arXiv subjects

Michel Nowak

Publications and source records attributed to Michel Nowak.

8 recordsLinked to original sources

arXiv2026

Satellite Mission Planning with Rydberg Atoms

Quantum computers relying on cold atoms are being built and promise a high flexibility in the way information in encoded into the physical system. In particular, the analog mode is spiking interest in the field of optimization as a classically intractable number of configurations can be tackled. In this work, we investigate a problem that requires every-day scheduling of critical tasks involving a large number of actors. Namely, fixing the planning for a Earth Observation satellite fleet composed of several of units exposed to a high density of targets to be scanned. We explore numerical schemes that convert the formulated problem into a cold-atoms friendly setup. We begin by a naive formulation of the Satellite Mission Planning problem without taking account for the agility of the satellites. We then extend the problem to take it into account based on the literature. By formulating the planning problem as a Maximum Independent Set problem, we are able to solve the problem with a QPU based on Rydberg atoms. We explore two ways of solving the MIS problem on the QPU, one relying on the graphs and on the Quadratic Unconstrained Binary Optimization Framework (QUBO). We show that the QUBO methodology is the most relevant and explore it more deeply with numerical experiments. We conclude on the potential utility of using a QPU to solve the Satellite Mission Planning problem in an operational context.

quant-ph↗

arXiv2026

Quantum Domain Decomposition for Preconditioning the Finite Element Method

Even in cases where quantum linear solvers provide significant speedup compared to their classical counterparts, their performance depends on some of the same parameters. In particular, the condition number of the matrix which is to be inverted is a decisive parameter. A well known classical, and now quantum, remedy is to precondition the linear system $A x = b$ by premultiplying it by a matrix $H$ in such a way that the condition number of $HA$ is significantly smaller than the condition number of $A$. In this work, we focus on a family of preconditioners called domain decomposition. First, we prove that it is feasible to apply quantum domain decomposition. We provide upper bounds for the block-encoding parameters of the Poisson problem discretized by the finite element method and preconditioned by the two-level Additive Schwarz preconditioner (one of the most fundamental domain decomposition techniques). From these bounds, we deduce the complexity of the quantum linear system solver. Second, we focus on a particular choice of local solver within the domain decomposition preconditioner by applying recent work by [Deiml and Peterseim, \textit{Math. Comput.}, 2025] on the Bramble--Pasciak--Xu (BPX) preconditioner. Finally, we provide details on how the operators are implemented.

math.NA↗

arXiv2025

High Performance Parallel Solvers for the time-harmonic Maxwell Equations

We consider the numerical solution of large scale time-harmonic Maxwell equations. To this day, this problem remains difficult, in particular because the equations are neither Hermitian nor semi-definite. Our approach is to compare different strategies for solving this set of equations with preconditioners that are available either in PETSc, MUMPS, or in hypre. Four different preconditioners are considered. The first is the sparse approximate inverse, which is often applied to electromagnetic problems. The second is Restricted Additive Schwarz, a domain decomposition preconditioner. The third is the Hiptmair-Xu preconditioner which is tailored to the positive Maxwell equations, a nearby problem. The final preconditioner is MUMPS's Block Low-Rank method, a compressed block procedure. We also compare the performance of this method to the standard LU factorization technique, which is a direct solver. Performance with respect to the mesh size, the number of CPU cores, the wavelength and the physical size of the domain are considered. This work in progress yields temporary conclusions in favour of the Hiptmair-Xu and the Block Low-Rank preconditioners.

math.NA↗

arXiv2025

Adaptive mesh refinement quantum algorithm for Maxwell's equations

Algorithms that promise to leverage resources of quantum computers efficiently to accelerate the finite element method have emerged. However, the finite element method is usually incorporated into a high-level numerical scheme which allows the adaptive refinement of the mesh on which the solution is approximated. In this work, we propose to extend adaptive mesh refinement to the quantum formalism, and apply our method to the resolution of Maxwell's equations. An important step in this procedure is the computation of error estimators, which guide the refinement. By using block-encoding, we propose a way to compute these estimators with quantum circuits. We present first numerical experiments on a 2D geometry.

quant-ph↗

arXiv2024

Monte Carlo particle transport on quantum computers

Monte Carlo particle transport codes are well established on classical hardware and are considered as the reference tool for nuclear applications. In a growing number of domains, the design of algorithms is progressively shifting towards the field of quantum computing, where theoretical speedups over their classical counterparts are expected. In some of these domains, Monte Carlo methods have already been converted to a quantum computing friendly setup where the expected and observed gain in complexity is quadratic. Surprisingly, particle transport has been left aside along the path and lacks an implementation on these new architectures. In this work, a numerical scheme for particle transport based on discrete-time quantum walks and its combination with the amplitude amplification routine are proposed to catch up with the promised speedups.

quant-ph↗

arXiv2024

BACQ -- Application-oriented Benchmarks for Quantum Computing

With the support of the national program on measurements, standards, and evaluation of quantum technologies MetriQs-France, a part of the French national quantum strategy, the BACQ project is dedicated to application-oriented benchmarks for quantum computing. The consortium gathering THALES, EVIDEN, an Atos business, CEA, CNRS, TERATEC, and LNE aims at establishing performance evaluation criteria of reference, meaningful for industry users.

quant-ph↗

arXiv2023

Variational quantum algorithms on cat qubits

Variational Quantum Algorithms (VQA) have emerged with a wide variety of applications. One question to ask is either they can efficiently be implemented and executed on existing architectures. Current hardware suffers from uncontrolled noise that can alter the expected results of one calculation. The nature of this noise is different from one technology to another. In this work, we chose to investigate a technology that is intrinsically resilient to bit-flips: cat qubits. To this end, we implement two noise models. The first one is hardware-agnostic -- in the sense that it is used in the literature to cover different hardware types. The second one is specific to cat qubits. We perform simulations on two types of problems that can be formulated with VQAs (Quantum Approximate Optimization Algorithm (QAOA) and the Variatinoal Quantum Linear Soler (VQLS)), study the impact of noise on the evolution of the cost function and extract noise level thresholds from which a noise-resilient regime can be considered. By tackling compilation issues, we discuss the need of implementing hardware-specific noise models as hardware-agnostic ones can lead to misleading conclusions regarding the regime of noise that is acceptable for an algorithm to run.

quant-ph↗

arXiv2021

Towards graph classification with Gaussian Boson Sampling by embedding graphs on the X8 photonic chip

Photonics chips on which one can perform Gaussian Boson Sampling have become accessible on the cloud, in particular the X8 chip of Xanadu. In this technical report, we study its potential use as a first step towards graph classification on quantum devices. In order to achieve this goal, we study the generated samples of the graph embedding method which leads to feature vectors. This is done on a restricted class of unweighted, undirected and loop-free graphs. Hardware constraints are matched to properties of graphs that can be encoded. We report experiments on the X8 chip as well as comparisons to numerical simulations on a classical computer and analytical solutions. We conclude this technical report by trying to take photon loss into account and explain the observed results accordingly.

quant-ph↗