Embedding quadratization gadgets on Chimera and Pegasus graphs

We group all known quadratizations of cubic and quartic terms in binary optimization problems into six and seven unique graphs respectively. We then perform a minor embedding of these graphs onto the well-known Chimera graph, and the brand new Pegasus graph. We conclude with recommendations for which gadgets are best to use when aiming to reduce the total number of qubits required to embed a problem.

[1]  Rob Thew,et al.  Quantum Science and Technology—one year on , 2018 .

[2]  W. Marsden.  I and J , 2012 .

[3]  Endre Boros,et al.  Quadratizations of symmetric pseudo-Boolean functions: sub-linear bounds on the number of auxiliary variables , 2018, ISAIM.

[4]  Xu Li-ping,et al.  Quantum Information Processing in Quantum Wires , 2004 .

[5]  Abira Sengupta.  IEEE Journal of Solid-State Circuits Updates [Society News] , 2016 .

[6]  Hartmut Neven,et al.  NIPS 2009 Demonstration: Binary Classification using Hardware Implementation of Quantum Annealing , 2009 .

[7]  Peter L. Hammer,et al.  Discrete Applied Mathematics , 1993 .

[8]  Akihisa Tomita,et al.  Quantum information processing with fiber optics: Quantum Fourier transform of 1024 qubits , 2005 .

[9]  Nikesh S. Dattani,et al.  Quadratization in discrete optimization and quantum mechanics , 2019, ArXiv.

[10]  N. Dattani,et al.  Reducing multi-qubit interactions in adiabatic quantum computation without adding auxiliary qubits. Part 2: The"split-reduc"method and its application to quantum determination of Ramsey numbers , 2015, 1508.07190.

[11]  Richard Tanburn,et al.  Reducing multi-qubit interactions in adiabatic quantum computation without adding auxiliary qubits. Part 1: The "deduc-reduc" method and its application to quantum factorization of numbers , 2015, ArXiv.

[12]  King-Sun Fu,et al.  IEEE Transactions on Pattern Analysis and Machine Intelligence Publication Information , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.