research-article

An MINLP Model for Scheduling and Placement of Quantum Circuits with a Heuristic Solution Approach

Authors:

Tayebeh Bahreini,

Naser MohammadzadehAuthors Info & Claims

ACM Journal on Emerging Technologies in Computing Systems (JETC), Volume 12, Issue 3

Article No.: 29, Pages 1 - 20

https://doi.org/10.1145/2766452

Published: 21 September 2015 Publication History

Abstract

Recent works on quantum physical design have pushed the scheduling and placement of quantum circuit into their prominent positions. In this article, a mixed integer nonlinear programming model is proposed for the placement and scheduling of quantum circuits in such a way that latency is minimized. The proposed model determines locations of gates and the sequence of operations. The proposed model is proved reducible to a quadratic assignment problem which is a well-known NP-complete combinatorial optimization problem. Since it is impossible to find the optimal solution of this NP-complete problem for large quantum circuits within a reasonable amount of time, a metaheuristic solution method is developed for the proposed model. Some experiments are conducted to evaluate the performance of the developed solution approach. Experimental results show that the proposed approach improves average latency by about 24.09% for the attempted benchmarks.

References

[1]

Ravindra K. Ahuja, Özlem Ergun, James B. Orlin, and Abraham P. Punnen. 2002. A survey of very large-scale neighborhood search techniques. Discr. Appl. Math. 123, 1, 75--102.

Digital Library

[2]

Thomas Bäck, David B. Fogel, and Zbigniew Michalewicz. 2000. Evolutionary Computation: Basic Algorithms and Operators, Vol. 1. CRC Press.

[3]

Steven Balensiefer, Lucas Kreger-Stickles, and Mark Oskin. 2005a. QUALE: Quantum architecture layout evaluator. Proc. SPIE 5815, 103--114.

[4]

Steven Balensiefer, Lucas Kregor-Stickles, and Mark Oskin. 2005b. An evaluation framework and instruction set architecture for ion-trap based quantum micro-architectures. ACM SIGARCH Comput. Archit. News 33, 2, 186--196.

Digital Library

[5]

Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. Divincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter. 1995. Elementary gates for quantum computation. Phys. Rev. A52, 5, 3457.

[6]

Mahdi Bashiri and Hossein Karimi. 2012. Effective heuristics and meta-heuristics for the quadratic assignment problem with tuned parameters and analytical comparisons. J. Industr. Engin. Int. 8, 1, 1--9.

[7]

Rainer E. Burkard and Franz Rendl. 1984. A thermodynamically motivated simulation procedure for combinatorial optimization problems. Euro. J. Oper. Res. 17, 2, 169--174.

[8]

Juan I. Cirac and Peter Zoller. 1995. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 20, 4091.

[9]

Andrew W. Cross. 2005. Synthesis and evaluation of fault-tolerant quantum computer architectures. Ph.D. dissertation. MIT, Cambridge, MA. http://dspace.mit.edu/handle/1721.1/30175

[10]

Andrew W. Cross, David P. Divincenzo, and Barbara M. Terhal. 2007. A comparative code study for quantum fault tolerance. Quantum Inf. Comput. 9, 7, 541--572.

Digital Library

[11]

Kenneth A. De Jong. 1975. An analysis of the behavior of a class of genetic adaptive. Ph.D. dissertation. University of Michigan, Michigan, USA.

Digital Library

[12]

David Deutsch. 1989. Quantum computational networks. Proc. Royal Soc. London. A. Math. Phys. Sci. 425, 73--90.

[13]

Mohammad J. Dousti and Massoud Pedram. 2012. Minimizing the latency of quantum circuits during mapping to the ion trap circuit fabric. In Proceedings of the Automation and Test in Europe Conference and Exhibition (DATE'12). 840--843.

Digital Library

[14]

Marshall L. Fisher. 2004. The Lagrangian relaxation method for solving integer programming problems. Manag. Sci. 50, 12, 1861--1871.

Digital Library

[15]

Michel Gendreau and Jean-Yves Potvin. 2010. Handbook of Metaheuristics, 2^nd ed. Springer.

Digital Library

[16]

Fred Glover and Manuel Laguna. 1999. Tabu search. In Handbook of Combinatorial Optimization. Springer, 2093--2229.

[17]

David E. Goldberg and Deb Kalyanmoy. 1991. A comparative analysis of selection schemes used in genetic algorithms. In Foundations of Genetic Algorithms. Morgan Kaufmann, San Fransisco, 69--93.

[18]

Hadi Goudarzi, Mohammad Javad Dousti, Alireza Shafaei, and Massoud Pedram. 2014. Design of a universal logic block for fault-tolerant realization of any logic operation in trapped-ion quantum circuits. Quantum Inf. Process. 13, 5, 1267--1299.

Digital Library

[19]

Markus Grassl. 2003. Circuits for quantum error-correcting codes. http://iaks-www.ira.uka.de/home/grassl/QECC/index.html.

[20]

Lov K. Grover. 1996. A fast quantum mechanical algorithm for database search. In Proceedings of the 28^th Annual ACM Symposium on Theory of Computing (STOC'96). 212--219.

Digital Library

[21]

Hartmut Häffner, Christian F. Roos, and Rainer Blatt. 2008. Quantum computing with trapped ions. Phys. Rep. 469, 4, 155--203.

[22]

David Hucul, Mark Yeo, Steven Olmschenk, Christopher Monroe, Winfried K. Hensinger, and James Rabchuk. 2008. On the transport of atomic ions in linear and multidimensional ion trap arrays. Quantum Inf. Comput. 8, 6, 501--578.

Digital Library

[23]

Nemanja Isailovic. 2010. An investigation into the realities of a quantum datapath. Ph.D. dissertation. University of California, Berkeley, CA. http://www.eecs.berkeley.edu/Pubs/TechRpts/2010/EECS-2010-60.pdf.

[24]

David Kielpinski, Christopher Monroe, and David J. Wineland. 2002. Architecture for a large-scale ion-trap quantum computer. Nature 417, 6890, 709--711.

[25]

Thaddeus D. Ladd, Fedor Jelezko, Raymond Laflamme, Yasunobu Nakamura, Christopher Monroe, and Jeremy L. O'Brien. 2010. Quantum computers. Nature 464, 7285, 45--53.

[26]

Dmitri Maslov, Gerhard W. Dueck, and Nathan Scott. 2005. Reversible logic synthesis benchmarks page. http://www.cs.uvic.ca/&sim;dmaslov.

[27]

Tzvetan S. Metodi, Darshan D. Thaker, Andrew W. Cross, Frederic T. Chong, and Isaac L. Chuang. 2006. Scheduling physical operations in a quantum information processor. In Proceedings of the Defense and Security Symposium. International Society for Optics and Photonics, 62440T.

[28]

Mina C. Moghadam, Naser Mohammadzadeh, Mehdi Sedighi, and Morteza Saheb ZAMANI. 2013. A hierarchical layout generation method for quantum circuits. In Proceedings of the 17^th CSI International Symposium on Computer Architecture and Digital Systems (CADS'13). 51--57.

[29]

Naser Mohammadzadeh, Mehdi Sedighi, and Morteza Saheb Zamani. 2010. Quantum physical synthesis: Improving physical design by netlist modifications. Microelectron. J. 41, 219--230.

Digital Library

[30]

Naser Mohammadzadeh, Morteza Saheb Zamani, and Mehdi Sedighi. 2011. Auxiliary qubit selection: A physical synthesis technique for quantum circuits. Quantum Inf. Process. 10, 2, 139--154.

Digital Library

[31]

Naser Mohammadzadeh, Morteza Saheb Zamani, and Mehdi Sedighi. 2012. Gate location changing: An optimization technique for quantum circuits. World Sci. Int. J. Quantum Inf. 10, 3, 1250037.1-1250037.20.

[32]

Naser Mohammadzadeh, Morteza Saheb Zamani, and Mehdi Sedighi. 2014a. Quantum circuit physical design methodology with emphasis on physical synthesis. Quantum Inf. Process. 13, 2, 445--465.

Digital Library

[33]

Naser Mohammadzadeh, Tayebeh Bahreini, and Hossein Badri. 2014b. Optimal ILP-based approach for gate location assignment and scheduling in quantum circuits. Modell. Simul. Engin. 2014, 7.

Digital Library

[34]

Christopher Monroe and Jungsang Kim. 2013. Scaling the ion trap quantum processor. Sci. 339, 6124, 1164--1169.

[35]

Mauricio G. C. Resende. 2001. Greedy randomized adaptive search procedures (GRASP). Encyclopedia Optimizat. 2, 373--382.

[36]

Sartaj Shani and Teofilo Gonzalez. 1976. P-complete approximation problems. J. ACM 23, 3, 555--565.

Digital Library

[37]

Peter W. Shor. 1997. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 5, 1484--1509.

Digital Library

[38]

Jadranka Skorin-Kapo. 1990. Tabu search applied to the quadratic assignment problem. ORSA J. Comput. 2, 1, 33--45.

[39]

Andrew M. Steane. 2003. Overhead and noise threshold of fault-tolerant quantum error correction. Phys. Rev. A68, 4.

[40]

Robin C. Sterling, Hwanjit Rattanasonti, Sebastian Weidt, Kimberley Lake, Prasanna Srinivasan, Simon Webster, Marcus Schultze-Kraft, and Winfried Hensinger. 2013. Two-dimensional ion trap lattice on a microchip. http://arxiv.org/abs/1302.3781.

[41]

Krista Svore, Andrew Cross, Alfred Aho, Isaac Chuang, and Igor Markov. 2006. A layered software architecture for quantum computing design tools. Comput. 39, 1, 74--83.

Digital Library

[42]

Krista Svore, Andrew Cross, Alfred Aho, Isaac Chuang, and Igor Markov. 2004. Toward a software architecture for quantum computing design tools. In Proceedings of the 2^nd International Workshop on Quantum Programming Languages (QPL'04). 145--162.

[43]

Mark G. Whitney, Nemanja Isailovic, Yatish Patel, and John Kubiatowicz. 2007. Automated generation of layout and control for quantum circuits. In Proceedings of the 4^th International Conference on Computing Frontiers (CF'07). 83--94.

Digital Library

[44]

Mark G. Whitney. 2009. Practical fault tolerance for quantum circuits, Ph.D. dissertation. University of California, Berkeley, CA. http://digitalassets.lib.berkeley.edu/techreports/ucb/text/EECS-2009-80.pdf.

Digital Library

[45]

Mark G. Whitney, Nemanja Isailovic, Yatish Patel, and John Kubiatowicz. 2009. A fault tolerant, area efficient architecture for Shor's factoring algorithm. ACM SIGARCH Comput. Archit. News 37, 3, 383--394.

Digital Library

[46]

David J. Wineland, C. Monroe, Wayne Itano, Dietrich Leibfried, Brian E. King, and Dawn M. Meekhof. 1997. Experimental issues in coherent quantum-state manipulation of trapped atomic ions. http://arxiv.org/abs/quant-ph/9710025.

[47]

William K. Wootters and Zurek H. Wojciech. 1982. A single quantum cannot be cloned. Nature 299, 802--803.

[48]

Maryam Yazdani, Morteza Saheb Zamani, and Mehdi Sedighi. 2013. A quantum physical design flow using ILP and graph drawing. Quantum Inf. Process. 12, 10, 3239--3264.

Digital Library

[49]

Christof Zalka. 1998. Simulating quantum systems on a quantum computer. Proc. Royal Soc. London Ser. A Math. Phys. Engin. Sci. 454, 1969, 313--322.

[50]

Xiao-Hu Zhi, Qingxiao Wang, Hua Zhang, Xiaowei Yang, Chun-Guang Zhou, and Chao Liang. 2004. A discrete PSO method for generalized TSP problem. In Proceedings of International Conference on Machine Learning and Cybernetics (ICMLC'04). 2378--2383.

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Keszocze OMohammadzadeh NWille R(2021)Exact Physical Design of Quantum Circuits for Ion-Trap-based Quantum Architectures2021 Design, Automation & Test in Europe Conference & Exhibition (DATE)10.23919/DATE51398.2021.9474188(344-349)Online publication date: 1-Feb-2021
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Index Terms

An MINLP Model for Scheduling and Placement of Quantum Circuits with a Heuristic Solution Approach

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Published In

cover image ACM Journal on Emerging Technologies in Computing Systems

ACM Journal on Emerging Technologies in Computing Systems Volume 12, Issue 3

Special Issue on Cross-Layer System Design and Regular Papers

September 2015

207 pages

ISSN:1550-4832

EISSN:1550-4840

DOI:10.1145/2828988

Editor:
Krishnendu Chakrabarty
Duke University, USA

Issue’s Table of Contents

Copyright © 2015 ACM.

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Association for Computing Machinery

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ACM Journals for the Design of Smart and Connected Systems

Publication History

Published: 21 September 2015

Accepted: 01 April 2015

Revised: 01 February 2015

Received: 01 September 2014

Published in JETC Volume 12, Issue 3

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Cited By

Dahi ZChicano FLuque G(2024)An Evolutionary Deep Learning Approach for Efficient Quantum Algorithms TranspilationApplications of Evolutionary Computation10.1007/978-3-031-56855-8_15(240-255)Online publication date: 3-Mar-2024
https://dl.acm.org/doi/10.1007/978-3-031-56855-8_15
Keszocze OMohammadzadeh NWille R(2021)Exact Physical Design of Quantum Circuits for Ion-Trap-based Quantum Architectures2021 Design, Automation & Test in Europe Conference & Exhibition (DATE)10.23919/DATE51398.2021.9474188(344-349)Online publication date: 1-Feb-2021
https://doi.org/10.23919/DATE51398.2021.9474188
Wu XDavis MChong FIancu C(2021)Reoptimization of Quantum Circuits via Hierarchical Synthesis2021 International Conference on Rebooting Computing (ICRC)10.1109/ICRC53822.2021.00016(35-46)Online publication date: Nov-2021
https://doi.org/10.1109/ICRC53822.2021.00016
Wu XDebroy DDing YBaker JAlexeev YBrown KChong F(2021)TILT: Achieving Higher Fidelity on a Trapped-Ion Linear-Tape Quantum Computing Architecture2021 IEEE International Symposium on High-Performance Computer Architecture (HPCA)10.1109/HPCA51647.2021.00023(153-166)Online publication date: Feb-2021
https://doi.org/10.1109/HPCA51647.2021.00023
Nikahd EMohammadzadeh NSedighi MZamani M(2021)Automated window-based partitioning of quantum circuitsPhysica Scripta10.1088/1402-4896/abd57c96:3(035102)Online publication date: 7-Jan-2021
https://doi.org/10.1088/1402-4896/abd57c
Almudever CLao LWille RGuerreschi G(2020)Realizing Quantum Algorithms on Real Quantum Computing Devices2020 Design, Automation & Test in Europe Conference & Exhibition (DATE)10.23919/DATE48585.2020.9116240(864-872)Online publication date: Mar-2020
https://doi.org/10.23919/DATE48585.2020.9116240
Itoko TImamichi T(2020)Scheduling of Operations in Quantum Compiler2020 IEEE International Conference on Quantum Computing and Engineering (QCE)10.1109/QCE49297.2020.00049(337-344)Online publication date: Oct-2020
https://doi.org/10.1109/QCE49297.2020.00049
Bandic MZarein HAlarcon EAlmudever C(2020)On Structured Design Space Exploration for Mapping of Quantum Algorithms2020 XXXV Conference on Design of Circuits and Integrated Systems (DCIS)10.1109/DCIS51330.2020.9268670(1-6)Online publication date: 18-Nov-2020
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Farghadan AMohammadzadeh N(2019)Mapping quantum circuits on 3D nearest-neighbor architecturesQuantum Science and Technology10.1088/2058-9565/ab177a4:3(035001)Online publication date: 30-Apr-2019
https://doi.org/10.1088/2058-9565/ab177a
Lao LWee BAshraf ISomeren JKhammassi NBertels KAlmudever C(2018)Mapping of lattice surgery-based quantum circuits on surface code architecturesQuantum Science and Technology10.1088/2058-9565/aadd1a4:1(015005)Online publication date: 12-Sep-2018
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