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
