Phase gadget compilation for diagonal qutrit gates

Wetering, John van de; Yeh, Lia

doi:10.48550/arxiv.2204.13681

Cited by 4 publications

(3 citation statements)

References 35 publications

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“…Recently, these qudit graphical calculi have been applied to achieve new results in qudit circuit synthesis. By leveraging the qutrit ZX-calculus, novel qutrit constructions have been elucidated from their qubit ZX-calculus counterparts, for instance, discovering a qutrit unitary that implements the qubit CCZ gate using only three single-qudit non-Clifford gates [57]. Another recent example is the application of qutrit ZX-calculus to synthesizing two-qutrit controlled phase gates on superconducting qutrits [13].…”

Section: Zx-calculus Is Good Atmentioning

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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Section: Zx-calculus Is Good Atmentioning

confidence: 99%

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

Poór¹,

Wang²,

Shaikh³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Based on this form, it becomes evident that the diagram corresponds to the operator iτ n ˆ1n ˆ2, which needs to be exponentiated. We employ the technique described by van de Wetering and Yeh [51] for constructing diagonal qudit gates using phase gadgets [20,38]. Firstly, note that the polynomial equation (x + y) 2 = x 2 + 2xy + y 2 implies that e iτ xy = e i τ 2 ((x+y) 2 −x 2 −y 2 ) = e i τ 2 (x+y) 2 e −i τ 2 x 2 e −i τ 2 y 2 .…”

Section: Appendix a Detailing The Zxw Calculus A1 Additional Notationsmentioning

confidence: 99%

Light-Matter Interaction in the ZXW Calculus

de Felice,

Shaikh,

Poór

et al. 2023

Electron. Proc. Theor. Comput. Sci.

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In this paper we develop a graphical calculus to rewrite photonic circuits involving lightmatter interactions and non-linear optical effects. We introduce the infinite ZW calculus, a graphical language for linear operators on the bosonic Fock space which captures both linear and non-linear photonic circuits. This calculus is obtained by combining the QPath calculus, a diagrammatic language for linear optics, and the recently developed qudit ZXW calculus, a complete axiomatisation of linear maps between qudits. It comes with a "lifting" theorem allowing to prove equalities between infinite operators by rewriting in the ZXW calculus. We give a method for representing bosonic and fermionic Hamiltonians in the infinite ZW calculus. This allows us to derive their exponentials by diagrammatic reasoning. Examples include phase shifts and beam splitters, as well as non-linear Kerr media and Jaynes-Cummings light-matter interaction.

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“…There exist several variations of the ZX-calculus that extend it to higher-dimensional qudits. Many have focused on the specific case of qutrit systems [65,39,65,62], with applications in quantum computation [70,63], and complexity theory [62]. Recent papers have focused on the stabiliser fragment of odd prime dimensional qudits, including Ref.…”

Section: Introductionmentioning

confidence: 99%

The Qupit Stabiliser ZX-travaganza: Simplified Axioms, Normal Forms and Graph-Theoretic Simplification

Poór,

Booth,

Carette

et al. 2023

Electron. Proc. Theor. Comput. Sci.

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We present a smorgasbord of results on the stabiliser ZX-calculus for odd prime-dimensional qudits (i.e. qupits). We derive a simplified rule set that closely resembles the original rules of qubit ZX-calculus. Using these rules, we demonstrate analogues of the spider-removing local complementation and pivoting rules. This allows for efficient reduction of diagrams to the affine with phases normal form. We also demonstrate a reduction to a unique form, providing an alternative and simpler proof of completeness. Furthermore, we introduce a different reduction to the graph state with local Cliffords normal form, which leads to a novel layered decomposition for qupit Clifford unitaries. Additionally, we propose a new approach to handle scalars formally, closely reflecting their practical usage. Finally, we have implemented many of these findings in DiZX, a new open-source Python library for qudit ZX-diagrammatic reasoning.

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Phase gadget compilation for diagonal qutrit gates

Cited by 4 publications

References 35 publications

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

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

Light-Matter Interaction in the ZXW Calculus

The Qupit Stabiliser ZX-travaganza: Simplified Axioms, Normal Forms and Graph-Theoretic Simplification

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