Five Starter Problems: Solving Quadratic Unconstrained Binary Optimization Models on Quantum Computers

Mazumder, Arul; Tayur, Sridhar

Five Starter Problems: Solving Quadratic Unconstrained Binary Optimization Models on Quantum Computers

Arul Mazumder
(
- Carnegie Mellon U.
)
,
Sridhar Tayur
(
- Carnegie Mellon U.
)

Jan 17, 2024

40 pages

e-Print:

2401.08989 [quant-ph]

View in:

ADS Abstract Service

pdf

reference search1 citation

Citations per year

Abstract: (arXiv)

This tutorial offers a quick hands-on introduction to solving Quadratic Unconstrained Binary Optimization (QUBO) problems on currently available quantum computers. We cover both IBM and D-Wave machines: IBM utilizes a gate/circuit architecture, and D-Wave is a quantum annealer. We provide examples of three canonical problems and two models from practical applications. An associated GitHub repository provides the implementations in five companion notebooks. In addition to undergraduate and graduate students in computationally intensive disciplines, this article aims to reach working industry professionals seeking to explore the potential of near-term quantum applications.

Note:

40 pages, 14 figures, 1 table

References(62)

Figures(20)

Vazquez AC, Ceroni J, Chen R, Frisch A, Gambetta J, Garion S, Gil L

Abbas A
,
Andersson S
,
Asfaw A
,
Corcoles A
,
Bello L

et al.

Pardalos PM, Resende MG Finding independent sets in a graph using continuous multivariable polynomial formulations

Abello J
,
Butenko S

- J.Global Optim. 21 (2001) 111-137
•
DOI:
- 10.1023/a:1011968411281

A Simple Proof that Toffoli and Hadamard are Quantum Universal

Dorit Aharonov
(
- Hebrew U. and
- Unlisted, US, CA
)

e-Print:
- quant-ph/0301040

Adiabatic quantum computation

Tameem Albash
(
- CIT-USC
)
,
Daniel A. Lidar
(
- Southern California U.
)

- Rev.Mod.Phys. 90 (2018) 1, 015002
•
e-Print:
- 1611.04471
•
DOI:
- 10.1103/RevModPhys.90.015002

Robertson AG, Tayur S

Alghassi H
,
Dridi R

•
DOI:
- 10.1101/845719

A new modeling and solution approach for the number partitioning problem. JAMDS 9:113-121, URL

Alidaee B
,
Glover F
,
Kochenberger G
,
Rego C

•
DOI:
- 10.1155/JAMDS.2005.113

Amazon Web Services Amazon Braket. URL

Israel RB, Lackey B

Bian Z
,
Chudak F

•
DOI:
- 10.3389/fict.2016.00014

Beyond quantum supremacy: the hunt for useful quantum computers. Nature 574(7776):19-21, ISSN 1476-4687, URL

Brooks M

•
DOI:
- 10.1038/d41586-019-02936-3

Kanj IA, Xia G

Chen J

- Comput.Sci. 238 (2006) 249

Simulated annealing: Searching for an optimal temperature schedule

Cohn H
,
Fielding M

•
DOI:
- 10.1137/S1052623497329683

Commander CW Maximum cut problem, MAX-CUTMaximum Cut Problem, MAX-CUT, 1991-1999 (Boston, MA:

•
DOI:
- 10.1007/978-0-387-74759-0_358

Cplex II (2009) V12. 1: User’s manual for cplex. International Business Machines Corporation 46(53):157

de Falco D
,
Tamascelli D

•
DOI:
- 10.1051/ita/2011013

A quantum approximate optimization algorithm

Farhi E
,
Goldstone J
,
Gutmann S

Sidarto KA, Sumarti N

Febrianti W

•
DOI:
- 10.3390/ijfs11010001

Author: Five Starter Problems: Solving Quadratic Unconstrained Binary Optimization Models on Quantum Computers Article submitted toINFORMS TutORials 37

Matou ¨ sek J ˇ Semidefinite Programming

Gartner B

•
DOI:
- 10.1007/978-3-642-22015-9_2

Genetic algorithms with local optima handling to solve sudoku puzzles. Proceedings of theInternational Conference on Computing and

Gerges F
,
Zouein G
,
Azar D

- Artificial Intel. 19 (2018) 22
•
DOI:
- 10.1145/3194452.3194463

Grover adaptive search for constrained polynomial binary optimization

Gilliam A
,
Woerner S
,
Gonciulea C

- Quantum 5 (2021) 428
•
DOI:
- 10.22331/q-2021-04-08-428

Un algorithme de programmation quadratique en variables binaires. RAIRO - Operations Research - Recherche Operationnelle ´ 3(V2):57-73, URL

Ginsburgh V. VPA

Tabu search—part i

Glover F

- ORSA J.Comput. 1 (1989) 190-206

Goemans MX, Williamson DP Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

- J.Assoc.Comput.Machinery 42 (1995) 1115-1145
•
DOI:
- 10.1145/227683.227684

QAOA for Max-Cut requires hundreds of qubits for quantum speed-up

- Sci.Rep. 9 (2019) 1, 6903
•
DOI:
- 10.1038/s41598-019-43176-9

Hammer PL

Rudeanu S

•
DOI:
- 10.1007/978-3-642-85823-9

Solving quadratic (0, 1)-problems by semidefinite programs and cutting planes

Helmberg C
,
Rendl F

- Math.Programming 82 (1998) 291-315
•
DOI:
- 10.1007/bf01580072

1-25 of 62
1
2
3
25 / page