2019/01/14 by Nike Dattani, Dattani, Nike · 9 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #05C50 #11A41 #11A51 #11N35 #11N36 #11N80 #11Y05 #65K10 #65P10 #65Y20 #68Q12 #81-08 #81P68 #81P94 #94A60 #B.2.4 #B.8.2 #C.1.3 #C.1.m #C.4 #Chemical Physics (physics.chem-ph) #Computability, Logic, AI Algorithms #Computer Vision and Pattern Recognition (cs.CV) #DNA and Biological Computing #Discrete Mathematics (cs.DM) #E.3 #F.2.1 #F.2.3 #F.4.1 #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #G.0 #G.1.0 #G.1.3 #G.1.5 #G.1.6 #G.2.0 #G.2.1 #I.1.2 #I.6.4 #J.2 #K.2 #Optimization and Control (math.OC) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #acm:05C50 #acm:11A41 #acm:11A51 #acm:11N35 #acm:11N36 #acm:11N80 #acm:11Y05 #acm:65K10 #acm:65P10 #acm:65Y20 #acm:68Q12 #acm:81P68 #cs.CV #cs.DM #math.OC #msc:05C50 #msc:11A41 #msc:11A51 #msc:11N35 #msc:11N36 #msc:11N80 #msc:11Y05 #msc:65K10 #msc:65P10 #msc:65Y20 #msc:68Q12 #msc:81-08 #msc:81P68 #msc:81P94 #msc:94A60 #physics.chem-ph #quant-ph
paper · pdf · doi:10.48550/arxiv.1901.04405
Contributors (in order of lines contributed on GitHub): Nike Dattani, Richard Tanburn, Andreas Soteriou, Nicholas Chancellor, Szilard Szalay, Elisabeth Rodriguez-Heck, Hou Tin Chau, Ka Wa Yip, Yudong Cao
openalex publication_date 2019/01/14 · arxiv created 2019/09/23 · arxiv updated 2019/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A book about turning high-degree optimization problems into quadratic optimization problems that maintain the same global minimum (ground state). This book explores quadratizations for pseudo-Boolean optimization, perturbative gadgets used in QMA completeness theorems, and also non-perturbative k-local to 2-local transformations used for quantum mechanics, quantum annealing and universal adiabatic quantum computing. The book contains ~70 different Hamiltonian transformations, each of them on a separate page, where the cost (in number of auxiliary binary variables or auxiliary qubits, or number of sub-modular terms, or in graph connectivity, etc.), pros, cons, examples, and references are given. One can therefore look up a quadratization appropriate for the specific term(s) that need to be quadratized, much like using an integral table to look up the integral that needs to be done. This book is therefore useful for writing compilers to transform general optimization problems, into a form that quantum annealing or universal adiabatic quantum computing hardware requires; or for transforming quantum chemistry problems written in the Jordan-Wigner or Bravyi-Kitaev form, into a form where all multi-qubit interactions become 2-qubit pairwise interactions, without changing the desired ground state. Applications cited include computer vision problems (e.g. image de-noising, un-blurring, etc.), number theory (e.g. integer factoring), graph theory (e.g. Ramsey number determination), and quantum chemistry. The book is open source, and anyone can make modifications here: https://github.com/HPQC-LABS/BookAboutQuadratization.