[PhD Proposal 2021] Semantic Foundations for Coherent Quantum Control

Title: Semantic Foundations for Coherent Quantum Control

Director: Simon Perdrix

Co-director: Vladimir Zamdzhiev

Summary

The recent developments of quantum technologies point out the necessity of filling the gap between theoretical quantum algorithms and the actual (prototypes of) quantum computers. As a consequence, quantum software and in particular quantum programming languages play a key role in the future development of quantum computing. A quantum programming language is a programming language that can be used to write programs that may be executed on a quantum computer. The development of these languages is the subject of an increasing number of publications in leading conferences. The thesis presented here focuses on the study of quantum control, i.e., intuitively the ability to apply multiple operations in superposition, which is a necessary element for achieving quantum advantage over classical algorithms. In most quantum programming languages, quantum control is reduced to simple primitives, such as CNot, that allow to define a quantum ‘controlled-not’ operation, forcing the programmer to define quantum algorithms at a very low level by describing quantum circuits. The usual control structures (conditionals, loops, recursion, etc.) remain classical in these languages. More ambitious quantum programming languages such as linear-algebraic quantum lambda calculi (allowing the superposition of lambda terms) allow high-level quantum control. The user can a priori describe arbitrary superpositions, requiring a typing system to guarantee a valid global evolution, making quantum measurement and recursion difficult to introduce for instance. The objective of the thesis is to propose a quantum programming language allowing a high level use of quantum control, in particular superpositions of causal orders. Primitives such as the quantum switch demonstrate that this type of quantum control can be physically implemented, and allows to achieve quantum advantage in quantum algorithms.

Detailed Proposal PDF: https://homepages.loria.fr/VZamdzhiev/papers/proposal.pdf

Application: To apply, please send an email to Simon Perdrix and Vladimir Zamdzhiev (firstName.lastName@loria.fr) with a CV, a 1-2 page motivation letter, your degree certificates and transcripts for Bachelor and Master (or equivalent) and arrange two letters of recommendation.

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