Symmetry Preserving Neural Quantum States

**About Pasqal**

PASQAL designs and develops Quantum Processing Units (QPUs) and associated software tools.
In addition to the exceptional computing power they provide, QPUs are highly energy efficient and will contribute to a significant reduction in the carbon footprint of the HPC industry.

Pasqal's Quantum Graph Machine Learning (QGML) team is a cutting-edge research & development team focused on advancing quantum computing and graph machine learning (ML). Their work leverages neutral atom QPU to solve complex problems in graph ML. These quantum systems naturally encode classical data like graphs by trapping atoms in a three-dimensional space, allowing us to explore novel approaches where quantum graph kernels and features can outperform classical methods.

We are looking for an intern interested in the field of Machine Learning applied to Quantum Computing with a solid background in machine learning and relevant knowledge in many-body physics to reinforce our team.

Quantum many-body systems are of great interest for many research areas, including physics, biology and chemistry. Due to the exponential growth of the Hilbert space dimension with system size, their simulation has remained a persistent challenge until today, making it exceedingly difficult to parameterize the wave functions of large systems using exact methods. Many computational techniques are used to overcome these limitations, the most common of which are variational methods, like tensor networks (TN) **[1]**, matrix product states (MPS) **[2]** and quantum Monte Carlo (MC) **[3]** to only cite these, where a certain functional form of the quantum state is assumed. More recently, the success of deep neural networks in approximating continuous functions on any compact subset of RN **[4]** motivated their use for the simulation of quantum systems **[5]**. To date, these so-called neural quantum states (NQS) have been shown to overcome many problems that are inherent to some conventional methods such as representing volume-law entangled states **[6**] and can hence (in principle) be used for a broad range of quantum systems. They can also be designed to be particularly well suited for two-dimensional problems. Most prominently, some architectures like convolutional neural networks were specifically designed for two-dimensional data, with relatively good performances on regular grids **[7]**.

**References**

**[3]** _Becca F and _Sorella S 2017 Quantum Monte Carlo Approaches for Correlated Systems (Cambridge University
- Press)_

**[4]** _Cybenko_ G 1989 Mathematics of Control, Signals and Systems 2 303-314

**[6]** _Sharir_ O, Shashua A and Carleo G 2022 Phys. Rev. B 106(20) 205136

In this internship, you will be working within PASQAL's quantum graph machine learning team, on a project that tackles the extension of NQS to arbitrary finite systems, with a particular focus on the inductive bias of such models, making them able to generalize to new unseen systems, sampled from the training distribution.

More particularly, you will be working closely with the team to implement generative models for the ground states of Rydberg systems. The latter offer many suitable properties that allow their simulation at large scales and are also possible to compute on PASQAL's QPU.

The main goals of the project can be summarized in the following:

- Implement novel approaches, based on models that efficiently embed the system's symmetries, enhancing their inductive bias
- Explore the power and the limits of machine learning in representing wave functions that lay in exponentially large Hilbert spaces
- Help in the process of verifying the validity of the obtained results through implementations on PASQAL’s QPU.

**About you**

You are actively enrolled in a Masters 2 or PhD Program in a related program (_i.e._ machine learning, quantum physics, quantum computing) and have the following assets:
Hard skills:

- Strong experience with programming in Python, including the training machine learning models in frameworks such as PyTorch, JAX
- Strong interest in one or many of the following : graph theory, geometric deep learning, graph neural networks, generative modeling
- Excellent algorithm development and coding practices
- Strong documentation and report writing skills
- Fluency in English

Bonus:

- Experience with one of the following: variational quantum algorithms, quantum machine learning, analog/digital quantum computing or simulation
- Previous research experience - Masters thesis, previous internship or similar experience
- Experience using quantum hardware

Soft skills:

- Autonmous
- Proactive
- Team player
- Curious

**What we offer**
- Offices in Massy, France
- Punctual remote work
- Type of contract: 6-months internship
- A dynamic and close-knit international team
- A key role in a growing start-up

**Recruitment process**
- An interview with our Talent Acquisition Specialist (~30 mins)
- An technical interview with the Hiring Manager