PhD Student position in Entanglement Detection and Classification for Stabilizer States

Quantum Information Group

Deadline for receipt of applications: May 23, 2025 23:59 AoE (24 May 2025, 13:59h Europe/Madrid Time)

Multipartite entanglement represents a key resource for quantum technologies such as quantum communication, sensing, and computation. One example of multipartite entangled states are stabilizer states, particularly graph states. These states are characterized by an efficient mathematical description via the stabilizer formalism and an intuitive graphical representation. A fundamental aspect of studying such entanglement involves its classification. Quantum states are considered equivalent if they are interconvertible by Local Operations and Classical Communication (SLOCC), or more restrictively, by Local Unitary (LU) operations. For stabilizer states, including graph states, these two notions of equivalence (SLOCC and LU) conveniently coincide, simplifying their classification compared to more general quantum states.

Within the framework of LU operations, Local Clifford (LC) operations—generated by single-qubit Hadamard, Phase, and Pauli gates—are significant, forming the basis for fault-tolerant quantum computation and preserving the set of stabilizer states. LC operations also have a clear graphical interpretation for graph states through local complementation. This has led to a crucial question: are the entanglement classes defined by LU operations already fully captured by the more restricted LC operations? Specifically, if two graph states (or stabilizer states) are LU-equivalent, does it imply they are also LC-equivalent? This project aims to investigate this LU-LC conjecture across various types of stabilizer states, probing the relationship between these fundamental equivalence classes.

The position offers:

• Full time contract
• Competitive salary
• A unique opportunity to work on fundamental problems essential for quantum computing and communication.
• IMDEA Networks promotes a tolerant, diverse and creative work environment that is respectful of all people as well as Gender Equality.
• High level of English (English will be the working language)

The position requires (as many as possible):

• Degree in Physics (with knowledge of Information Theory) or in Computer Science / Mathematics (with knowledge of Quantum Physics).
• A clear understanding of the basics of quantum computation and communication (qubit modalities, Bell inequalities, entanglement witnesses, etc.) is a must.
• Knowledge of classical machine learning algorithms and libraries (PyTorch, Tensorflow, Python Data Science Stack) is a strong plus.
• Knowledge of a graph analysis and visualization library is a strong plus (such as NetworkX or similar)
• Previous experience with Qiskit or any other quantum programming language is a plus.
• Proficiency in written and spoken English is essential.
• A desire to work on topics at the edge of modern research as well as publishing in top conferences and journals is mandatory.

Equal Employment Opportunity:

IMDEA Networks Institute aims to increase the proportion of women and therefore qualified female applicants are explicitly encouraged to apply. Until a balanced ratio of men and women has been achieved at the institute, preference will be given to women if applicants have similar qualifications. IMDEA Networks Institute actively promotes diversity and equal opportunities. Applicants are not to be discriminated against in personnel selection procedures on the grounds of gender, ethnicity, religion or ideology, age, sexual orientation (anti-discrimination). People with disabilities who have the relevant qualifications are expressly invited to apply