it possible to manipulate complex quantum problems in diagrammatic form, thereby offering a visual and algorithmic alternative to state-of-the-art numerical methods.
PhD Subject:
Originally developed to simplify quantum circuits (see Figure), the ZX calculus [1] relies on diagrams representing tensor networks, which can be simplified using rigorous graphical rewriting rules. While many studies exploit this tool to optimize quantum circuits, its application to the quantum many-body problem remains largely unexplored [2]. We have recently contributed to providing the first example demonstrating that the ZX calculus can resolve open questions in the context of the many-body problem [3]. We developed a graphical method, for analytically solvable cases (the toric code and the color code), that allows one to unambiguously determine whether a quantum many-body state exhibits long-range, so-called “topological”, entanglement. This property is essential for quantum error correction and for the emergence of robust phenomena in condensed matter physics, such as the quantum Hall effect. Our method avoids the well-known ambiguities associated with traditional classifications based on entanglement entropy. The potential of the ZX calculus beyond analytically solvable models remains largely unexplored. This PhD Thesis will show that diagrammatic structures derived in the ZX framework for exactly solvable models also emerge in non–exactly solvable cases, for instance by breaking the integrability of the toric code through the addition of a magnetic field, where the states are obtained using standard tensor-network-based algorithms. This project would lead to the first demonstration of the usefulness of diagrammatic reasoning beyond analytically solvable models, potentially enabling the development of new algorithms inspired by graphical structures derived from the ZX calculus.
Required Skills:
- Familiarity with concepts of Advanced Quantum Mechanics, Many-Body Quantum Physics, Quantum Field Theory, Quantum Information
- Coding skills in Python
Additional Information
Eligibility criteria
Applicants must hold a Master’s degree or an equivalent qualification by the application deadline and must not already hold a doctoral degree. Applicants must also comply with the MSCA mobility rule: they must not have resided or carried out their main activity (work, studies, etc.) in France for more than 12 months during the 36 months immediately preceding the application deadline. Applicants must not be current employees of the host laboratory. There are no nationality or age restrictions.
Selection process
Applications must be submitted through the QuanG2 online application platform by 7 September 2026 at 12:00 PM (Paris time). After the application deadline, all applications will first undergo an eligibility check. Eligible applications will then be reviewed during the pre-selection phase, scheduled for mid-October 2026. Shortlisted candidates will be invited to online interviews at the end of October 2026. Candidates selected following this first interview stage will then be invited to in-person interviews in Grenoble in early December 2026, with the final selection taking place after these interviews. All candidates will be informed of the outcome of the selection process following the final stage.
Additional comments
About the QuanG2 PhD Call
This PhD position is offered as part of the QuanG2 PhD Call for Applications, a doctoral programme coordinated by Université Grenoble Alpes and dedicated to training the next generation of researchers in quantum science and technology. The programme offers fully funded three-year PhD positions within the Grenoble quantum research ecosystem, providing doctoral candidates with a high-level international research environment and dedicated funding for their research and training activities.
