Quantum computing is a potential game changer in many areas, such as for instance seismic imaging. In this internship you will work on a mathematical formulation of an optimization problem to be used for seismic imaging and run on a quantum computer.


Den Haag

Education type

university (wo)


Internship and graduation project

Hours a week

Fulltime – 40


Apply now


What will you be doing?

Quantum computing could be a potential game-changer for many industries heavily relying on solving large scale inverse and global optimization problem. A prominent example is the problem of seismic imaging, which is used in near surface surveying for construction projects, identification of hydrocarbon reservoirs, sites of CO2 sequestration, or mapping out of deep subsurface aquifers

Residual statics estimation (RSE) is an important and computationally challenging problem used to correct the subsurface image. Local, often strong, and unpredictable near-surface wave propagation velocity anomalies result in highly misaligned images of the surface rendering any further subsurface work practically impossible. The RSE aims to determine the additional time shifts (so-called “statics”) for each vertical set of pixels (a trace), such that all traces are optimally aligned and form an (a priori unknown) image of geological structures.

There can be many (almost equally viable) solutions to the RSE problem. Each solution corresponds to some local minimum of the objective function, but only one is the best, corresponding to the global minimum. Classical solvers however tend to get stuck in minima and we are never able to determine if the found solution corresponds to a local or global minimum.

In this internship you will take a first step in answering this question by solving the residual statics estimation problem for seismic data, using a quantum annealing computing approach.

The starting point of the assignment is the work done by Rothman and Bosisio ( in which the residual statics estimation problem is solved by simulated annealing. The first step would be redoing the work of Rothman and Bosisio fora simple, but typical, seismic data set with a known solution. The second step is solving residual statics estimation problem for the same data set by quantum annealing. This requires finding the appropriate mathematical formulation of the problem, translating it into an Ising model or a Quadratic Unconstrained Binary Optimization (QUBO) problem and finally running/solving the problem on an actual D-Wave systems quantum computer.

Time allowing, the final step would be to explore whether there is a potential advantage of using quantum annealing computers and determine the minimum requirements of such a system to solve real sized problems. For this step a realistic seismic dataset will be provided.

What do we require of you?

We are searching for enthusiastic students in mathematics, physics and/or computer science that are will to do their graduation internship in a vibrant and diverse team of researchers. As the problem is mainly a mathematical one, knowledge of quantum computing/quantum annealing is a pre, however, not a necessity. As the field of quantum computing is still relatively new and there is still a lot unknown, a positive and can-do working attitude is important, as is the desire to go beyond what is known.

We expect that the assignment will take 6-9 months. The outcome of the assignment needs to be documented in a report and/or paper and it’s likely that the results will have to be presented on a conference or workshop. A collaboration with an R&D team of a major oil company is currently sought.

What can you expect of your work situation?

TNO is an independent research organisation, who, based on her expertise and research, provides an important part to the international position of companies and organisations and to the economy as a whole. With about 3,000 employees, TNO works for a wide range of clients: governments, SME's, internationals and civil society organisations. Together we work on new knowledge, better products and clear advice. Everything we do is about creating impact.

You will be part of a mixed and enthusiastic team of about fifty researchers, working on various topics such as quantum communication and quantum computing and cyber security.

What can TNO offer you?

You want to work on the precursor of your career; an internship gives you an opportunity to take a good look at your prospective future employer. TNO goes a step further. It’s not just looking that interests us; you and your knowledge are essential to our innovation. That’s why we attach a great deal of value to your personal and professional development. You will, of course, be properly supervised during your internship and be given the scope for you to get the best out of yourself. Naturally, we provide suitable internship compensation.

Has this vacancy sparked your interest?

Then please feel free to apply on this vacancy! For further questions don’t hesitate to contact us.

Due to Covid-19 and the consequent uncertainties and restrictions, students who are not residing in the Netherlands may currently not be able to start an internship or graduation project at TNO.

Contact: Niels Neumann
Phone number: +31 (0)6-152 41055

Note that applications via email and third party applications are not taken into consideration.


Apply now



Stay up to date with our latest news, activities and vacancies collects and processes data in accordance with the applicable privacy regulations for an optimal user experience and marketing practices.
This data can easily be removed from your temporary profile page at any time.
You can also view our privacy statement or cookie statement.