A diagrammatic calculus of fermionic quantum circuits

Felice, Giovanni de; Hadzihasanovic, Amar; Ng, Kang Feng

doi:10.23638/lmcs-15(3:26)2019

Cited by 7 publications

(5 citation statements)

References 38 publications

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“…These operators are easily represented in ZW ∞ using the W node. The W algebra was indeed already shown to have an important role in fermionic quantum computing [41]. We show the anti-commutation relation for these operators and finally, we represent the Jaynes-Cummings Hamiltonian describing the interaction of bosons and fermions.…”

Section: Towards Light-matter Interactionmentioning

confidence: 87%

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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Section: Towards Light-matter Interactionmentioning

confidence: 87%

Light-Matter Interaction in the ZXW Calculus

de Felice,

Shaikh,

Poór

et al. 2023

Electron. Proc. Theor. Comput. Sci.

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“…In our model, similar generators and rewriting rules form part of the ZW-calculus Hadzihasanovic (2015). ZW-calculus was developed for qubits, it is a sound and complete semantic for graphical treatments inside categorical quantum theory Abramsky and Coecke (2004), and also a useful graphical language to reconstruct different aspects of physical theories Coecke (2011); Coecke and Kissinger (2010); De Felice et al (2019);Hadzihasanovic (2015). Without lacking any mathematical rigour, across this article we have reinterpreted the nature of a partial set of their generators and rewriting rules.…”

Section: Discussionmentioning

confidence: 99%

Reasoning about conscious experience with axiomatic and graphical mathematics

Signorelli¹,

Wang²,

Coecke³

2021

Preprint

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We cast aspects of consciousness in axiomatic mathematical terms, using the graphical calculus of general process theories (a.k.a symmetric monoidal categories and Frobenius algebras therein). This calculus exploits the ontological neutrality of process theories. A toy example using the axiomatic calculus is given to show the power of this approach, recovering other aspects of conscious experience, such as external and internal subjective distinction, privacy or unreadability of personal subjective experience, and phenomenal unity, one of the main issues for scientific studies of consciousness. In fact, these features naturally arise from the compositional nature of axiomatic calculus.

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“…Blute et al [36] studied Fock space as exponential modality for linear logic. The fermionic version of the Fock space has been studied in [37], it forms the W core of the ZW calculus introduced by Coecke, Kissinger and Hadzihasanovic [38,39,40]. More recently, there has been work on a diagrammatic calculus for reasoning about polarising beam splitters for quantum control [41], an informal essay describing bosonic linear optics with category theory [42], and a complete rewriting system for the single photon semantics of linear optical circuits [43].…”

Section: Related Workmentioning

confidence: 99%