In the attached Jupyter notebook, I have presented a Variational Quantum Algorithm (VQA) [1] for a Quadratic Unconstrained Binary Optimization (QUBO) problem. A QUBO belongs to the NP-hard class, and it is equivalent to find the minimum energy (ground) state of a spin (Ising) Hamiltonian [2]. Here, the implementation of VQA is done using PyTorch.

Problem instance

Algorithm: VQA

Solution

[1] Peruzzo, A., McClean, J., Shadbolt, P. et al. A variational eigenvalue solver on a photonic quantum processor. Nat Commun 5, 4213 (2014).

[2] Lucas A (2014) Ising formulations of many NP problems. Front. Physics 2:5.

[3] Marcello Benedetti et al 2019 Quantum Sci. Technol. 4 043001