Quantum circuit evolutionary framework applied on set partitioning problem

> Figure 1: Plot of the convergence curves of the VQE, QCE, and QCE-APCD algorithms for 14 qubits instance of the set of partitioning.

Overview

Quantum algorithms hold significant potential for solving optimization problems. Among them, variational algorithms are particularly promising for near-term quantum devices due to their hybrid quantum-classical approach to parameter optimization. However, challenges like convergence stagnation, such as barren plateaus, often hinder their performance.

This repository introduces a quantum circuit framework with variable topology to address these challenges. The framework incorporates two approaches:

1. The quantum circuit evolution method known from literature [1].
2. A novel pseudo-counterdiabatic evolutionary term, inspired by counterdiabatic physics [2], tailored to the Hamiltonian structure.

Both approaches were applied to the Set Partitioning Problem in this study, as detailed in Quantum circuit evolutionary framework applid on the set partitioning problem (12/2024)

Instances_Benchmark:

We evaluated our algorithms using 35 benchmark instances from Svensson et al., tailored to the Set Partitioning Problem.

Functions:

1. _utility.py: Contains utility functions for reading benchmark files, building Hamiltonians, and solving instances using Gurobi.
2. qce.py: Implements the Quantum Circuit Evolutionary (QCE) algorithm. To choose between AF-QCE and APCD-QCE, refer to the experiment_qce.ipynb notebook.

Notebooks:

1. experiment_vqe.ipynb: Demonstrates the Variational Quantum Eigensolver (VQE) based on the configuration used by Cacao et al. in [3].
2. experiment_qce.ipynb: Explores the AF-QCE and APCD-QCE methods in both noiseless and noisy scenarios.

Figure 2: Counterdiabatic circuit structure for the APCD-QCE method, where only the term $U_{PCD}$ undergoes topology variations.

Reference

1. Franken, L., et al. "Quantum Circuit Evolution on NISQ Devices," 2022 IEEE Congress on Evolutionary Computation (CEC), Padua, Italy, 2022, pp. 1-8. Available at: 10.1109/CEC55065.2022.9870269.
2. Hegade, N. N., Chen, X., & Solano, E. "Digitized Counterdiabatic Quantum Optimization," Physical Review Research, vol. 4, no. 4, 2022, p. L042030. Available at: https://link.aps.org/doi/10.1103/PhysRevResearch.4.L042030.
3. Cacao, R., Cortez, L. R. C. T., & Forner, J. et al. "The Set Partitioning Problem in a Quantum Context," Optimization Letters, vol. 18, pp. 1–17, 2024. Available at: 10.1007/s11590-023-02029-1.
4. Fernandez, B. O., Bloot, R., and Moret, M. A., "Quantum Circuit Evolutionary Framework Applied on Set Partitioning Problem," (In review at Springer).