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A book about turning high-degree optimization problems into quadratic optimization problems that maintain the same global minimum (ground state).
Nike Dattani, Quadratization in discrete optimization and quantum mechanics (2019) arXiv:1901.04405
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1909
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Endre Boros and Peter L. Hammer, “Pseudo-Boolean optimization,” Discrete Applied Mathematics 123
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V. Kolmogorov and R. Zabih, “What energy functions can be minimized via graph cuts?” IEEE Transactions on Pattern Analysis and Machine Intelligence 26
2004
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D. Freedman and P. Drineas, “Energy Minimization via Graph Cuts: Settling What is Possible,” in 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05) , Vol. 2 (IEEE, 2005) pp. 939–946
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Julia Kempe, Alexei Kitaev, and Oded Regev, “The Complexity of the Local Hamiltonian Problem,” SIAM Journal on Computing 35
2006
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Asem M. Ali, Aly A. Farag, and Georgy L. Gimel’farb, “Optimizing Binary MRFs with Higher Order Cliques,” (Springer, Berlin, Heidelberg, 2008) pp. 98–111
2008
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Vicky Choi, “Minor-embedding in adiabatic quantum computation: I. the parameter setting problem,” Quantum Information Processing 7
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Alejandro Perdomo, Colin Truncik, Ivan Tubert-Brohman, Geordie Rose, and Alán Aspuru-Guzik, “Construction of model Hamiltonians for adiabatic quantum computation and its application to finding low-energy conformations of lattice protein models,” Phys. Rev. A 78
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Sergey Bravyi, David P. DiVincenzo, Daniel Loss, and Barbara M. Terhal, “Quantum Simulation of Many-Body Hamiltonians Using Perturbation Theory with Bounded-Strength Interactions,” Physical Review Letters 101
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Stephen P. Jordan and Edward Farhi, “Perturbative gadgets at arbitrary orders,” Physical Review A 77
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Jacob D. Biamonte and Peter J. Love, “Realizable Hamiltonians for universal adiabatic quantum computers,” Physical Review A 78
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Hartmut Neven, Vasil S Denchev, Marshall Drew-Brook, Jiayong Zhang, William G Macready, and Geordie Rose, NIPS 2009 Demonstration: Binary Classification using Hardware Implementation of Quantum Annealing , Tech. Rep. (2009)
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Daniel Nagaj, “Fast universal quantum computation with railroad-switch local Hamiltonians,” Journal of Mathematical Physics 51
2010
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Gernot Schaller and Ralf Schützhold, “The role of symmetries in adiabatic quantum algorithms,” Quantum Information & Computation 10
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H Ishikawa, “Transformation of General Binary MRF Minimization to the First-Order Case,” IEEE Transactions on Pattern Analysis and Machine Intelligence 33
2011
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Andrew C. Gallagher, Dhruv Batra, and Devi Parikh, “Inference for order reduction in Markov random fields,” in CVPR 2011 (IEEE, 2011) pp. 1857–1864
2011
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Alexander Fix, Aritanan Gruber, Endre Boros, and Ramin Zabih, “A graph cut algorithm for higher-order Markov Random Fields,” in 2011 International Conference on Computer Vision (IEEE, 2011) pp. 1020–1027
Yudong Cao, Ryan Babbush, Jacob Biamonte, and Sabre Kais, “Hamiltonian gadgets with reduced resource requirements,” Physical Review A 91
2015
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Yudong Cao and Daniel Nagaj, Quantum Information & Computation , Vol. 15 (Rinton Press, 2015) pp. 1197–1222
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2016
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Martin Anthony, Endre Boros, Yves Crama, and Aritanan Gruber, “Quadratization of symmetric pseudo-Boolean functions,” Discrete Applied Mathematics 203
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Andrea Rocchetto, Simon C Benjamin, and Ying Li, “Stabilizers as a design tool for new forms of the Lechner-Hauke-Zoller annealer,” Science Advances 2
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2011
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Kahl and Strandmark, “Generalized Roof Duality for Pseudo-Boolean Optimization,” International Conference on Computer Vision (2011)
2011
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Samuel A. Ocko and Beni Yoshida, “Nonperturbative Gadget for Topological Quantum Codes,” Physical Review Letters 107
2011
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Qian-Heng Duan and Ping-Xing Chen, “Realization of universal adiabatic quantum computation with fewer physical resources,” Physical Review A 84
2011
Cited alongside, same era.
Courtney G Brell, Steven T Flammia, Stephen D Bartlett, and Andrew C Doherty, “Toric codes and quantum doubles from two-body Hamiltonians,” New Journal of Physics 13
2011
Cited alongside, same era.
Vicky Choi, “Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design,” Quantum Information Processing 10
2011
Cited alongside, same era.
Daniel Nagaj, “Universal two-body-Hamiltonian quantum computing,” Physical Review A 85
2012
Cited alongside, same era.
Nanyang Xu, Jing Zhu, Dawei Lu, Xianyi Zhou, Xinhua Peng, and Jiangfeng Du, “Quantum Factorization of 143 on a Dipolar-Coupling Nuclear Magnetic Resonance System,” Physical Review Letters 108
2012
Cited alongside, same era.
2016
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Nicholas Chancellor, “Max-k-SAT, Multi-Body Frustration, & Multi-Body Sampling on a Two Local Ising System,” AQC 2016 https://www.youtube.com/watch?v=aC-6hg_h3EA (2016)
2016
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Gemma De las Cuevas and Toby S. Cubitt, “Simple universal models capture all classical spin physics,” Science 351
2016
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Yigit Subasi and Christopher Jarzynski, “Nonperturbative embedding for highly nonlocal Hamiltonians,” Physical Review A 94
2016
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Seth Lloyd and Barbara M Terhal, “Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions,” New Journal of Physics 18
2016
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Martin Anthony, Endre Boros, Yves Crama, and Aritanan Gruber, “Quadratic reformulations of nonlinear binary optimization problems,” Mathematical Programming 162
2017
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N Chancellor, S Zohren, and P A Warburton, “Circuit design for multi-body interactions in superconducting quantum annealing systems with applications to a scalable architecture,” npj Quantum Information 3
2017
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Jianbing Shen, Jianteng Peng, Xingping Dong, Ling Shao, and Fatih Porikli, “Higher Order Energies for Image Segmentation,” IEEE Transactions on Image Processing 26
2017
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Joel Strand, Anthony Przybysz, David Ferguson, and Ken Zick, “ZZZ coupler for native embedding of MAX-3SAT problem instances in quantum annealing hardware,” Bulletin of the American Physical Society Volume 62, Number 4
2017
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David Ferguson, Anthony Przybysz, and Joel Strand, “ZZZ coupler for superconducting qubits,” US Patent: 20180261752A1 (2017)
2017
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Endre Boros, Yves Crama, and Elisabeth Rodríguez-Heck, “Quadratizations of symmetric pseudo-boolean functions: sub-linear bounds on the number of auxiliary variables,” in ISAIM (2018)
2018
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Endre Boros, Yves Crama, and Elisabeth Rodríguez-Heck, “Compact quadratizations for pseudo-boolean functions,” in unpublished (2018)
2018
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David Ferguson, Anthony Przybysz, and Joel Strand, “ZZZ coupler for superconducting qubits,” US Patent: 20180342663A1 (2018)
2018
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2018
Later among the works it cites.
Ka Wa Yip, Hong Xu, T. K. Satish Kumar, and Sven Koenig, “Quadratic reformulation of nonlinear pseudo-boolean functions via the constraint composite graph,” in the International Conference on Integration of Artificial Intelligence and Operations Research Techniques in Constraint Programming (2019) pp. 643–660
2019
Closest in time.
Aron J. Cohen, Hongjun Luo, Kai Guther, Werner Dobrautz, David P. Tew, and Ali Alavi, “Similarity transformation of the electronic Schrödinger equation via Jastrow factorization,” The Journal of Chemical Physics 151
2019
Closest in time.
Tim Menke, Cyrus Hirjibehedin, Steven Weber, Gabriel Samach, Simon Gustavsson, Alan Aspuru-Guzik, William Oliver, and Andrew Kerman, “A many-body coupler for coherent 4-local interaction of superconducting flux qubits,” APS March Meeting 2019, abstract id.A42.011 (2019)
2019
Closest in time.