Giovanni de Felice ; Amar Hadzihasanovic ; Kang Feng Ng - A diagrammatic calculus of fermionic quantum circuits

lmcs:5143 - Logical Methods in Computer Science, September 2, 2019, Volume 15, Issue 3 -
A diagrammatic calculus of fermionic quantum circuits

Authors: Giovanni de Felice ; Amar Hadzihasanovic ; Kang Feng Ng

We introduce the fermionic ZW calculus, a string-diagrammatic language for fermionic quantum computing (FQC). After defining a fermionic circuit model, we present the basic components of the calculus, together with their interpretation, and show how the main physical gates of interest in FQC can be represented in our language. We then list our axioms, and derive some additional equations. We prove that the axioms provide a complete equational axiomatisation of the monoidal category whose objects are systems of finitely many local fermionic modes (LFMs), with maps that preserve or reverse the parity of states, and the tensor product as monoidal product. We achieve this through a procedure that rewrites any diagram in a normal form. As an example, we show how the statistics of a fermionic Mach-Zehnder interferometer can be calculated in the diagrammatic language. We conclude by giving a diagrammatic treatment of the dual-rail encoding, a standard method in optical quantum computing used to perform universal quantum computation.

Volume: Volume 15, Issue 3
Published on: September 2, 2019
Accepted on: September 2, 2019
Submitted on: January 31, 2019
Keywords: Computer Science - Logic in Computer Science,Quantum Physics,81P68, 18D10


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