research-article

Qubit Mapping and Routing via MaxSAT

Authors:

Aws AlbarghouthiAuthors Info & Claims

MICRO '22: Proceedings of the 55th Annual IEEE/ACM International Symposium on Microarchitecture

Pages 1078 - 1091

https://doi.org/10.1109/MICRO56248.2022.00077

Published: 18 December 2023 Publication History

Abstract

Near-term quantum computers will operate in a noisy environment, without error correction. A critical problem for near-term quantum computing is laying out a logical circuit onto a physical device with limited connectivity between qubits. This is known as the qubit mapping and routing (QMR) problem, an intractable combinatorial problem. It is important to solve QMR as optimally as possible to reduce the amount of added noise, which may render a quantum computation useless. In this paper, we present a novel approach for optimally solving the QMR problem via a reduction to maximum satisfiability (MAXSAT). Additionally, we present two novel relaxation ideas that shrink the size of the MAXSAT constraints by exploiting the structure of a quantum circuit. Our thorough empirical evaluation demonstrates (1) the scalability of our approach compared to state-of-the-art optimal QMR techniques (solves more than 3x benchmarks with 40x speedup), (2) the significant cost reduction compared to state-of-the-art heuristic approaches (an average of ~5x swap reduction), and (3) the power of our proposed constraint relaxations.

References

[1]

M. A. Nielsen and I. Chuang, "Quantum computation and quantum information," 2002.

Digital Library

[2]

J. Preskill, "Quantum computing in the nisq era and beyond," Quantum, vol. 2, p. 79, 2018.

[3]

A. Cowtan, S. Dilkes, R. Duncan, A. Krajenbrink, W. Simmons, and S. Sivarajah, "On the qubit routing problem," arXiv preprint arXiv:1902.08091, 2019.

[4]

B. Tan and J. Cong, "Optimality study of existing quantum computing layout synthesis tools," IEEE Transactions on Computers, vol. 70, no. 9, pp. 1363--1373, 2020.

Digital Library

[5]

B. Tan, "Optimal layout synthesis for quantum computing," in 2020 IEEE/ACM International Conference On Computer Aided Design (IC-CAD). IEEE, 2020, pp. 1--9.

[6]

R. Wille, L. Burgholzer, and A. Zulehner, "Mapping quantum circuits to ibm qx architectures using the minimal number of swap and h operations," in 2019 56th ACM/IEEE Design Automation Conference (DAC). IEEE, 2019, pp. 1--6.

[7]

P. Murali, J. M. Baker, A. J. Abhari, F. T. Chong, and M. Martonosi, "Noise-adaptive compiler mappings for noisy intermediate-scale quantum computers," arXiv preprint arXiv:1901.11054, 2019.

[8]

A. Biere, M. Heule, and H. van Maaren, Handbook of satisfiability. IOS press, 2009, vol. 185.

Digital Library

[9]

J. Backes, P. Bolignano, B. Cook, C. Dodge, A. Gacek, K. Luckow, N. Rungta, O. Tkachuk, and C. Varming, "Semantic-based automated reasoning for aws access policies using smt," in 2018 Formal Methods in Computer Aided Design (FMCAD). IEEE, 2018, pp. 1--9.

[10]

A. Zulehner, A. Paler, and R. Wille, "An efficient methodology for mapping quantum circuits to the ibm qx architectures," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 38, no. 7, pp. 1226--1236, 2018.

[11]

A. Solar-Lezama, Program synthesis by sketching. University of California, Berkeley, 2008.

Digital Library

[12]

E. Farhi, J. Goldstone, and S. Gutmann, "A quantum approximate optimization algorithm," arXiv preprint:1411.4028, 2014.

[13]

I. P. Gent and P. Nightingale, "A new encoding of alldifferent into sat," in International Workshop on Modelling and Reformulating Constraint Satisfaction, 2004, pp. 95--110.

[14]

S. Joshi, P. Kumar, V. Manquinho, R. Martins, A. Nadel, and S. Rao, "Open-WBO-Inc in MaxSAT Evaluation 2018," in MaxSAT Evaluation 2018: Solver and Benchmark Descriptions, vol. B-2018-2. Department of Computer Science, University of Helsinki, 2018, pp. 16--17.

[15]

R. Wille, D. Große, L. Teuber, G. W. Dueck, and R. Drechsler, "Revlib: An online resource for reversible functions and reversible circuits," in 38th International Symposium on Multiple Valued Logic (ismvl 2008), 2008, pp. 220--225.

[16]

A. S. Green, P. L. Lumsdaine, N. J. Ross, P. Selinger, and B. Valiron, "Quipper: A scalable quantum programming language," CoRR, vol. abs/1304.3390, 2013. [Online]. Available: http://arxiv.org/abs/1304.3390

[17]

A. JavadiAbhari, S. Patil, D. Kudrow, J. Heckey, A. Lvov, F. T. Chong, and M. Martonosi, "Scaffcc: A framework for compilation and analysis of quantum computing programs," in Proceedings of the 11th ACM Conference on Computing Frontiers, ser. CF '14. New York, NY, USA: Association for Computing Machinery, 2014. [Online].

Digital Library

[18]

G. Li, Y. Ding, and Y. Xie, "Tackling the qubit mapping problem for nisqera quantum devices," in Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, 2019, pp. 1001--1014.

Digital Library

[19]

M. Y. Siraichi, V. F. d. Santos, C. Collange, and F. M. Q. Pereira, "Qubit allocation as a combination of subgraph isomorphism and token swapping," Proceedings of the ACM on Programming Languages, vol. 3, no. OOPSLA, pp. 1--29, 2019.

Digital Library

[20]

D. Bhattacharjee, A. A. Saki, M. Alam, A. Chattopadhyay, and S. Ghosh, "Muqut: Multi-constraint quantum circuit mapping on nisq computers," in 2019 IEEE/ACM International Conference on Computer-Aided Design (ICCAD). IEEE, 2019, pp. 1--7.

[21]

A. Chakrabarti, S. Sur-Kolay, and A. Chaudhury, "Linear nearest neighbor synthesis of reversible circuits by graph partitioning," arXiv preprint arXiv:1112.0564, 2011.

[22]

D. Bhattacharjee and A. Chattopadhyay, "Depth-optimal quantum circuit placement for arbitrary topologies," arXiv preprint arXiv:1703.08540, 2017.

[23]

M. Y. Siraichi, V. F. d. Santos, S. Collange, and F. M. Q. Pereira, "Qubit allocation," in Proceedings of the 2018 International Symposium on Code Generation and Optimization. ACM, 2018, pp. 113--125.

Digital Library

[24]

D. Venturelli, M. Do, E. G. Rieffel, and J. Frank, "Temporal planning for compilation of quantum approximate optimization circuits." in IJCAI, 2017, pp. 4440--4446.

[25]

D. Venturelli, M. Do, E. Rieffel, and J. Frank, "Compiling quantum circuits to realistic hardware architectures using temporal planners," Quantum Science and Technology, vol. 3, no. 2, p. 025004, 2018.

[26]

C. Zhang, A. B. Hayes, L. Qiu, Y. Jin, Y. Chen, and E. Z. Zhang, "Time-optimal qubit mapping," in Proceedings of the 26th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, 2021, pp. 360--374.

[27]

A. M. Childs, E. Schoute, and C. M. Unsal, "Circuit transformations for quantum architectures," arXiv preprint arXiv:1902.09102, 2019.

[28]

B. O'Gorman, W. J. Huggins, E. G. Rieffel, and K. B. Whaley, "Generalized swap networks for near-term quantum computing," arXiv preprint arXiv:1905.05118, 2019.

[29]

S. Sivarajah, S. Dilkes, A. Cowtan, W. Simmons, A. Edgington, and R. Duncan, "t|ket〉: a retargetable compiler for nisq devices," Quantum Science and Technology, vol. 6, no. 1, p. 014003, 2020.

[30]

D. Maslov, S. M. Falconer, and M. Mosca, "Quantum circuit placement: optimizing qubit-to-qubit interactions through mapping quantum circuits into a physical experiment," in Proceedings of the 44th annual Design Automation Conference. ACM, 2007, pp. 962--965.

[31]

Y. Hirata, M. Nakanishi, S. Yamashita, and Y. Nakashima, "An efficient conversion of quantum circuits to a linear nearest neighbor architecture," Quantum Information & Computation, vol. 11, no. 1, pp. 142--166, 2011.

Digital Library

[32]

M. Saeedi, R. Wille, and R. Drechsler, "Synthesis of quantum circuits for linear nearest neighbor architectures," Quantum Information Processing, vol. 10, no. 3, pp. 355--377, 2011.

Digital Library

[33]

A. Shafaei, M. Saeedi, and M. Pedram, "Optimization of quantum circuits for interaction distance in linear nearest neighbor architectures," in 2013 50th ACM/EDAC/IEEE Design Automation Conference (DAC). IEEE, 2013, pp. 1--6.

[34]

R. Wille, O. Keszocze, M. Walter, P. Rohrs, A. Chattopadhyay, and R. Drechsler, "Look-ahead schemes for nearest neighbor optimization of 1d and 2d quantum circuits," in 2016 21st Asia and South Pacific design automation conference (ASP-DAC). IEEE, 2016, pp. 292--297.

[35]

A. Zulehner and R. Wille, "Compiling su (4) quantum circuits to ibm qx architectures," in Proceedings of the 24th Asia and South Pacific Design Automation Conference, 2019, pp. 185--190.

[36]

A. Kole, S. Hillmich, K. Datta, R. Wille, and I. Sengupta, "Improved mapping of quantum circuits to ibm qx architectures," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 39, no. 10, pp. 2375--2383, 2019.

[37]

G. G. Guerreschi and J. Park, "Two-step approach to scheduling quantum circuits," Quantum Science and Technology, vol. 3, no. 4, p. 045003, 2018.

[38]

M. Alam, A. Ash-Saki, and S. Ghosh, "Circuit compilation methodologies for quantum approximate optimization algorithm," in 2020 53rd Annual IEEE/ACM International Symposium on Microarchitecture (MICRO). IEEE, 2020, pp. 215--228.

[39]

S. S. Tannu and M. K. Qureshi, "Not all qubits are created equal: a case for variability-aware policies for nisq-era quantum computers," in Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, 2019, pp. 987--999.

Digital Library

[40]

P. Das, S. Tannu, S. Dangwal, and M. Qureshi, "Adapt: Mitigating idling errors in qubits via adaptive dynamical decoupling," in MICRO-54: 54th Annual IEEE/ACM International Symposium on Microarchitecture, 2021, pp. 950--962.

[41]

P. Das, S. Tannu, and M. Qureshi, "Jigsaw: Boosting fidelity of nisq programs via measurement subsetting," in MICRO-54: 54th Annual IEEE/ACM International Symposium on Microarchitecture, 2021, pp. 937--949.

[42]

P. Jurcevic, A. Javadi-Abhari, L. S. Bishop, I. Lauer, D. F. Bogorin, M. Brink, L. Capelluto, O. Günlük, T. Itoko, N. Kanazawa et al., "Demonstration of quantum volume 64 on a superconducting quantum computing system," Quantum Science and Technology, vol. 6, no. 2, p. 025020, 2021.

[43]

S. S. Tannu and M. Qureshi, "Ensemble of diverse mappings: Improving reliability of quantum computers by orchestrating dissimilar mistakes," in Proceedings of the 52nd Annual IEEE/ACM International Symposium on Microarchitecture, 2019, pp. 253--265.

[44]

T. Patel and D. Tiwari, "Veritas: accurately estimating the correct output on noisy intermediate-scale quantum computers," in 2020 SC20: International Conference for High Performance Computing, Networking, Storage and Analysis (SC). IEEE Computer Society, 2020, pp. 188--203.

[45]

S. Stein, N. Wiebe, Y. Ding, P. Bo, K. Kowalski, N. Baker, J. Ang, and A. Li, "Eqc: ensembled quantum computing for variational quantum algorithms," in Proceedings of the 49th Annual International Symposium on Computer Architecture, 2022, pp. 59--71.

Cited By

Ushijima Mwesigwa HLiu X(2023)An Ising-based Model for Qubit MappingProceedings of the SC '23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis10.1145/3624062.3624225(1492-1498)Online publication date: 12-Nov-2023
https://dl.acm.org/doi/10.1145/3624062.3624225
Jin YHua FChen YHayes AZhang CZhang EAamodt TSwift MJerger N(2023)Exploiting the Regular Structure of Modern Quantum Architectures for Compiling and Optimizing Programs with Permutable OperatorsProceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 410.1145/3623278.3624751(108-124)Online publication date: 25-Mar-2023
https://dl.acm.org/doi/10.1145/3623278.3624751
Tan SLang CXiang LWang SJia XTan ZLi TYin JShang YPython ALu LYin J(2023)QuCT: A Framework for Analyzing Quantum Circuit by Extracting Contextual and Topological FeaturesProceedings of the 56th Annual IEEE/ACM International Symposium on Microarchitecture10.1145/3613424.3614274(494-508)Online publication date: 28-Oct-2023
https://dl.acm.org/doi/10.1145/3613424.3614274
Show More Cited By

Index Terms

Qubit Mapping and Routing via MaxSAT

Index terms have been assigned to the content through auto-classification.

Recommendations

Time-optimal Qubit mapping
ASPLOS '21: Proceedings of the 26th ACM International Conference on Architectural Support for Programming Languages and Operating Systems

Rapid progress in the physical implementation of quantum computers gave birth to multiple recent quantum machines implemented with superconducting technology. In these NISQ machines, each qubit is physically connected to a bounded number of neighbors. ...
QuCloud+: A Holistic Qubit Mapping Scheme for Single/Multi-programming on 2D/3D NISQ Quantum Computers
Qubit mapping for NISQ superconducting quantum computers is essential to fidelity and resource utilization. The existing qubit mapping schemes meet challenges, e.g., crosstalk, SWAP overheads, diverse device topologies, etc., leading to qubit resource ...
Satisfiability Modulo Theories-Based Qubit Mapping for Trapped-Ion Quantum Computing Systems
ISPD '24: Proceedings of the 2024 International Symposium on Physical Design

Qubit mapping is crucial in optimizing the performance of quantum algorithms for physical executions on quantum computing architectures. Many qubit mapping algorithms have been proposed for superconducting systems recently. However, due to their ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

MICRO '22: Proceedings of the 55th Annual IEEE/ACM International Symposium on Microarchitecture

October 2022

1498 pages

ISBN:9781665462723

General Chairs:
Nikos Hardavellas
Northwestern University
,
Simone Campanoni
Northwestern University
,
Program Chairs:
Boris Grot
University of Edinburgh
,
Ulya Karpuzcu
University of Minnesota, Twin Cities

Sponsors

SIGMICRO: ACM Special Interest Group on Microarchitectural Research and Processing

Publisher

IEEE Press

Publication History

Published: 18 December 2023

Check for updates

Author Tags

Qualifiers

Research-article

Conference

MICRO '22

Sponsor:

SIGMICRO

MICRO '22: 55th Annual IEEE/ACM International Symposium on Microarchitecture

October 1 - 5, 2022

Illinois, Chicago, USA

Acceptance Rates

Overall Acceptance Rate 484 of 2,242 submissions, 22%

Upcoming Conference

MICRO '24

Sponsor:
sigmicro

57th Annual IEEE/ACM International Symposium on Microarchitecture

November 2 - 6, 2024

Austin , TX , USA

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

4
Total Citations
View Citations
15
Total Downloads

Downloads (Last 12 months)15
Downloads (Last 6 weeks)2

Reflects downloads up to 27 Jul 2024

Other Metrics

View Author Metrics

Citations

Cited By

Ushijima Mwesigwa HLiu X(2023)An Ising-based Model for Qubit MappingProceedings of the SC '23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis10.1145/3624062.3624225(1492-1498)Online publication date: 12-Nov-2023
https://dl.acm.org/doi/10.1145/3624062.3624225
Jin YHua FChen YHayes AZhang CZhang EAamodt TSwift MJerger N(2023)Exploiting the Regular Structure of Modern Quantum Architectures for Compiling and Optimizing Programs with Permutable OperatorsProceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 410.1145/3623278.3624751(108-124)Online publication date: 25-Mar-2023
https://dl.acm.org/doi/10.1145/3623278.3624751
Tan SLang CXiang LWang SJia XTan ZLi TYin JShang YPython ALu LYin J(2023)QuCT: A Framework for Analyzing Quantum Circuit by Extracting Contextual and Topological FeaturesProceedings of the 56th Annual IEEE/ACM International Symposium on Microarchitecture10.1145/3613424.3614274(494-508)Online publication date: 28-Oct-2023
https://dl.acm.org/doi/10.1145/3613424.3614274
Xu SHann CFoxman BGirvin SDing Y(2023)Systems Architecture for Quantum Random Access MemoryProceedings of the 56th Annual IEEE/ACM International Symposium on Microarchitecture10.1145/3613424.3614270(526-538)Online publication date: 28-Oct-2023
https://dl.acm.org/doi/10.1145/3613424.3614270

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents