# Quantum Optimization Heuristics with an Application to Knapsack Problems

@article{Dam2021QuantumOH,
title={Quantum Optimization Heuristics with an Application to Knapsack Problems},
author={Wim van Dam and Karim M. El Defrawy and Nicholas Genise and Natalie Parham},
journal={2021 IEEE International Conference on Quantum Computing and Engineering (QCE)},
year={2021},
pages={160-170}
}
• Published 19 August 2021
• Computer Science, Physics
• 2021 IEEE International Conference on Quantum Computing and Engineering (QCE)
This paper introduces two techniques that make the standard Quantum Approximate Optimization Algorithm (QAOA) more suitable for constrained optimization problems. The first technique describes how to use the outcome of a prior greedy classical algorithm to define an initial quantum state and mixing operation to adjust the quantum optimization algorithm to explore the possible answers around this initial greedy solution. The second technique is used to nudge the quantum exploration to avoid the…
5 Citations

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## References

SHOWING 1-10 OF 12 REFERENCES

• Computer Science
Quantum
• 2021
Results indicate that warm-starting the Quantum Approximate Optimization Algorithm (QAOA) is particularly beneficial at low depth, and it is straightforward to apply the same ideas to other randomized-rounding schemes and optimization problems.
• Computer Science
2020 IEEE International Conference on Quantum Computing and Engineering (QCE)
• 2020
We propose GM-QAOA, a variation of the Quantum Alternating Operator Ansatz (QAOA) that uses Grover-like selective phase shift mixing operators. GM-QAOA works on any NP optimization problem for which
• Computer Science
• 2020
This paper explores strategies for enforcing hard constraints by using $XY$ Hamiltonians as mixing operators (mixers) and demonstrates that, for an integer variable admitting $\ensuremath{\kappa}$ discrete values represented through one-hot encoding, certain classes of the mixer Hamiltonian can be implemented without Trotter error in depth.
Abstract A bivariate distribution is not determined by the knowledge of the margins. Two bivariate distributions with exponential margins are analyzed and another is briefly mentioned. In the first
Association between two variables has in the past been measured or tested by several coefficients, among them (i) Product moment correlation coefficient. (ii) Spearman's rank correlation coefficient.
• Mathematics
• 2005
This article is based on a talk presented at a conference “Quantum Annealing and Other Optimization Methods” held at Kolkata, India on March 2–5, 2005. It will be published in the proceedings
• Physics
Algorithms
• 2019
The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter.
• Computer Science, Mathematics
• 2014
A quantum algorithm that produces approximate solutions for combinatorial optimization problems that depends on a positive integer p and the quality of the approximation improves as p is increased, and is studied as applied to MaxCut on regular graphs.
• Computer Science
2007 Information Theory and Applications Workshop
• 2007
The results demonstrate that efficient filter allocation significantly improves the tradeoff between the number of filters used and the amount of legitimate traffic preserved.