PhD Position F/M Exploiting causal indefiniteness in quantum computational models

January 15, 2023
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2022-05619 - PhD Position F/M Exploiting causal indefiniteness in quantum computational models

Contract type : Fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : PhD Position

About the research centre or Inria department

The Inria research centre in Lyon (previously the Lyon branch of the Inria centre in Grenoble) is the 9th Inria research centre, formally created in December 2021. It brings together approximately 270 people (including 110 Inria employees) in 15 research teams and research support services.

Its staff are distributed at this stage on 2 campuses: in Villeurbanne La Doua (Centre / INSA Lyon / UCBL) on the one hand, and Lyon Gerland (ENS de Lyon) on the other. A third site should be opened in the course of 2022. The teams are mainly hosted with our partners. The centre's teams work closely with research and higher education institutions (ENS de Lyon, UCBL, INSA Lyon, etc.), their laboratories, and other research organisations in Lyon (CNRS, INRAE, competitiveness clusters, etc.), but also with Lyon and regional economic players. Many international collaborations are also underway.

The Lyon centre is active in the fields of software, distributed and high- performance computing, embedded systems, quantum computing and privacy in the digital world, but also in digital health and computational biology.


The successful PhD candidate will joint the QInfo group, and will be jointly supervised by Alastair Abbott (Inria, QInfo) and Cyril Branciard at the nearby Institut Néel (CNRS).

The QInfo group is a newly formed Inria team bilocalised in Grenoble and Lyon working on the theory of quantum information. In Grenoble, the group also collaborates closely with members of the CAPP team at LIG working on quantum information.

The PhD project is part of a recently awarded ANR collaborative project "Taming Quantum Causality (TaQC)" set to start in January 2023. There will be opportunities to collaborate with partners of the project at the Inria Saclay Centre (QuaCS team) and CEA Saclay. Funding is available in the project to attend pertinent conferences and travel to collaborate with partners.


Quantum computation exploits non-classical resources – such as entanglement and superposition – in quantum systems to obtain computational advantages. The standard model of quantum computation is that of quantum circuits, in which quantum gates are applied in a fixed “causal” order. Recent foundational work has highlighted the novel possibility to process information in an indefinite causal order. Initial work on a simple protocol, known as the quantum switch 1, shows that causally indefinite computations may provide new advantages for quantum information processing even beyond quantum circuits 2.

Several models have recently been developed in an attempt to understand and explore causally indefinite computations, including quantum circuits with quantum control of causal order 3, addressable quantum gates 4, causal boxes 5, routed circuits 6 and the PBS-calculus 7. The relation between these approaches is not yet properly understood however, let alone the potential advantages of causally indefinite computation beyond a few specific examples.

This PhD project will work to address this situation, taking a step towards developing a more systematic understanding of the computational capabilities of causal indefiniteness.

The initial goal will be to build on recent preliminary work relating some of these diverse models of causally indefinite processes, seeking to find the common ground between these models and hence provide a consistent framework in which to study the computational power of causal indefiniteness. This work will notably exploit axiomatic approaches to understand what types of causal indefiniteness correspond to physical computations.

The core of the project will then be to develop our understanding of the computational power of these models. This will involve, in the first place, studying new computational advantages in quantum query complexity that are not based on the quantum switch, before extending these to exhibit advantages in standard computational problems. The project will then seek to place these advantages within a broader complexity theoretic framework, allowing them to be compared rigorously on a common footing with both classical and standard (i.e., causally ordered) quantum computation.

1 G. Chiribella, G. M. D'Ariano, P. Perinotti, B. Valiron, Quantum computations without definite causal structure, Phys. Rev. A 88, 022318 (2013); arXiv:0912.0195 2 M. Araújo, F. Costa, C. Brukner, Computational advantage from quantum- controlled ordering of gates, Phys. Rev. Lett. 113, 250402 (2014); arXiv:1401.8127 3 J. Wechs, H. Dourdent, A. A. Abbott, C. Branciard, Quantum circuits with classical versus quantum control of causal order, PRX Quantum 2, 030335 (2021) 4 P. Arrighi, C. Cedzich, M. Costes, U. Rémond, B. Valiron, Addressable quantum gates, arXiv:2109.08050 5 C. Portmann, C. Matt, U. Maurer, R. Renner, B. Tackmann, Causal Boxes: Quantum Information-Processing Systems Closed Under Composition, IEEE Trans. Inf. Theory 63, 3277–3305 (2017) 6 A. Vanrietvelde, N. Omrod, H. Kristjánsson, J. Barrett, Consistent circuits for indefinite causal order, arXiv:2206.10042 7 A. Clément, S. Perdrix, PBS-Calculus: A Graphical Language for Coherent Control of Quantum Computations, Proc. MFCS 2020; arXiv:2002.09387 quant- ph

Main activities

As during any PhD, the candidate will be expected to:

  • Analyse the scientific literature relevant to the research topic
  • Devise innovative solutions to the problems at hand
  • Program and conduct numerical or analytical analysis when required
  • Contribute to writing scientific papers on results
  • Present results at workshops and conferences (as posters or talks)
  • Synthesise their results while writing their PhD thesis
  • Attend research seminars, summer schools, etc., where relevant
  • Skills

    The candidate should have experience working in quantum information theory, ideally having completed a research internship or project on the subject. Experience working with MATLAB and/or Mathematica would be an advantage, as would knowledge of convex optimisation methods (linear programming, semidefinite programming), but not essential.

    The candidate should have a strong aptitude for scientific collaboration to work in this interdisciplinary subject, and an inquisitive spirit is essential.

    Languages: Good proficiency in both oral and written English is required.

    Benefits package
  • 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 (90 days / year) 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 under conditions
  • Remuneration

    1st and 2nd year: 2 051 euros gross salary /month

    3rd year: 2 158 euros gross salary / month

    General Information
  • Theme/Domain : Algorithmics, Computer Algebra and Cryptology
  • Town/city : Grenoble
  • Inria Center : Centre Inria de Lyon
  • Starting date : 2023-03-01
  • Duration of contract : 3 years
  • Deadline to apply : 2023-01-15
  • Contacts
  • Inria Team : QINFO
  • PhD Supervisor : Abbott Alastair /
  • The keys to success

    The subject is at the forefront of new ideas in quantum information, and an inquisitive mind and the determination to ask important questions and follow them up is essential. The subject is at the intersection of several aspects of quantum information and quantum foundations, so the desire to gain a wide understanding of the field is important. As with any research work, determination and perseverance are also crucial traits.

    About Inria

    Inria is the French national research institute dedicated to digital science and technology. It employs 2,600 people. Its 200 agile project teams, generally run jointly with academic partners, include more than 3,500 scientists and engineers working to meet the challenges of digital technology, often at the interface with other disciplines. The Institute also employs numerous talents in over forty different professions. 900 research support staff contribute to the preparation and development of scientific and entrepreneurial projects that have a worldwide impact.

    Instruction to apply

    Applications must be submitted online on the Inria website.

    Processing of applications sent by other channels is not guaranteed.

    Defence Security : This position is likely to be situated in a restricted area (ZRR), as defined in Decree No. 2011-1425 relating to the protection of national scientific and technical potential (PPST).Authorisation to enter an area is granted by the director of the unit, following a favourable Ministerial decision, as defined in the decree of 3 July 2012 relating to the PPST. An unfavourable Ministerial decision in respect of a position situated in a ZRR would result in the cancellation of the appointment.

    Recruitment Policy : As part of its diversity policy, all Inria positions are accessible to people with disabilities.

    Warning : you must enter your e-mail address in order to save your application to Inria. Applications must be submitted online on the Inria website. Processing of applications sent from other channels is not guaranteed.

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