Unifying flavors of fault tolerance with the ZX calculus

Unifying flavors of fault tolerance with the ZX calculus

Time Stamp: June 18, 2024 6:49 AM

Hector Bombin, Daniel Litinski, Naomi Nickerson, Fernando Pastawski, and Sam Roberts

PsiQuantum, Palo Alto

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Abstract

There are several models of quantum computation which exhibit shared fundamental fault-tolerance properties. This article makes commonalities explicit by presenting these different models in a unifying framework based on the ZX calculus. We focus on models of topological fault tolerance – specifically surface codes – including circuit-based, measurement-based and fusion-based quantum computation, as well as the recently introduced model of Floquet codes. We find that all of these models can be viewed as different flavors of the same underlying stabilizer fault-tolerance structure, and sustain this through a set of local equivalence transformations which allow mapping between flavors. We anticipate that this unifying perspective will pave the way to transferring progress among the different views of stabilizer fault-tolerance and help researchers familiar with one model easily understand others.

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Featured image: The shared backbone of surface-code style stabilizer fault-tolerance is represented using the diagrammatic notation of the ZX calculus (graph with green and red nodes). Features specific to each compuational paradigm are highlighted such as physical qubit world-lines in the circuit model (red) or floquet model (blue) and resource states for fusion based model (purple).

Popular summary

There are different models of quantum computation such as circuit-based, measurement-based, fusion-based. While each model is based on different elementary primitives , they are know to have the same expressive power. For each of these models, fault-tolerance allows implementing reliable quantum computation when these primitives are unreliable. This article shows how a fault-tolerant realization in each of these models can be expressed in the diagrammatic language of the ZX calculus, a graphical notation based on very few elements. Doing so, makes the common fault-tolerance structure self-evident. This unifying perspective aims to facilitate knowledge transfer and understanding across different paradigms, potentially accelerating progress in quantum computing research.

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Cited by

[1] M. Sohaib Alam and Eleanor Rieffel, “Dynamical Logical Qubits in the Bacon-Shor Code”, arXiv:2403.03291, (2024).

[2] Daniel Bochen Tan, Murphy Yuezhen Niu, and Craig Gidney, “A SAT Scalpel for Lattice Surgery: Representation and Synthesis of Subroutines for Surface-Code Fault-Tolerant Quantum Computing”, arXiv:2404.18369, (2024).

[3] Markus S. Kesselring, Julio C. Magdalena de la Fuente, Felix Thomsen, Jens Eisert, Stephen D. Bartlett, and Benjamin J. Brown, “Anyon Condensation and the Color Code”, PRX Quantum 5 1, 010342 (2024).

[4] Nicholas Chancellor, Aleks Kissinger, Stefan Zohren, Joschka Roffe, and Dominic Horsman, “Graphical structures for design and verification of quantum error correction”, Quantum Science and Technology 8 4, 045028 (2023).

[5] Rahul Sahay and Ruben Verresen, “Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements”, arXiv:2404.16753, (2024).

[6] Guo-Yi Zhu, Nathanan Tantivasadakarn, and Simon Trebst, “Structured volume-law entanglement in an interacting, monitored Majorana spin liquid”, arXiv:2303.17627, (2023).

[7] Arpit Dua, Nathanan Tantivasadakarn, Joseph Sullivan, and Tyler D. Ellison, “Engineering 3D Floquet Codes by Rewinding”, PRX Quantum 5 2, 020305 (2024).

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[24] Ashot Avanesov, Alexander Shurinov, Ivan Dyakonov, and Stanislav Straupe, “Building a fusion-based quantum computer using teleported gates”, arXiv:2404.01477, (2024).

The above citations are from SAO/NASA ADS (last updated successfully 2024-06-18 10:50:26). The list may be incomplete as not all publishers provide suitable and complete citation data.

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