Section: New Results

Diagrammatic quantum computing

• Participants: Titouan Carette, Dominic Horsman, Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart.

This year, we have contributed in several ways to the foundations and the applications of the ZX-calculus, a diagrammatic language for quantum computing.

Emmanuel Jeandel, Simon Perdrix, and Renaud Vilmart have introduced a general normal form for ZX-diagrams implying completeness results for various (almost all) fragments of quantum mechanics [28]. Renaud Vilmart has also introduced the simple, meaningful axiomatisation of the full ZX-calculus [31]. This two papers have been published at LICS'19.

Titouan Carette, Emmanuel Jeandel, Simon Perdrix, and Renaud Vilmart, have introduced a new simple categorical construction allowing to deal with non pure quantum evolutions (i.e. involving quantum measurements, discard of quantum systems, and probability mixtures). Wen this new construction coincides with the existing constructions, it provides simpler axiomatisation. For instance, this construction provides a complete equational theory for an extension of the ZX-calculus for arbitrary (non necessary pure) quantum evolutions. This result has been published at ICALP'19 [24].

Titouan Carette, Dominic Horsman (form LIG Grenoble) and Simon Perdrix have provided an axiomatisation for a scalable ZX-calculus where each wire represents a register of qubits, instead of a single qubit in the standard ZX-calculus. The scalable ZX-calculus allows compact representation of quantum algorithms, protocols and quantum codes. This result has been published at MFCS'19 [23]