Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements

Thomas McElvanney; Miriam Backens

Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements

Thomas McElvanney, Miriam Backens

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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Abstract

In the one-way model of measurement-based quantum computation (MBQC), computation proceeds via measurements on some standard resource state. So-called flow conditions ensure that the overall computation is deterministic in a suitable sense, with Pauli flow being the most general of these. Existing work on rewriting MBQC patterns while preserving the existence of flow has focused on rewrites that reduce the number of qubits.

In this work, we show that introducing new Z-measured qubits, connected to any subset of the existing qubits, preserves the existence of Pauli flow. Furthermore, we give a unique canonical form for stabilizer ZX-diagrams inspired by recent work of Hu & Khesin [17]. We prove that any MBQClike stabilizer ZX-diagram with Pauli flow can be rewritten into this canonical form using only rules which preserve the existence of Pauli flow and that each of these rules can be reversed while also preserving the existence of Pauli flow. Hence we have complete graphical rewriting for MBQC-like stabilizer ZX-diagrams with Pauli flow.

Original language	English
Title of host publication	Proceedings 19th International Conference on Quantum Physics and Logic (QPL 2022)
Subtitle of host publication	Wolfson College, Oxford, UK, 27 June - 1 July 2022
Editors	Stefano Gogioso, Matty Hoban
Publisher	Open Publishing Association
Pages	66-82
Number of pages	17
Publication status	Published - 16 Nov 2023
Event	19th International Conference on Quantum Physics and Logic - Wolfson College, Oxford, United Kingdom Duration: 27 Jun 2022 → 1 Jul 2022

Publication series

Name	Electronic proceedings in theoretical computer science
Volume	394
ISSN (Electronic)	2075-2180

Conference

Conference	19th International Conference on Quantum Physics and Logic
Abbreviated title	QPL 2022
Country/Territory	United Kingdom
City	Oxford
Period	27/06/22 → 1/07/22

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McElvanney, T., & Backens, M. (2023). Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements. In S. Gogioso, & M. Hoban (Eds.), Proceedings 19th International Conference on Quantum Physics and Logic (QPL 2022): Wolfson College, Oxford, UK, 27 June - 1 July 2022 (pp. 66-82). (Electronic proceedings in theoretical computer science; Vol. 394). Open Publishing Association. https://www.qplconference.org/proceedings2022/QPL_2022_paper_21.pdf

McElvanney, Thomas ; Backens, Miriam. / Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements. Proceedings 19th International Conference on Quantum Physics and Logic (QPL 2022): Wolfson College, Oxford, UK, 27 June - 1 July 2022. editor / Stefano Gogioso ; Matty Hoban. Open Publishing Association, 2023. pp. 66-82 (Electronic proceedings in theoretical computer science).

@inproceedings{7db8b7e5e5c24ac9a48f649ef2727984,

title = "Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements",

abstract = "In the one-way model of measurement-based quantum computation (MBQC), computation proceeds via measurements on some standard resource state. So-called flow conditions ensure that the overall computation is deterministic in a suitable sense, with Pauli flow being the most general of these. Existing work on rewriting MBQC patterns while preserving the existence of flow has focused on rewrites that reduce the number of qubits. In this work, we show that introducing new Z-measured qubits, connected to any subset of the existing qubits, preserves the existence of Pauli flow. Furthermore, we give a unique canonical form for stabilizer ZX-diagrams inspired by recent work of Hu & Khesin [17]. We prove that any MBQClike stabilizer ZX-diagram with Pauli flow can be rewritten into this canonical form using only rules which preserve the existence of Pauli flow and that each of these rules can be reversed while also preserving the existence of Pauli flow. Hence we have complete graphical rewriting for MBQC-like stabilizer ZX-diagrams with Pauli flow.",

author = "Thomas McElvanney and Miriam Backens",

year = "2023",

month = nov,

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language = "English",

series = "Electronic proceedings in theoretical computer science",

publisher = "Open Publishing Association",

pages = "66--82",

editor = "Stefano Gogioso and Matty Hoban",

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note = "19th International Conference on Quantum Physics and Logic, QPL 2022 ; Conference date: 27-06-2022 Through 01-07-2022",

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McElvanney, T & Backens, M 2023, Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements. in S Gogioso & M Hoban (eds), Proceedings 19th International Conference on Quantum Physics and Logic (QPL 2022): Wolfson College, Oxford, UK, 27 June - 1 July 2022. Electronic proceedings in theoretical computer science, vol. 394, Open Publishing Association, pp. 66-82, 19th International Conference on Quantum Physics and Logic, Oxford, United Kingdom, 27/06/22. <https://www.qplconference.org/proceedings2022/QPL_2022_paper_21.pdf>

Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements. / McElvanney, Thomas; Backens, Miriam.
Proceedings 19th International Conference on Quantum Physics and Logic (QPL 2022): Wolfson College, Oxford, UK, 27 June - 1 July 2022. ed. / Stefano Gogioso; Matty Hoban. Open Publishing Association, 2023. p. 66-82 (Electronic proceedings in theoretical computer science; Vol. 394).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements

AU - McElvanney, Thomas

AU - Backens, Miriam

PY - 2023/11/16

Y1 - 2023/11/16

N2 - In the one-way model of measurement-based quantum computation (MBQC), computation proceeds via measurements on some standard resource state. So-called flow conditions ensure that the overall computation is deterministic in a suitable sense, with Pauli flow being the most general of these. Existing work on rewriting MBQC patterns while preserving the existence of flow has focused on rewrites that reduce the number of qubits. In this work, we show that introducing new Z-measured qubits, connected to any subset of the existing qubits, preserves the existence of Pauli flow. Furthermore, we give a unique canonical form for stabilizer ZX-diagrams inspired by recent work of Hu & Khesin [17]. We prove that any MBQClike stabilizer ZX-diagram with Pauli flow can be rewritten into this canonical form using only rules which preserve the existence of Pauli flow and that each of these rules can be reversed while also preserving the existence of Pauli flow. Hence we have complete graphical rewriting for MBQC-like stabilizer ZX-diagrams with Pauli flow.

AB - In the one-way model of measurement-based quantum computation (MBQC), computation proceeds via measurements on some standard resource state. So-called flow conditions ensure that the overall computation is deterministic in a suitable sense, with Pauli flow being the most general of these. Existing work on rewriting MBQC patterns while preserving the existence of flow has focused on rewrites that reduce the number of qubits. In this work, we show that introducing new Z-measured qubits, connected to any subset of the existing qubits, preserves the existence of Pauli flow. Furthermore, we give a unique canonical form for stabilizer ZX-diagrams inspired by recent work of Hu & Khesin [17]. We prove that any MBQClike stabilizer ZX-diagram with Pauli flow can be rewritten into this canonical form using only rules which preserve the existence of Pauli flow and that each of these rules can be reversed while also preserving the existence of Pauli flow. Hence we have complete graphical rewriting for MBQC-like stabilizer ZX-diagrams with Pauli flow.

UR - https://doi.org/10.48550/arXiv.2205.02009

M3 - Conference contribution

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BT - Proceedings 19th International Conference on Quantum Physics and Logic (QPL 2022)

A2 - Gogioso, Stefano

A2 - Hoban, Matty

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T2 - 19th International Conference on Quantum Physics and Logic

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McElvanney T, Backens M. Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements. In Gogioso S, Hoban M, editors, Proceedings 19th International Conference on Quantum Physics and Logic (QPL 2022): Wolfson College, Oxford, UK, 27 June - 1 July 2022. Open Publishing Association. 2023. p. 66-82. (Electronic proceedings in theoretical computer science).

Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements

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