Switching Time Optimization for Binary Control Pulse in Quantum Systems

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

In our paper, we first introduce two algorithms to derive controller sequences from discretized continuous controls. The algorithms include:

• Extraction based on objective values (Obj)
• Extraction based on cumulative difference (SUR)

Then we propose a switching time optimization model for the binary quantum control problem with given controller sequences and a gradient method to solve it. In addition, we design a pre-computing acceleration technique to accelerate the time evolution simulation.

Citation

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

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

@article{fei2023switching,
  title={Switching Time Optimization for Binary Quantum Optimal Control},
  author={Fei, Xinyu and Brady, Lucas T and Larson, Jeffrey and Leyffer, Sven and Shen, Siqian},
  journal={arXiv preprint arXiv:2308.03132},
  year={2023}
}

Installation

Prerequisites

• Python >= 3.8
• qiskit >= 0.29.0, scipy >= 1.6.2, qutip >= 4.6

Installation Steps

1. Clone the repository
2. Set up a virtual environment (optional)
3. Install the above dependencies by

pip install qiskit scipy qutip

Test instances

In our paper, we test our algorithms on four quantum control instances:

• Energy minimization problem
• CNOT gate estimation problem
• NOT gate estimation problem with energy leakage
• Circuit compilation problem

For each instance, we solve the switching time optimization model with controller sequences obtained from the following three methods respectively:

• Discretized control in the paper Binary Control Pulse Optimization for Quantum Systems
  
• Extraction based on objective values (Obj)
• Extraction based on cumulative difference (SUR)

Usage

Parameter lists

Required parameters

• --name: name of the instance
• --n: number of qubits
• --evo_time: evolution time
• --n_ts: number of time steps
• --initial_type: initial type of the control time intervals, including 'warm', 'average', and 'random'
  • 'warm': the initial control time intervals are set as the value of obtained discretized binary control intervals
  • 'average': the initial control time intervals are set as evolution time / number of intervals
  • 'random': the initial control time intervals are set as random values between 0 and evolution time
• --extract: extraction algorithm, including 'binary', 'obj', and 'sur'
  • 'binary': discretized control in the paper Binary Control Pulse Optimization for Quantum Systems
  • 'obj': extraction based on objective values
  • 'sur': extraction based on cumulative difference
• --alpha: parameter for the extraction algorithm Obj/SUR
• --c_control: file path of the discretized continuous control

Energy minimization problem only parameters

• --num_edge: number of edges in the randomly generated graph for Hamiltonian controllers
• --rgraph: whether to generate a random graph for Hamiltonian controllers
• --seed: random seed for generating the random graph

Other instances only parameters

• --target: file path of the target unitary operator
• --phase: phase parameter to compute infidelity objective function

Molecule compilation problem only parameters

• --molecule: molecule name, including 'BeH2', 'LiH', 'H2'

Discretized control parameters

• --b_control: file path of the discretized binary control for controller sequences

Stored results

All the control results are stored in the folder result/control/SwitchTime/. All the output control figures are stored in result/figure/SwitchTime. The output files are stored in result/output/Switchtime/. 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.

Example data files

• Discretized continuous control files (input as parameter result/control/c_control).
• Target unitary operator for circuit compilation problem (input as parameter result/control/Target).

Both required files should be .csv files.

Usage examples

To run an energy minimization problem with 6 qubits, randomly generated graph for Hamiltonian controllers, evolution time as 5, time steps as 100, extracting controller sequences by previous discretized binary solution:

python energy_acc.py --name=EnergyAccD --n=6 --num_edge=3 --rgraph=1 --seed=1 --evo_time=5 --n_ts=100 --initial_type='warm' --extract="binary" \
  --c_control="../result/c_control/Continuous/Energy6_evotime5.0_n_ts100_ptypeCONSTANT_offset0.5_instance1.csv" \
  --b_control="..result/b_control/TR+MT/Energy6_evotime5.0_n_ts100_ptypeCONSTANT_offset0.5_instance1_alpha0.01_sigma0.25_eta0.001_threshold30_iter100_typetvc_minup10_1_sigma0.25_eta0.001_threshold30_iter100_typeminup_time10.csv"

To run circuit compilation problem on molecule BeH2 with evolution time 20, time steps 200, extracting controller sequences by Method 2 (Obj) with switching penalty 0:

python Molecule_acc.py --name=MoleculeAccC --molecule=BeH2 --qubit_num=6 --evo_time=20 --n_ts=200 \
  --initial_type='warm' --extract="obj" --alpha=0 \
  --target="../new_result/c_control/Target/BeH2_target.csv" \
  --c_control="../new_result/c_control/Continuous/MoleculeVQENew_BeH2_evotime20.0_n_ts200_ptypeCONSTANT_offset0.5_objUNIT_sum_penalty0.01.csv"

Important modules

• example: different quantum control examples
• script: testing script examples
• switchint: algorithm to obtain controller sequences and solve switching time optimization model
• utils: utility functions

Acknowledgement

We thank Dr. Lucas Brady for providing the code used in the paper Optimal Protocols in Quantum Annealing and QAOA Problems.

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

We refer to the paper Binary Control Pulse Optimization for Quantum Systems and solve the model with TV regularizer to obtain discretized continuous control for extracting controller sequences. Their code is presented at https://github.com/xinyufei/Quantum-Control-qutip.

References

[1] Brady, Lucas T., et al. "Optimal protocols in quantum annealing and quantum approximate optimization algorithm problems." Physical Review Letters 126.7 (2021): 070505.

[2] Gokhale, Pranav, et al. "Partial compilation of variational algorithms for noisy intermediate-scale quantum machines." Proceedings of the 52nd Annual IEEE/ACM International Symposium on Microarchitecture. 2019.

[3] Fei, Xinyu, et al. "Binary control pulse optimization for quantum systems." Quantum 7 (2023): 892.

Developers

Xinyu Fei (xinyuf@umich.edu)

Contact

Xinyu Fei (xinyuf@umich.edu)

Siqian Shen (siqian@umich.edu)