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Quantum Computing

Olivia Brenner, Loria - 12/09/2019

Quantum Computing: Renaud Vilmart has received an award for the best student paper at LICS

Two diagram transformations allowed in the ZX-Calculation Two diagram transformations allowed in the ZX-Calculation - @ Renaud Vilmart

Renaud Vilmart is a doctoral student at the Université de Lorraine and belongs to the joint Inria-Loria Mocqua team. He was awarded the Kleene Award  for the best student paper at LICS, the major conference on logic in computer science, which took place in Vancouver from June 24th to 27th.

The article, “A near optimal axiomatisation of ZX Calculus for Pure Quantum Mechanics”, proposes a series of equations which axiomatize quantum mechanics. The ZX Calculation language can be used to represent a quantum evolution in the form of diagrams in the same way as the classical form of circuits is used to represent Boolean functions. This avoids using Hilbert spaces which are part of the standard quantum formalism. “A diagram expresses more and is more graphic than the element of Hilbert’s space associated with it. It offers a more simplified vision which remains formal and helps visualize where the qubits are and to schematize certain equations” added the young award-winner. The theory of categories ensures a certain consistency between mathematical formulae and diagrams.

What is a qubit?

A qubit is the quantum state representing the smallest possible quantum information storage unit. It is the quantum equivalent of the bit with quantum effects which appear at the atomic scale. Classical bits only have two possible states – “0” or “1”. The qubit is a linear combination of these two states and can be represented using the ZX Calculus language. Qubits have relatively tangible applications such as algorithm or circuit analysis. The ZX Calculus language can also be used for protocol checks without requiring a quantum computer.

What is the purpose of a quantum computer?

Quantum computers have more computing power than their conventional counterparts. The best example is the Shor algorithm which can be used to efficiently factor a prime number which is considered problematic for a standard computer. Quantum computers already exist but currently remain very small because the number of qubits is itself very small. The larger a system is, the more difficult it is for its quantum properties to be retained.

Quantum theory can be captured by axioms on logic gates that constitute a quantum circuit. It is a viable alternative to quantum computation in Hilbert spaces, spaces which enable lengths and angles to be measured. The ZX Calculus quantum language provides a set of axioms which captures quantum mechanics with the objective of making it possible to derive any transformations allowed from axioms. This is the subject of the award-winning article. A strong software community is already working on this language particularly in Oxford, Nijmegen and Grenoble.

What advice would you give to students who would like to prepare a thesis?

“I would tell them that the working environment is great and provides all the right conditions for working on a thesis. I chose this job and this subject because the environment is stimulating and very lively with the possibility of your work being recognized world wide”.

Renaud Vilmart studied at Mines Nancy where a course by Simon Perdrix on quantum computing inspired him to select this research theme for his thesis. He is now in his 3rdyear of studies and plans to defend his thesis at the start of the academic year before taking up a postdoctoral position.

Keywords: Quantum computing Renaud Vilmart Best paper

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