo_time=2 --n_ts=40 --initial_type=WARM \
    --initial_control="../control/Continuous/Energy4_evotime2.0_n_ts240_ptypeCONSTANT_offset0.5_instance1.csv" \
    --alpha=1e-2 --rho=10 --max_iter_admm=50

Rounding

First, change to the example file folder:

cd example/Rounding/

To run SUR on energy minimization problem, run:

python energy.py --n=4 --rgraph=1 --seed=1 --num_edges=2 --evo_time=2 --n_ts=40 \
    --initial_control="../control/Continuous/Energy4_evotime2.0_n_ts40_ptypeCONSTANT_offset0.5_instance1.csv" \
    --type=SUR

To run CIA with min-up time constraints on energy minimization problem, run:

python energy.py --n=4 --rgraph=1 --seed=1 --num_edges=2 --evo_time=2 --n_ts=40 \
    --initial_control="../control/Continuous/Energy4_evotime2.0_n_ts40_ptypeCONSTANT_offset0.5_instance1.csv" \
    --type=minup --min_up=10

Improvement heuristic

First, change to the example file folder:

cd example/Trustregion/

To run the improvement heuristic on energy minimization problem for improve the solutions with TV regularizer, run:

python energy.py --n=4 --rgraph=1 --seed=4 --evo_time=2 --n_ts=40 \
    --initial_file="../control/Rounding/EnergyADMM4_evotime2.0_n_ts40_ptypeWARM_offset0.5_penalty0.01_ADMM_10.0_iter100_instance4_1_SUR.csv" \
    --alpha=0.01 --tr_type="tv"

To run the improvement heuristic on energy minimization problem for improve the solutions with min-up time constraints, run:

python energy.py --n=4 --num_edges=2 --rgraph=1 --seed=4 --evo_time=2 --n_ts=40 \
    --initial_file="../control/Rounding/EnergyADMM4_evotime2.0_n_ts40_ptypeWARM_offset0.5_penalty0.01_ADMM_10.0_iter100_instance4_minup10_1.csv" \
    --alpha=0.01 --tr_type="hard" --hard_type="minup" --min_up=10

Acknowledgement

We thank Dr.Lucas Brady for providing the code used in the paper Optimal Protocols in Quantum Annealing and QAOA Problems (https://arxiv.org/pdf/2003.08952.pdf).

We refer to the paper Partial Compilation of Variational Algorithms for Noisy Intermediate-Scale Quantum Machines (https://arxiv.org/pdf/1909.07522.pdf) for generating the circuit compilation problem. Their code is presented at https://github.com/epiqc/PartialCompilation.

Developers

Xinyu Fei (xinyuf@umich.edu)

Contact

Xinyu Fei (xinyuf@umich.edu)

Siqian Shen (siqian@umich.edu)