Graphical quantum Clifford-encoder compilers from the ZX calculus

Khesin, Andrey Boris; Lu, Jonathan Z.

doi:10.48550/arxiv.2301.02356

Cited by 7 publications

(6 citation statements)

References 33 publications

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“…This may include different microscopic models (i.e., crystal structures [27,29]), features (boundary conditions, logical blocks [14], transversal gates, etc. ), as well as different faulttolerance protocols based on color codes [30,31], low-density parity check codes [32] or other Clifford encoders [33]. We found the ZX calculus to be a versatile toolbox that can be used at all levels of fault tolerance, from the physical level of different models of quantum computation, to the structure of checks used in decoding [34], and the methodical construction of logical operations [35].…”

Section: Discussionmentioning

confidence: 99%

Logical Blocks for Fault-Tolerant Topological Quantum Computation

et al. 2023

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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 codesincluding 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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Section: Discussionmentioning

confidence: 99%

Logical Blocks for Fault-Tolerant Topological Quantum Computation

et al. 2023

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“…It has become an immensely useful tool in the industry and is used in major quantum computing companies such as Quantinuum, IBM, Google, PsiQuantum, Quandela, and many more. Since its introduction, the ZX-calculus has been successful in many areas such as quantum circuit optimisation [6,7,44], quantum error correction [30,43,42], measurementbased quantum computation [17,34,46], quantum natural language processing [18,47], quantum simulation [45], quantum foundations [23,4], cognition [55], and quantum education [25,24]. More detailed accounts on the ZX-calculus can be found in [27,56] and a more extensive overview of its applications in [26].…”

Section: Introductionmentioning

confidence: 99%

Completeness for arbitrary finite dimensions of ZXW-calculus, a unifying calculus

Poór¹,

Wang²,

Shaikh³

et al. 2023

Preprint

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The ZX-calculus is a universal graphical language for qubit quantum computation, meaning that every linear map between qubits can be expressed in the ZX-calculus. Furthermore, it is a complete graphical rewrite system: any equation involving linear maps that is derivable in the Hilbert space formalism for quantum theory can also be derived in the calculus by rewriting. It has widespread usage within quantum industry and academia for a variety of tasks such as quantum circuit optimisation, error-correction, and education.The ZW-calculus is an alternative universal graphical language that is also complete for qubit quantum computing. In fact, its completeness was used to prove that the ZX-calculus is universally complete. This calculus has advanced how quantum circuits are compiled into photonic hardware architectures in the industry.Recently, by combining these two calculi, a new calculus has emerged for qubit quantum computation, the ZXW-calculus. Using this calculus, graphical-differentiation, -integration, and -exponentiation were made possible, thus enabling the development of novel techniques in the domains of quantum machine learning and quantum chemistry.Here, we generalise the ZXW-calculus to arbitrary finite dimensions, that is, to qudits.

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“…ZX-calculus [7,8,9] has already been around as long as 2007, but it only has become widely used in the past couple of years, and especially with the emergence of quantum industry, given the new scientific and technological challenges this poses [12]. Areas where it has become prominent include compilation [17,27], circuit optimisation [20,28], error-correction [18,22], quantum natural language processing [6], QML [35,34], and also many issues surrounding photonic quantum computing [19,29].…”

Section: Introductionmentioning

confidence: 99%

Basic ZX-calculus for students and professionals

Coecke¹

2023

Preprint

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These are the lecture notes of guest lectures for Artur Ekert's course Introduction to Quantum Information at the Mathematical Institute of Oxford University, Hilary Term 2023. Some basic familiarity with Dirac notation is assumed.For the readers of Quantum in Pictures who have some basic quantum background, these notes also constitute the shortest path to an explanation of how what they learn in QIP relates to the traditional quantum formalism.

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Graphical quantum Clifford-encoder compilers from the ZX calculus

Cited by 7 publications

References 33 publications

Logical Blocks for Fault-Tolerant Topological Quantum Computation

Logical Blocks for Fault-Tolerant Topological Quantum Computation

Completeness for arbitrary finite dimensions of ZXW-calculus, a unifying calculus

Basic ZX-calculus for students and professionals

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