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## Machine Learning and Quantum Computing for Quantum Molecular Dynamics

#### CECAM-FR-MOSER

#### Organisers

The *Machine Learning and Quantum Computing for Quantum Molecular Dynamics* [MLQCDyn]**school** aims at offering state-of-the-art training in quantum molecular dynamics (QMD), machine learning (ML), and quantum computing (QC) to early-stage scientists, including PhD and postdoctoral researchers coming mainly from the molecular dynamics community. The MLQCDyn school is meant to be part of a **Thematic Program of the Pascal Institute of the University Paris-Saclay** that will span a total of 4 weeks and will be dedicated to the discussion of the implications of machine learning and quantum computing in the field of quantum molecular dynamics (funding for the thematic program has already been approved). The MLQCDyn school will open the Thematic Program, and some of the participants in the school (lecturers and students) will also remain for one or more of the following weeks. Such an event will strengthen the collaboration between Pascal Institute and the CECAM.

**Nowadays, machine learning is** routinely used in a wide range of industrial applications, ranging from targeted commercials on Google and Facebook to self-driving cars. Importantly, this field has been widely democratized by the diffusion of a series of freely available computer libraries such as Scikit-Learn and Tensorflow. It comes as no surprise that ML has recently attracted broad interest in atomic and molecular physics and computational chemistry communities. To mention a few examples, the current applications of ML in these fields include the classification of phases of matter [1], the description of many-body wavefunctions [2], prediction of molecular excited-state properties [3] and photodynamics [4], and the computational discovery of new compounds [5] and molecules [6]. Since the seminal works of Manzhos-Carrington [7] and Behler-Parrinello [8], the use of ML algorithms has also been proven to be effective in describing high-dimensional potential energy surfaces in the context of QMD. Equally promising new applications have emerged more recently, from the use of supervised ML in astrochemistry to train a predictor of the H_{2} molecular density using a limited set of molecular lines in the Orion B molecular cloud [9], to the application of machine learning to the calculation of reactive cross-section [10], or to the first tests of these methods for optimizing coherent control [11].

**Quantum molecular dynamics** requires the (approximate and numerically expensive) solution of the electronic Schrödinger equation at each time-step of the simulation; by properly training an ML model, most of these expensive quantum mechanical calculations can be replaced by inexpensive predictions. The main outcome of this idea is that the quantum molecular dynamics can be simulated at a cost comparable to that of a classical force field. This type of methodology and its variants can be used, for example, to create general-purpose force fields [12], to treat huge systems with hundreds of millions of atoms [13], or to extend the applicability of sophisticated quantum approximations (e.g., coupled-cluster theory) to MD simulations [14], [15]. QMD also yields an enormous amount of data. Once more, ML models can be trained to analyze these data and automatically or semi-automatically recognize patterns and make classifications [3].

**Quantum computing** holds the promise to solve computational problems whose complexity would be intractable by traditional computers. Among those, the Schrödinger equation is considered a particularly suitable problem for QC. While classical computers can perform operations on bits that are either 0 or 1, quantum computers take advantage of superposition states to encode significantly more information in a quantum bit (qubit) form. Creating superpositions and entangling multiple qubits allows one to create exponentially more complicated wavefunctions required for the solution of the Schrödinger equation. Practical algorithms have been developed and implemented on real quantum hardware to compute the ground state energy of an interacting quantum many-body system [16], [17]. This field is evolving rapidly, and very recently, quantum algorithms have been proposed for the numerical computation of atomic forces [18] and *ab initio* molecular dynamics simulations [19]. As we are now entering the noisy intermediate-scale quantum (NISQ) era [20], quantum computers with 50 (or more) qubits will soon be available. They will allow computational scientists to address problems hardly solvable by classical computers.

Current research efforts in the development of quantum algorithms focus on various aspects, aiming to efficiently exploit quantum computers with a constantly increasing number of qubits and solve problems of interest in chemistry and physics. For instance, the treatment of noise caused by decoherence effects affecting each and any quantum systems, thus qubits as well, falls in the first category. It is becoming of utmost importance as quantum hardware evolves [19], [21]. However, for direct applications of quantum algorithms in QMD, probably the most interesting problems that the community is addressing are the use of quantum computers to improve ML algorithms [22], the unitary evolution of a quantum system to propagate quantum dynamics, and the development of techniques to map an “electronic configuration space” into qubit systems for electronic structure calculations [23].

## References

**Canada**

Artur Izmaylov (University of Toronto) - Organiser

**China**

Pavlo O. Dral (Xiamen University) - Organiser

**France**

Mario Barbatti (Aix Marseille University) - Organiser

Majdi Hochlaf (Université Gustave Eiffel) - Organiser

**United Kingdom**

Julia Maria Westermayr (University of Warwick) - Organiser

**United States**

Dario Rocca (QC Ware Corp.) - Organiser