PhD Position F/M Resource-Aware Quantum Lambda Calculi with Coherent Control

Le descriptif de l'offre ci-dessous est en Anglais

Type de contrat : CDD

Niveau de diplôme exigé : Bac + 5 ou équivalent

Fonction : Doctorant

Contexte et atouts du poste

The PhD is funded by funded by PEPR EPiQ will be carried out at Inria Nancy Grand-Est within the Inria mocqua project team.

Mission confiée

Quantum programming languages with quantum control allow the execution flow of programs to depend on

quantum data, enabling superpositions of computational paths, as exemplified by the Quantum Switch [1].

While this paradigm provides a natural and expressive way to model quantum computation, it raises

fundamental challenges regarding physical implementability and computational complexity. In particular,

programs with quantum control must respect both the laws of quantum mechanics and strict resource

bounds in order to admit efficient physical realizations.

Recent work [2, 3] has shown that type systems inspired by linear logic and realizability techniques can be

used to ensure key physical properties of quantum programs, such as unitarity and feasibility. However, the

interaction between quantum control, higher-order features, and resource guarantees remains only partially

understood. In particular, there is currently no fully satisfactory typed framework that simultaneously

supports quantum control, higher-order quantum lambda calculi, and precise certifications of time and space

complexity.

The goal of this PhD is to develop a typed quantum programming language with quantum control in which

resource consumption is certified by construction. The approach will rely on light linear logic and realizability

techniques to control duplication and iteration, ensuring that programs normalize within prescribed

complexity bounds while remaining physically meaningful.

A central objective is to design a type system that characterizes quantum complexity classes such as BQP and

FBQP in a sound and complete way. This includes establishing a correspondence between typable programs

and families of quantum circuits with polynomial-time (and potentially polynomial-space) bounds, thereby

providing an implicit-complexity-style characterization of quantum complexity classes in a higher-order

setting.

References

[1] O. Oreshkov, F. Costa and Č. Brukner, "Quantum correlations with no causal order," Nature Communications, no. 1092, 2012.

[2] A. Díaz-Caro, M. Guillermo, A. Miquel and B. Valiron, "Realizability in the Unitary Sphere," in 34th Annual ACM/IEEE Symposium on Logic in

Computer Science (LICS), 2019.

[3] E. Hainry, R. Péchoux and M. Silva, "Branch Sequentialization in Quantum Polytime," in 10th International Conference on Formal Structures

for Computation and Deduction (FSCD), 2025.

Principales activités

More specifically, the PhD will address the following research directions:

• the design of a typed quantum lambda calculus with quantum control, combining linear and light
  
  linear logic modalities with realizability-based semantics, in order to certify polynomial-time
  
  normalization of quantum programs;
• the development of sound and complete characterizations of quantum complexity classes such as
  
  BQP and FBQP via typing disciplines, extending existing first-order or classically controlled results to
  
  higher-order and quantum controlled languages;
• the identification of a well-behaved fragment of the language in which programs can be compiled
  
  into quantum circuits (or alternative low-level models) of polynomial size, preserving both semantics
  
  and complexity guarantees;
• the extension of the analysis to space complexity, with the aim of controlling and certifying the
  
  number of qubits used during program execution.

The obtained results will be published in main conferences and main journals of the domain.

Compétences

Technical skills and level required :

Good level in quantum computing

Good level in functional programming

Knowledge on type systems

Knowledge in complexity theory

Languages : english (mandatory) + french

Avantages

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage

Rémunération

2300€ gross/month

Informations générales

• Thème/Domaine : Preuves et vérification

Ingénierie logicielle (BAP E)
- Ville : Villers lès Nancy
- Centre Inria : Centre Inria de l'Université de Lorraine
- Date de prise de fonction souhaitée :
- Durée de contrat : 3 ans
- Date limite pour postuler :

Attention: Les candidatures doivent être déposées en ligne sur le site Inria. Le traitement des candidatures adressées par d'autres canaux n'est pas garanti.

Consignes pour postuler

Sécurité défense :

Ce poste est susceptible d'être affecté dans une zone à régime restrictif (ZRR), telle que définie dans le décret n° relatif à la protection du potentiel scientifique et technique de la nation (PPST). L'autorisation d'accès à une zone est délivrée par le chef d'établissement, après avis ministériel favorable, tel que défini dans l'arrêté du 03 juillet 2012, relatif à la PPST. Un avis ministériel défavorable pour un poste affecté dans une ZRR aurait pour conséquence l'annulation du recrutement.

Politique de recrutement :

Dans le cadre de sa politique diversité, tous les postes Inria sont accessibles aux personnes en situation de handicap.

Contacts

• Équipe Inria : MOCQUA
• Directeur de thèse :

Péchoux Romain /

A propos d'Inria

Inria est l'institut national de recherche dédié aux sciences et technologies du numérique. Il emploie 2600 personnes. Ses 215 équipes-projets agiles, en général communes avec des partenaires académiques, impliquent plus de 3900 scientifiques pour relever les défis du numérique, souvent à l'interface d'autres disciplines. L'institut fait appel à de nombreux talents dans plus d'une quarantaine de métiers différents. 900 personnels d'appui à la recherche et à l'innovation contribuent à faire émerger et grandir des projets scientifiques ou entrepreneuriaux qui impactent le monde. Inria travaille avec de nombreuses entreprises et a accompagné la création de plus de 200 start-up. L'institut s'efforce ainsi de répondre aux enjeux de la transformation numérique de la science, de la société et de l'économie.

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