On Post-processing the Results of Quantum Optimizers
The use of quantum computing for applications involving optimization has been regarded as one of the areas it may prove to be advantageous (against classical computation). To further improve the solutions, post-processing techniques are often used on the results of quantum optimization. One such recent approach is the Multi Qubit Correction (MQC) algorithm by Dorband. In this paper, we will discuss and analyze the strengths and weaknesses of this technique. Based on our discussion, we perform an experiment on (i) how pairing heuristics on the input of MQC can affect the results of a quantum optimizer and (ii) a comparison between MQC and the built-in optimization method that D-wave Systems offers. Among our results, we are able to show that the built-in post-processing rarely beats MQC in our tests. We hope that by using the ideas and insights presented in this paper, researchers and developers will be able to make a more informed decision on what kind of post-processing methods to use for their quantum optimization needs.
KeywordsQuantum optimization Quantum annealing Approximation Evolutionary algorithm D-wave QAOA
We would like to thank John Dorband, Milton Halem and Samuel Lomonaco, Helmut Katzgraber and Nicholas Chancellor for their feedback. A special thanks to D-wave Systems for providing us access to their machines.
- 1.The d-wave post-processing documentation. https://docs.dwavesys.com/docs/latest
- 2.Adachi, S.H., Henderson, M.P.: Application of quantum annealing to training of deep neural networks. arXiv preprint arXiv:1510.06356 (2015)
- 3.Dorband, J.E.: Stochastic characteristics of qubits and qubit chains on the D-wave 2X. arXiv preprint arXiv:1606.05550 (2016)
- 4.Dorband, J.E.: A method of finding a lower energy solution to a qubo/ising objective function. arXiv preprint arXiv:1801.04849 (2018)
- 5.Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028 (2014)
- 6.Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution. arXiv preprint quant-ph/0001106 (2000)Google Scholar
- 8.Greenwood, G.W.: Finding solutions to NP problems: philosophical differences between quantum and evolutionary search algorithms. In: Proceedings of the 2001 Congress on Evolutionary Computation, vol. 2, pp. 815–822. IEEE (2001)Google Scholar
- 12.Jensen, F.V.: Bayesian updating in causal probabilistic networks by local computations. An introduction to Bayesian networks (1996)Google Scholar
- 16.Katzgraber, H.G., Hamze, F., Andrist, R.S.: Glassy chimeras could be blind to quantum speedup: designing better benchmarks for quantum annealing machines. Phys. Rev. X 4(2), 021008 (2014)Google Scholar
- 23.Preskill, J.: Quantum computing in the NISQ era and beyond. arXiv preprint arXiv:1801.00862 (2018)
- 24.Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: 1994 Proceedings of 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. IEEE (1994)Google Scholar