Research internship on mixed-dimension gate teleportation

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

Niveau de diplôme exigé : Bac + 4 ou équivalent

Fonction : Stagiaire de la recherche

Contexte et atouts du poste

Gate teleportation [1] is a common strategy to overcome the Eastin-Knill theorem, which prevents the transversal (fault-tolerant) realization of a universal set of gates in any quantum error correcting code. In gate teleportation, a non-stabilizer state is introduced in a Clifford circuit together with a state to be processed. Using a modified teleportation circuit, the measurement back-action can be used to use the resource state’s “non-Stabilizerness” to apply a non-Clifford gate to the input.

The production of good resource states is more efficient if qudits are used instead of qubits. However, qubits remain the main building block for which hardware and software are developed. This project aims at bridging the two by asking whether it is possible to use a qutrit state in a gate-teleportation circuit to implement a non-Clifford unitary gate on an input qubit and, if the answer is yes, characterize the conditions that allow it. A converse outcome would be proving that it is never possible. 

The project is particularly interesting for architectures that can natively host both qubits and qudits, such as bosonic platforms, especially Gottesman-Kitaev-Preskill codes, for which Clifford circuits are implemented via to Gaussian transformations and homodyne detection.

[1] https://en.wikipedia.org/wiki/Quantum_gate_teleportation

[2] https://arxiv.org/abs/2106.12989

Collaboration: The successful candidate will work with Francesco Arzani and potentially in collaboration with other members of the QAT team at INRIA Paris and other members of the Franco-German ANR project BoLaCo at the Free University of Berlin.

Mission confiée

The selected candidate will carry out analytical and numerical calculations to establish the conditions under which it is possible (or impossible) to use non-stabilizer qutrit states to implement non-Clifford qubit gates.

Principales activités

Main activities  : formalization of the problem, design of the circuits, analysis for finite-dimensional systems and GKP codes

Additional activities  : dissemination of the results in scientific workshops and conferences

Compétences

Technical skills and level required : working knowledge of a modern programming language (Pyrhon, Julia, ...)

Languages : good English communication skills

Relational skills : willingness to work in a team

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 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