Editing Knapsack problem (section)

====Quantum approximate optimization====
[[Quantum approximate optimization algorithm]] (QAOA) can be employed to solve Knapsack problem using [[quantum computation]] by minimizing the [[Hamiltonian (quantum mechanics)|Hamiltonian]] of the problem. The Knapsack Hamiltonian is constructed via embedding the constraint condition to the cost function of the problem with a penalty term.<ref>{{Cite journal |last=Lucas |first=Andrew |date=2014 |title=Ising formulations of many NP problems |journal=Frontiers in Physics |volume=2 |page=5 |doi=10.3389/fphy.2014.00005 |doi-access=free |arxiv=1302.5843 |bibcode=2014FrP.....2....5L |issn=2296-424X}}</ref><math display="block">
{H} = -\sum_{i=1}^n v_i x_i + P \left(\sum_{i=1}^n w_i x_i - W\right)^2, 
</math>where <math>
P 
</math> is the penalty constant which is determined by case-specific fine-tuning.