A polynomial size model with implicit SWAP gate counting for exact qubit reordering

Jesse Mulderij; K.I. Aardal; Irina Chiscop; Frank Phillipson

doi:10.1007/978-3-031-36030-5_7

A polynomial size model with implicit SWAP gate counting for exact qubit reordering

Jesse Mulderij, K.I. Aardal, Irina Chiscop, Frank Phillipson^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

Due to the physics behind quantum computing, quantum circuit designers must adhere to the constraints posed by the limited interaction distance of qubits. Existing circuits need therefore to be modified via the insertion of SWAP gates, which alter the qubit order by interchanging the location of two qubits’ quantum states. We consider the Nearest Neighbor Compliance problem on a linear array, where the number of required SWAP gates is to be minimized. We introduce an Integer Linear Programming model of the problem of which the size scales polynomially in the number of qubits and gates. Furthermore, we solve 131 benchmark instances to optimality using the commercial solver CPLEX. The benchmark instances are substantially larger in comparison to those evaluated with exact methods before. The largest circuits contain up to 18 qubits or over 100 quantum gates. This formulation also seems to be suitable for developing heuristic methods since (near) optimal solutions are discovered quickly in the search process.

Original language	English
Title of host publication	Computational Science – ICCS 2023
Subtitle of host publication	23rd International Conference Prague, Czech Republic, July 3-5, 2023 Proceedings, Part V
Editors	Jiří Mikyška, Clélia de Mulatier, Valeria V. Krzhizhanovskaya, Peter M. A. Sloot, Maciej Paszynski, Jack J. Dongarra
Publisher	Springer, Cham
Pages	72-89
Number of pages	18
ISBN (Electronic)	978-3-031-36030-5
ISBN (Print)	978-3-031-36029-9
DOIs	https://doi.org/10.1007/978-3-031-36030-5_7
Publication status	Published - 2023

Publication series

Series	Lecture Notes in Computer Science
Volume	10477
ISSN	0302-9743

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10.1007/978-3-031-36030-5_7

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Mulderij, J., Aardal, K. I., Chiscop, I., & Phillipson, F. (2023). A polynomial size model with implicit SWAP gate counting for exact qubit reordering. In J. Mikyška, C. de Mulatier, V. V. Krzhizhanovskaya, P. M. A. Sloot, M. Paszynski, & J. J. Dongarra (Eds.), Computational Science – ICCS 2023: 23rd International Conference Prague, Czech Republic, July 3-5, 2023 Proceedings, Part V (pp. 72-89). Springer, Cham. https://doi.org/10.1007/978-3-031-36030-5_7

Mulderij, Jesse ; Aardal, K.I. ; Chiscop, Irina et al. / A polynomial size model with implicit SWAP gate counting for exact qubit reordering. Computational Science – ICCS 2023: 23rd International Conference Prague, Czech Republic, July 3-5, 2023 Proceedings, Part V. editor / Jiří Mikyška ; Clélia de Mulatier ; Valeria V. Krzhizhanovskaya ; Peter M. A. Sloot ; Maciej Paszynski ; Jack J. Dongarra. Springer, Cham, 2023. pp. 72-89 (Lecture Notes in Computer Science, Vol. 10477).

@inproceedings{31b14b9038594f7b84f1d9bc9a7faadd,

title = "A polynomial size model with implicit SWAP gate counting for exact qubit reordering",

abstract = "Due to the physics behind quantum computing, quantum circuit designers must adhere to the constraints posed by the limited interaction distance of qubits. Existing circuits need therefore to be modified via the insertion of SWAP gates, which alter the qubit order by interchanging the location of two qubits{\textquoteright} quantum states. We consider the Nearest Neighbor Compliance problem on a linear array, where the number of required SWAP gates is to be minimized. We introduce an Integer Linear Programming model of the problem of which the size scales polynomially in the number of qubits and gates. Furthermore, we solve 131 benchmark instances to optimality using the commercial solver CPLEX. The benchmark instances are substantially larger in comparison to those evaluated with exact methods before. The largest circuits contain up to 18 qubits or over 100 quantum gates. This formulation also seems to be suitable for developing heuristic methods since (near) optimal solutions are discovered quickly in the search process.",

author = "Jesse Mulderij and K.I. Aardal and Irina Chiscop and Frank Phillipson",

note = "Data used from: Wille, R., et al.: RevLib: an online resource for reversible functions and reversible circuits. In: Multiple Valued Logic, pp. 220–225 (2008)",

year = "2023",

doi = "10.1007/978-3-031-36030-5_7",

language = "English",

isbn = "978-3-031-36029-9",

series = "Lecture Notes in Computer Science",

publisher = "Springer, Cham",

pages = "72--89",

editor = "Ji{\v r}{\'i} Miky{\v s}ka and {de Mulatier}, Cl{\'e}lia and Krzhizhanovskaya, {Valeria V.} and Sloot, {Peter M. A.} and Maciej Paszynski and Dongarra, {Jack J.}",

booktitle = "Computational Science – ICCS 2023",

address = "Switzerland",

}

Mulderij, J, Aardal, KI, Chiscop, I & Phillipson, F 2023, A polynomial size model with implicit SWAP gate counting for exact qubit reordering. in J Mikyška, C de Mulatier, VV Krzhizhanovskaya, PMA Sloot, M Paszynski & JJ Dongarra (eds), Computational Science – ICCS 2023: 23rd International Conference Prague, Czech Republic, July 3-5, 2023 Proceedings, Part V. Springer, Cham, Lecture Notes in Computer Science, vol. 10477, pp. 72-89. https://doi.org/10.1007/978-3-031-36030-5_7

A polynomial size model with implicit SWAP gate counting for exact qubit reordering. / Mulderij, Jesse; Aardal, K.I.; Chiscop, Irina et al.
Computational Science – ICCS 2023: 23rd International Conference Prague, Czech Republic, July 3-5, 2023 Proceedings, Part V. ed. / Jiří Mikyška; Clélia de Mulatier; Valeria V. Krzhizhanovskaya; Peter M. A. Sloot; Maciej Paszynski; Jack J. Dongarra. Springer, Cham, 2023. p. 72-89 (Lecture Notes in Computer Science, Vol. 10477).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

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T1 - A polynomial size model with implicit SWAP gate counting for exact qubit reordering

AU - Mulderij, Jesse

AU - Aardal, K.I.

AU - Chiscop, Irina

AU - Phillipson, Frank

N1 - Data used from: Wille, R., et al.: RevLib: an online resource for reversible functions and reversible circuits. In: Multiple Valued Logic, pp. 220–225 (2008)

PY - 2023

Y1 - 2023

N2 - Due to the physics behind quantum computing, quantum circuit designers must adhere to the constraints posed by the limited interaction distance of qubits. Existing circuits need therefore to be modified via the insertion of SWAP gates, which alter the qubit order by interchanging the location of two qubits’ quantum states. We consider the Nearest Neighbor Compliance problem on a linear array, where the number of required SWAP gates is to be minimized. We introduce an Integer Linear Programming model of the problem of which the size scales polynomially in the number of qubits and gates. Furthermore, we solve 131 benchmark instances to optimality using the commercial solver CPLEX. The benchmark instances are substantially larger in comparison to those evaluated with exact methods before. The largest circuits contain up to 18 qubits or over 100 quantum gates. This formulation also seems to be suitable for developing heuristic methods since (near) optimal solutions are discovered quickly in the search process.

AB - Due to the physics behind quantum computing, quantum circuit designers must adhere to the constraints posed by the limited interaction distance of qubits. Existing circuits need therefore to be modified via the insertion of SWAP gates, which alter the qubit order by interchanging the location of two qubits’ quantum states. We consider the Nearest Neighbor Compliance problem on a linear array, where the number of required SWAP gates is to be minimized. We introduce an Integer Linear Programming model of the problem of which the size scales polynomially in the number of qubits and gates. Furthermore, we solve 131 benchmark instances to optimality using the commercial solver CPLEX. The benchmark instances are substantially larger in comparison to those evaluated with exact methods before. The largest circuits contain up to 18 qubits or over 100 quantum gates. This formulation also seems to be suitable for developing heuristic methods since (near) optimal solutions are discovered quickly in the search process.

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DO - 10.1007/978-3-031-36030-5_7

M3 - Conference article in proceeding

SN - 978-3-031-36029-9

T3 - Lecture Notes in Computer Science

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BT - Computational Science – ICCS 2023

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Mulderij J, Aardal KI, Chiscop I, Phillipson F. A polynomial size model with implicit SWAP gate counting for exact qubit reordering. In Mikyška J, de Mulatier C, Krzhizhanovskaya VV, Sloot PMA, Paszynski M, Dongarra JJ, editors, Computational Science – ICCS 2023: 23rd International Conference Prague, Czech Republic, July 3-5, 2023 Proceedings, Part V. Springer, Cham. 2023. p. 72-89. (Lecture Notes in Computer Science, Vol. 10477). doi: 10.1007/978-3-031-36030-5_7

A polynomial size model with implicit SWAP gate counting for exact qubit reordering

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