Binary Quantum Control Optimization with Uncertain Hamiltonians

This repository contains the source code used in the computational experiments of the paper: Binary Quantum Control Optimization with Uncertain Hamiltonians.

In our paper, we first develop a stochastic optimization model balancing risk-neutral and risk-averse measurements. We design a gradient-based optimization algorithm to solve the continuous relaxation, then propose a rounding method to obtain binary controls.

Citation

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

Binary Quantum Control Optimization with Uncertain Hamiltonians
Xinyu Fei, Lucas T. Brady, Jeffrey Larson, Sven Leyffer, Siqian Shen

@article{fei2024binary,
title={Binary Quantum Control Optimization with Uncertain Hamiltonians},
author={Fei, Xinyu and Brady, Lucas T and Larson, Jeffrey and Leyffer, Sven and Shen, Siqian},
journal={arXiv preprint arXiv:2401.10120},
year={2024}
}

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
• Circuit compilation problem

For each instance, we solve the stochastic optimization model with different variance settings and weight parameters. We compare the results of deterministic and stochastic controls.

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
• --c_control: file path of the discretized continuous control
• --num_scenario: number of sampled scenarios for stochastic optimization model
• --cvar: CVaR penalty parameter
• --var: variation of Hamiltonian noise, can be a list of values
• --binary: whether to solve the binary control problem
• --weight: weight parameter balancing risk-neutral and risk-averse measurements
• --ts_b: time steps for rounding method

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

Molecule compilation problem only parameters

• --molecule: molecule name, including 'BeH2', 'LiH', 'H2'
• (Optional) --lr: learning rate for the gradient-based optimization algorithm

Stored results

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

Example data files

• Target unitary operator for circuit compilation problem (input as parameter result/target).

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 5, time steps 50, scenarios 300, CVaR penalty 0.05, variation of Hamiltonian noise 0.01, weight parameter 0.5, and rounding time steps 200:

python example/StochasticModel/energy_ratio.py --name='EnergyRevision' --n=6 --num_edges=3 --rgraph=1 --g_seed=1 --evo_time=5 --n_ts=50 --r_seed=0 \
  --initial_type='CONSTANT' --offset=0.5 --num_scenario=300 --cvar=0.05 --var=0.01 --binary=1 --weight=0.5 --ts_b=200

To run an out of sample test for energy minimization problem with 10 groups, each having 500 scenarios:

python example/OutSampleTest/energy_ratio.py --n=6 --num_edges=3 --rgraph=1 --g_seed=1 --evo_time=5 --n_ts=50 --r_seed=1000 --group=10 --num_scenario=500 \
  --var=0.01 --cvar=0.05 --draw=0 --control="../../result/control/Direct/Energy6_evotime5.0_n_ts50_ptypeCONSTANT_offset0.5_instance1_scenario300_cvar0.05_mean0_var0.01_weight1.0.csv"

To run circuit compilation problem on molecule H2 with evolution time 20, time steps 50, scenarios 20, CVaR penalty 0.05, variation of Hamiltonian noise 0.01, weight parameter 0.5, learning rate 0.05, and rounding time steps 4000:

python example/StochasticModel/Molecule.py --name="Molecule" --molecule="H2" --qubit_num=2 --evo_time=20 --n_ts=50 --r_seed=0 --gen_target=0 \
   --target="../../result/target/Molecule_H2_target.csv" --sum_penalty=1 --max_iter=2000 \
   --initial_type="CONSTANT" --offset=0.2 --num_scenario=20 --cvar=0.05 --var=0.01 --binary=1 --ts_b=4000 --weight=0.5 --lr=0.05

To run an out of sample test for circuit compilation problem with 10 groups, each having 500 scenarios:

python example/OutSampleTest/Molecule.py --name="Molecule" --molecule="H2" --qubit_num=2 --evo_time=20 --n_ts=50 --r_seed=1000 --gen_target=0 \
  --target="../../result/target/Molecule_H2_target.csv" --group=10 --num_scenario=500 --cvar=0.05 --var=0.05 --draw=0 \
  --control="../../result/control/Stochastic/Molecule_H2_evotime20.0_n_ts50_ptypeCONSTANT_offset0.2_sum_penalty1.0_scenario20_cvar0.05_mean0_var0.05_weight0.5.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.

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 ([email protected])

Contact

Xinyu Fei ([email protected])

Siqian Shen ([email protected])