PhD Position F/M Systematic Classification of Non-Gaussian States for Quantum Error Correction

Context and team: The Quantum computing Architectures, Algorithms, Applications and their Theory (QAT) team at Inria Paris is seeking a motivated PhD student to work under the supervision of Francesco Arzani on a project related to the systematic, physically-grounded discovery and classification of non-Gaussian quantum states for quantum error correction (QEC). The team takes an experimentally mindful approach to quantum information processing, focusing on the integration of architectures, algorithms, and applications.

Project Description: The development of fault-tolerant quantum computers hinges on the creation and control of quantum states with robust properties. While Gaussian states are well understood, it is the vast landscape of non-Gaussian states that holds the key to unlocking true quantum advantage, yet the discovery of new non-Gaussian states has so far often been ad-hoc. This project introduces a systematic, bottom-up methodology to discover and classify non-Gaussian states by identifying them as the ground states of specifically constructed polynomial Hamiltonians, defined as solutions to a nullifier equation. This ensures every discovered state has a clear physical genesis as the ground state of the corresponding positive semi-definite Hamiltonian, providing a direct pathway from algebraic formulation to potential experimental implementation. A central theme of the project is the deep connection between the symmetries of the parent Hamiltonian and the error-correcting capabilities of its ground states, which will be used as a first-principles tool for evaluating a state's utility as a quantum resource, including links to CSS-like codes and homological algebra.

We offer:

• Full funding for 3 years
• Opportunity to collaborate with experimental and theoretical groups
• Access to state-of-the-art research facilities
• Collaborative and stimulating research environment

The recruited person will be tasked with

• systematically generating and classifying the ground-state manifolds of low-degree polynomial Hamiltonians defined via nullifier equations;
• identifying and exploiting the discrete symmetries (e.g. phase-space rotations, translations) of these parent Hamiltonians to predict the physical properties and structure of the corresponding ground states;
• evaluating the quantum error correction capabilities of the identified states, assessing their resilience against prevalent noise channels such as photon loss and dephasing;
• extending the framework toward novel CSS-like codes and exploring generalizations to higher-order polynomials.

Research, including exploration of the relevant literature, analytical derivation of nullifier polynomials and their ground states, development of methods to extract symmetry groups, systematic parameter-space scans, and coding of the associated numerical simulations. Writing reports on results.

Communication of the main results through scientific publications.

Dissemination of the results through participation in scientific conferences and workshops.

• Familiarity with quantum error correction concepts (particularly bosonic/continuous-variable codes) is a plus
• Proficiency in analytical/algebraic derivations
• proficiency in English for oral and written communication

• 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