A quantum walk-assisted approximate algorithm for bounded NP optimisation problems

This paper describes an application of the quantum approximate optimisation algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO PB). We consider a generalisation of the QAOA state evolution...

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Published in:	Quantum information processing Vol. 18; no. 3; pp. 1 - 18
Main Authors:	Marsh, S., Wang, J. B.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.03.2019 Springer Nature B.V
Subjects:	Algorithms Computer simulation Data Structures and Information Theory Mathematical Physics Optimization Physics Physics and Astronomy Quantum Computing Quantum Information Technology Quantum Physics Spintronics Minimum vertex cover Quantum walks Quantum optimisation QAOA
ISSN:	1570-0755, 1573-1332
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Abstract	This paper describes an application of the quantum approximate optimisation algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO PB). We consider a generalisation of the QAOA state evolution to alternating quantum walks and solution-quality-dependent phase shifts and use the quantum walks to integrate the problem constraints of NPO problems. We apply the concept of a hybrid quantum-classical variational scheme to attempt finding the highest expectation value, which contains a high-quality solution. We synthesise an efficient quantum circuit for the constrained optimisation algorithm, and we numerically demonstrate the behaviour of the circuit with respect to an illustrative NP optimisation problem with constraints, minimum vertex cover. With examples, this paper demonstrates that the degree of accuracy to which the quantum walks are simulated can be treated as an additional optimisation parameter, leading to improved results.
AbstractList	This paper describes an application of the quantum approximate optimisation algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO PB). We consider a generalisation of the QAOA state evolution to alternating quantum walks and solution-quality-dependent phase shifts and use the quantum walks to integrate the problem constraints of NPO problems. We apply the concept of a hybrid quantum-classical variational scheme to attempt finding the highest expectation value, which contains a high-quality solution. We synthesise an efficient quantum circuit for the constrained optimisation algorithm, and we numerically demonstrate the behaviour of the circuit with respect to an illustrative NP optimisation problem with constraints, minimum vertex cover. With examples, this paper demonstrates that the degree of accuracy to which the quantum walks are simulated can be treated as an additional optimisation parameter, leading to improved results.
ArticleNumber	61
Author	Wang, J. B. Marsh, S.
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Cites_doi	10.1126/science.1229957 10.1016/j.disc.2011.06.032 10.1016/0004-3702(94)90019-1 10.1007/978-3-642-36014-5 10.1016/0375-9601(92)90335-J 10.1038/ncomms11511 10.1103/PhysRevA.81.052313 10.1137/S0097539795293172 10.3389/fphy.2014.00005 10.1088/1751-8113/48/35/355301 10.1103/PhysRevA.70.022314 10.1103/PhysRevA.58.915 10.1103/PhysRevLett.118.080501 10.7153/jmi-04-32 10.1007/s11128-016-1456-z 10.1088/1367-2630/aab701 10.1103/PhysRevA.95.032318 10.1145/966049.781528 10.1088/1367-2630/16/3/033040 10.1093/comjnl/7.4.308 10.1038/ncomms5213 10.1023/A:1007627028578 10.1090/S0002-9904-1945-08448-1 10.1007/3-540-60246-1_129 10.1145/780542.780552 10.1007/3-540-44676-1_15 10.1145/780542.780546 10.1007/3-540-56939-1_61 10.1145/237814.237866 10.1007/978-1-4684-2001-2_9
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References	Peruzzo, McClean, Shadbolt, Yung, Zhou, Love, Aspuru-Guzik, O’Brien (CR16) 2014; 5 Nelder, Mead (CR36) 1965; 7 Suzuki (CR33) 1992; 165 CR19 Lau, Pooser, Siopsis, Weedbrook (CR34) 2017; 118 Manouchehri, Wang (CR14) 2014 CR35 CR32 Childs, Gosset, Webb (CR7) 2013; 339 CR31 Godsil (CR25) 2012; 312 Shor (CR1) 1997; 26 Izaac, Zhan, Bian, Wang, Li, Wang, Xue (CR8) 2017; 95 Childs, Goldstone (CR12) 2004; 70 O’Callahan, Choi (CR20) 2003; 38 Xu, Sun, Wu, Zhang, Arshed, Sanders (CR11) 2018; 20 Welch, Greenbaum, Mostame, Aspuru-Guzik (CR30) 2014; 16 Feller (CR28) 1945; 51 Lucas (CR17) 2014; 2 Gamble, Friesen, Zhou, Joynt, Coppersmith (CR10) 2010; 81 Erdős, Rényi (CR37) 1959; 6 CR2 Loke, Tang, Rodriguez, Small, Wang (CR9) 2017; 16 CR4 CR3 CR5 CR27 CR26 Sharma, Gupta, Kapoor (CR29) 2010; 4 CR24 CR23 Domingo, Mishra, Pitt (CR22) 1999; 37 Farhi, Gutmann (CR6) 1998; 58 Filiol, Franc, Gubbioli, Moquet, Roblot (CR18) 2007; 23 Hou (CR21) 1994; 65 Li, Wang (CR13) 2015; 48 Qiang, Loke, Montanaro, Aungskunsiri, Zhou, O’Brien, Wang, Matthews (CR15) 2016; 7 H-K Lau (2171_CR34) 2017; 118 2171_CR5 R O’Callahan (2171_CR20) 2003; 38 A Lucas (2171_CR17) 2014; 2 AM Childs (2171_CR7) 2013; 339 2171_CR32 X Qiang (2171_CR15) 2016; 7 C Domingo (2171_CR22) 1999; 37 2171_CR35 C Godsil (2171_CR25) 2012; 312 JA Nelder (2171_CR36) 1965; 7 2171_CR31 T Loke (2171_CR9) 2017; 16 2171_CR19 Aimin Hou (2171_CR21) 1994; 65 E Farhi (2171_CR6) 1998; 58 Z-J Li (2171_CR13) 2015; 48 S Xu (2171_CR11) 2018; 20 W Feller (2171_CR28) 1945; 51 JA Izaac (2171_CR8) 2017; 95 M Suzuki (2171_CR33) 1992; 165 K Manouchehri (2171_CR14) 2014 2171_CR24 2171_CR23 P Erdős (2171_CR37) 1959; 6 J Welch (2171_CR30) 2014; 16 R Sharma (2171_CR29) 2010; 4 2171_CR2 E Filiol (2171_CR18) 2007; 23 2171_CR4 2171_CR3 JK Gamble (2171_CR10) 2010; 81 2171_CR26 PW Shor (2171_CR1) 1997; 26 AM Childs (2171_CR12) 2004; 70 A Peruzzo (2171_CR16) 2014; 5 2171_CR27
References_xml	– volume: 339 start-page: 791 year: 2013 ident: CR7 article-title: Universal computation by multiparticle quantum walk publication-title: Science doi: 10.1126/science.1229957 – volume: 312 start-page: 129 year: 2012 ident: CR25 article-title: State transfer on graphs publication-title: Discrete Math. doi: 10.1016/j.disc.2011.06.032 – ident: CR4 – volume: 65 start-page: 281 year: 1994 ident: CR21 article-title: A theory of measurement in diagnosis from first principles publication-title: Artif. Intell. doi: 10.1016/0004-3702(94)90019-1 – ident: CR2 – volume: 6 start-page: 290 year: 1959 ident: CR37 article-title: On random graphs. I publication-title: Publ. Math. – year: 2014 ident: CR14 publication-title: Physical Implementation of Quantum Walks doi: 10.1007/978-3-642-36014-5 – volume: 165 start-page: 387 year: 1992 ident: CR33 article-title: General theory of higher-order decomposition of exponential operators and symplectic integrators publication-title: Phys. Lett. A doi: 10.1016/0375-9601(92)90335-J – ident: CR35 – volume: 7 start-page: 11511 year: 2016 ident: CR15 article-title: Efficient quantum walk on a quantum processor publication-title: Nat. Commun. doi: 10.1038/ncomms11511 – volume: 81 start-page: 052313 year: 2010 ident: CR10 article-title: Two-particle quantum walks applied to the graph isomorphism problem publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.81.052313 – volume: 26 start-page: 1484 year: 1997 ident: CR1 article-title: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer publication-title: SIAM J. Comput. doi: 10.1137/S0097539795293172 – ident: CR27 – volume: 2 start-page: 5 year: 2014 ident: CR17 article-title: Ising formulations of many np problems publication-title: Front. Phys. doi: 10.3389/fphy.2014.00005 – ident: CR23 – volume: 48 start-page: 355301 year: 2015 ident: CR13 article-title: An analytical study of quantum walk through glued-tree graphs publication-title: J. Phys. A Math. Theor. doi: 10.1088/1751-8113/48/35/355301 – volume: 70 start-page: 022314 year: 2004 ident: CR12 article-title: Spatial search by quantum walk publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.70.022314 – ident: CR19 – volume: 58 start-page: 915 year: 1998 ident: CR6 article-title: Quantum computation and decision trees publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.58.915 – volume: 23 start-page: 373 year: 2007 ident: CR18 article-title: Combinatorial optimisation of worm propagation on an unknown network publication-title: World Acad. Sci. Eng. Technol. – volume: 118 start-page: 080501 year: 2017 ident: CR34 article-title: Quantum machine learning over infinite dimensions publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.118.080501 – volume: 4 start-page: 355 year: 2010 ident: CR29 article-title: Some better bounds on the variance with applications publication-title: J. Math. Inequal. doi: 10.7153/jmi-04-32 – ident: CR3 – volume: 16 start-page: 25 year: 2017 ident: CR9 article-title: Comparing classical and quantum PageRanks publication-title: Quantum Inf. Process. doi: 10.1007/s11128-016-1456-z – volume: 20 start-page: 053039 year: 2018 ident: CR11 article-title: Quantum walk on a chimera graph publication-title: N. J. Phys. doi: 10.1088/1367-2630/aab701 – volume: 95 start-page: 032318 year: 2017 ident: CR8 article-title: Centrality measure based on continuous-time quantum walks and experimental realization publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.95.032318 – ident: CR31 – volume: 38 start-page: 167 year: 2003 ident: CR20 article-title: Hybrid dynamic data race detection publication-title: ACM SIGPLAN Not. doi: 10.1145/966049.781528 – volume: 16 start-page: 033040 year: 2014 ident: CR30 article-title: Efficient quantum circuits for diagonal unitaries without ancillas publication-title: N. J. Phys. doi: 10.1088/1367-2630/16/3/033040 – volume: 7 start-page: 308 year: 1965 ident: CR36 article-title: A simplex method for function minimization publication-title: Comput. J. doi: 10.1093/comjnl/7.4.308 – ident: CR32 – ident: CR5 – volume: 5 start-page: 4213 year: 2014 ident: CR16 article-title: A variational eigenvalue solver on a photonic quantum processor publication-title: Nat. Commun. doi: 10.1038/ncomms5213 – volume: 37 start-page: 89 year: 1999 ident: CR22 article-title: Efficient read-restricted monotone CNF/DNF dualization by learning with membership queries publication-title: Mach. Learn. doi: 10.1023/A:1007627028578 – ident: CR26 – ident: CR24 – volume: 51 start-page: 800 year: 1945 ident: CR28 article-title: The fundamental limit theorems in probability publication-title: Bull. Am. Math. Soc doi: 10.1090/S0002-9904-1945-08448-1 – volume: 51 start-page: 800 year: 1945 ident: 2171_CR28 publication-title: Bull. Am. Math. Soc doi: 10.1090/S0002-9904-1945-08448-1 – volume: 37 start-page: 89 year: 1999 ident: 2171_CR22 publication-title: Mach. Learn. doi: 10.1023/A:1007627028578 – volume: 65 start-page: 281 year: 1994 ident: 2171_CR21 publication-title: Artif. Intell. doi: 10.1016/0004-3702(94)90019-1 – volume: 23 start-page: 373 year: 2007 ident: 2171_CR18 publication-title: World Acad. Sci. Eng. Technol. – volume: 26 start-page: 1484 year: 1997 ident: 2171_CR1 publication-title: SIAM J. Comput. doi: 10.1137/S0097539795293172 – volume: 5 start-page: 4213 year: 2014 ident: 2171_CR16 publication-title: Nat. Commun. doi: 10.1038/ncomms5213 – volume: 7 start-page: 11511 year: 2016 ident: 2171_CR15 publication-title: Nat. Commun. doi: 10.1038/ncomms11511 – volume: 38 start-page: 167 year: 2003 ident: 2171_CR20 publication-title: ACM SIGPLAN Not. doi: 10.1145/966049.781528 – volume: 118 start-page: 080501 year: 2017 ident: 2171_CR34 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.118.080501 – volume: 95 start-page: 032318 year: 2017 ident: 2171_CR8 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.95.032318 – volume: 16 start-page: 25 year: 2017 ident: 2171_CR9 publication-title: Quantum Inf. Process. doi: 10.1007/s11128-016-1456-z – ident: 2171_CR23 doi: 10.1007/3-540-60246-1_129 – ident: 2171_CR2 doi: 10.1145/780542.780552 – volume: 16 start-page: 033040 year: 2014 ident: 2171_CR30 publication-title: N. J. Phys. doi: 10.1088/1367-2630/16/3/033040 – volume: 70 start-page: 022314 year: 2004 ident: 2171_CR12 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.70.022314 – volume: 2 start-page: 5 year: 2014 ident: 2171_CR17 publication-title: Front. Phys. doi: 10.3389/fphy.2014.00005 – volume-title: Physical Implementation of Quantum Walks year: 2014 ident: 2171_CR14 doi: 10.1007/978-3-642-36014-5 – ident: 2171_CR19 doi: 10.1007/3-540-44676-1_15 – volume: 6 start-page: 290 year: 1959 ident: 2171_CR37 publication-title: Publ. Math. – ident: 2171_CR35 – ident: 2171_CR5 – ident: 2171_CR32 doi: 10.1145/780542.780546 – ident: 2171_CR24 doi: 10.1007/3-540-56939-1_61 – ident: 2171_CR31 – volume: 312 start-page: 129 year: 2012 ident: 2171_CR25 publication-title: Discrete Math. doi: 10.1016/j.disc.2011.06.032 – ident: 2171_CR3 doi: 10.1145/237814.237866 – volume: 7 start-page: 308 year: 1965 ident: 2171_CR36 publication-title: Comput. J. doi: 10.1093/comjnl/7.4.308 – volume: 48 start-page: 355301 year: 2015 ident: 2171_CR13 publication-title: J. Phys. A Math. Theor. doi: 10.1088/1751-8113/48/35/355301 – volume: 4 start-page: 355 year: 2010 ident: 2171_CR29 publication-title: J. Math. Inequal. doi: 10.7153/jmi-04-32 – ident: 2171_CR27 – ident: 2171_CR26 doi: 10.1007/978-1-4684-2001-2_9 – volume: 81 start-page: 052313 year: 2010 ident: 2171_CR10 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.81.052313 – volume: 165 start-page: 387 year: 1992 ident: 2171_CR33 publication-title: Phys. Lett. A doi: 10.1016/0375-9601(92)90335-J – volume: 20 start-page: 053039 year: 2018 ident: 2171_CR11 publication-title: N. J. Phys. doi: 10.1088/1367-2630/aab701 – volume: 58 start-page: 915 year: 1998 ident: 2171_CR6 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.58.915 – volume: 339 start-page: 791 year: 2013 ident: 2171_CR7 publication-title: Science doi: 10.1126/science.1229957 – ident: 2171_CR4
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SubjectTerms	Algorithms Computer simulation Data Structures and Information Theory Mathematical Physics Optimization Physics Physics and Astronomy Quantum Computing Quantum Information Technology Quantum Physics Spintronics
Title	A quantum walk-assisted approximate algorithm for bounded NP optimisation problems
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