Post-Doctoral Research Visit F/M Postdoctoral Position in Quantum Cryptography and Complexity Theory at ENS Paris

We are seeking a highly motivated and talented postdoctoral researcher to join the QAT team. The successful candidate will conduct research on Quantum Cyrptography and Complexity Theory. The candidate will contribute to a variety of projects within the Hybrid HPC-Quantum Initiative and Quantum Internet Alliance.

QAT is a newly-formed team at ENS Paris, dedicated to exploring the foundations and applications of quantum computing. Our focus areas include quantum machine learning, quantum cryptographic primitives, quantum complexity, and quantum error correction. As part of this team, you will work with leading experts to push the boundaries of quantum technologies and contribute to transformative advancements in the field.

The verification of quantum computations is a fundamental challenge in the quest for building secure, trustable quantum computing systems. The objective of this research line is to explore the verification of quantum computations using interactive proof systems. These systems enable a prover to convince a verifier that a given computation was performed correctly, and they provide an essential framework for ensuring the security of quantum computations.

Quantum interactive proof systems offer the ability to leverage quantum mechanics for verification, raising fundamental questions about how computational resources (both quantum and classical) can be utilized to guarantee security.
One of the key goals of this research line is to develop quantum protocols for verification and to study their complexity and efficiency. In particular, we are interested in understanding the conditions under which quantum communication is essential for the security of the protocol, and whether quantum communication can be substituted by classical communication without compromising security. The motivation here lies in optimizing the efficiency of verification protocols, where using classical communication could drastically reduce the required quantum resources, thereby improving the practicality of quantum systems.

Preliminary results in the team suggest that for certain types of protocols, the communication overhead may be proportional to the amount of non-classical resources used in the computation. This line of investigation involves:
- Quantum-to-classical communication trade-offs: We aim to derive precise conditions under which quantum communication can be replaced by classical communication in the verification process, studying the costs involved (in terms of both security and efficiency).
- Resource-efficient protocols: Investigate the minimal quantum communication required for secure verification, considering the amount of quantum information transmitted in proportion to the computational resources used.
- Universal quantum gate sets: Explore how these findings scale in the context of various universal quantum gate sets, and their impact on the complexity of verification protocols.

Another important aspect of the research is to extend these verification protocols to continuous variable quantum systems, which are of growing interest due to their potential applications. Unlike traditional quantum systems that use discrete variables (such as qubits), continuous variable quantum systems (CVQs) manipulate quantum states with continuous variables, such as position and momentum.

The main goals include:
- Adapting protocols for CV: The verification protocols developed for discrete quantum systems must be re-examined and potentially modified to work with CV, taking into account the continuous nature of the quantum information.
- Scaling quantum verification: Investigate how continuous-variable quantum systems can be integrated into the broader framework of quantum interactive proof systems, and determine the complexity of verification in this extended setting.
- Security in CV-based verification: Assess the security of these protocols in the context of CV-based communication, considering potential vulnerabilities unique to continuous-variable systems.

- Conduct cutting-edge research in quantum cryptography and complexity theory and contribute to the development of new verification protocols.
- Study the trade-off between security and quantum communication needs.
- Investigate the applicability and limitations of these protocols for NISQ-era devices.
- Collaborate with interdisciplinary teams and propose extensions of the research line towards eg. benchmarking.
- Contribute to the design of quantum protocols using both quantum and classical methods.
- Publish research findings in top-tier journals and present at international conferences.

Required Qualifications
- Ph.D. in quantum computing, theoretical computer science, physics, or a related field.
- Strong background in quantum computing and familiarity with quantum cryptography.
- Strong analytical and mathematical skills, including a solid understanding of linear algebra, cryptographic proof techniques for statistical and computational security
- Ability to work independently and as part of a collaborative team.
- Excellent written and oral communication skills in English.

Desired Qualifications
- Experience in verification of quantum computation.
- Familiarity with Abstract Cryptography or other composable security framework.
- Interest in interdisciplinary research and hybrid quantum-classical systems.

• 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