Context :

Quantum algorithms represent a new branch of algorithms, offering potential advantages over classical algorithms for certain binary problems (such as maximum stable size or maximum cut) or problems naturally formulated as binary quadratic programming problems without constraints (QUBO). Many energy management problems have components that fit this description. However, quantum algorithms also have intrinsic limitations or those stemming from the constraints of current machines [1], [2]:

Probabilistic nature and noise: The probabilistic nature of measurements and noise issues do not guarantee the optimal solution.
Lack of expressiveness: Different quantum approaches do not efficiently account for all the constraints of an industrial problem, particularly those involving continuous variables.
Hardware limitations: Current quantum machines are limited in terms of the number of qubits and the number of operations that can be performed, which restricts the size of the problems that can be solved.

To overcome these limitations, we propose developing a hybrid classical-quantum approach with the following features:

Iterative resolution: To avoid being limited by suboptimal solutions induced by probabilistic measurements and noise.
Two-level resolution structure: To include aspects not considered by quantum algorithms.
Control over the size of the quantum problem solved: To manage the limitations of current quantum machines.

Primal heuristics based on decompositions, such as cut and column generation [3], exhibit these characteristics by building an approximation of the initial problem through the addition of variables or constraints, and controlling the size of the problem through branching.

Objective :

The goal of the internship is to study the possibilities offered by hybrid classical-quantum approaches, particularly within the framework of iterative heuristic approaches based on decompositions. Results from previous studies conducted in EDF's R&D department can be used for some components of the approach to be developed, notably variational quantum algorithms (QAA and QAOA), quantum search (Grover's algorithm, amplitude amplification), as well as results obtained during a previous CIFRE thesis [4].

The internship may be followed by a CIFRE thesis.

References

[1] Preskill, J. (2018). Quantum computing in the NISQ era and beyond. Quantum, 2, 79.

[2] Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S. C., Endo, S., Fujii, K., ... & Coles, P. J. (2021). Variational quantum algorithms. Nature Reviews Physics, 3(9), 625-644.

[3] Sadykov, R., Vanderbeck, F., Pessoa, A., Tahiri, I., & Uchoa, E. (2019). Primal heuristics for branch and price: The assets of diving methods. INFORMS Journal on Computing, 31(2), 251-267.

[4] Veshchezerova, M. (2022). Quantum algorithms for energy management optimization problems. Theses, Université de Lorraine, December.

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Hybrid Classical/Quantum Decomposition Approach for Energy Management Problems at EDF